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THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
by
CHUNG KWAI LUI
A THESIS
submitted to the
OREGON STATE COLLEGE
in partial fulfillment of the requirements for the
degree of
DOCTOR OF PHILOSOPHY
June 1941
- - - -
fin^Jo frofesson)
Redacted for Privacy
AN ABSTNACT OF TIE TIIE8IS OF
-9Fgq 5rtl-l-gt - - ror trre -EljD-- - - 1r - -[ssfa-sshy( ttarae ) ( Degree ) ( ua5 or )
Date Ehe s ls pne senteaJhf l-- -1-q4-1- - - shy11s1--lllrs--cgurtgl-ampo-tqette-gt--19-Qtegttt1q-tc-l-rgtsl9--shy
-c-rurltlrl
Abstnact Approved
By neana of a eensltlve eunrent lneasurng devloe oonshyueotod la senles rlth a d-tertarlc aeld cnystall a flor of ounnont can bo detected rhen tbc c4yetal ls lllunlnatedl rltblleht fron an ordlnary tungsten ftlaent larap lfre cunrent rosponse ls greatly deBendont ou the onlentatlon of tho orTsshytal rlth neapeot to the dlneetlon of the lnoldent bcan ofItght Uogt of the cnystal faces glve a ourront rccponse upon lllumlnatton rlrlsb rlses napldly to a naxtnuu Just aftor tJee 1lgbt 1g trrrned oar then decrcageg and flael3y neaobes a ooastant ya1ue |l|hls type of reeponso ls callcQnlhe nortaleffect
lllhere are oentain neglons of the cr1rstaI horeven Chtohglve e cuJplrent flor rlrlcb gtantg out ln ono dfupectloa Justaftcn the llgpt ls turtred oa deeneasss naplclly rlth the ttne of lllrutnatloa and tben florE ln the opposlte dlneetlonEhls ls ealled the abnomal effeot It ts found that thls abnoraal effect alrays ocours rhen a polnt (srall neglon) ls tlhmlnated tbet LLog betseen tro regtons rhose nomel ounnent flors eno opBosltely dllrected Iho Buporposltlm of ths tro nomel orurncnt-ttne rosBonso onrYes glvoe a nesu1taut rhloh agneor rlth the obsenved abnomal rosponso rlthll the expenlshyuental error
A study ras uade of the verlatioa of pbotoounent dth taperature betveen 23oC end 15100 llhe crnrent ras found to hecrease rapidIy as tbe tcn1renature ras raleed fp 25oC to SOoC et rbloh point tbe orrrnent becaoe too mall to mealurolt 151oC a maII rovorro onpreat ras noted
Palntlag tbe onystal faoes drlch mede oonteot lth the eleetrodes r][th iaguidagi resuted la aa lncroase tn Bbotoshyourent
- 2 shy
The current response was studied when the crystal was examined with a light probe When the light fell on the crystal near the electrodes the response was found to be slightly less than when the light probe was used mid-waybetween the two electrodes
The fatigue effect of the crystals was examined bymeasuring the current response after comparatively longperiods ot illumination It was found that the decrease in current caused by the illumination was much greater for freshly grown crystals than for those grown several months before the test
Several theories relating to the crystal photoeffect are discussed With a alight extension the assumption of a bullconductivity axisbull or direction of max~ conductivitythe diffusion theory explains all results obtained includingthe new bullabnormal effect
IDPROVEDT
Redacted for Privacy
Xa Gbarge of ltral or
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
Ghslruea of State Collcgo
ACKNOWLEDGMENT
The author wishes to express her gratitude to
Dr James J Brady Associate Professor ot Physics
who suggested the problem and whose untiling interest
and helpful suggestions have proved invaluable for
the completion ot the work
The author also wishes to thank Dr w Weniger
Head of the Physics Department who has made the
necessary apparatus available
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
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37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
- - - -
fin^Jo frofesson)
Redacted for Privacy
AN ABSTNACT OF TIE TIIE8IS OF
-9Fgq 5rtl-l-gt - - ror trre -EljD-- - - 1r - -[ssfa-sshy( ttarae ) ( Degree ) ( ua5 or )
Date Ehe s ls pne senteaJhf l-- -1-q4-1- - - shy11s1--lllrs--cgurtgl-ampo-tqette-gt--19-Qtegttt1q-tc-l-rgtsl9--shy
-c-rurltlrl
Abstnact Approved
By neana of a eensltlve eunrent lneasurng devloe oonshyueotod la senles rlth a d-tertarlc aeld cnystall a flor of ounnont can bo detected rhen tbc c4yetal ls lllunlnatedl rltblleht fron an ordlnary tungsten ftlaent larap lfre cunrent rosponse ls greatly deBendont ou the onlentatlon of tho orTsshytal rlth neapeot to the dlneetlon of the lnoldent bcan ofItght Uogt of the cnystal faces glve a ourront rccponse upon lllumlnatton rlrlsb rlses napldly to a naxtnuu Just aftor tJee 1lgbt 1g trrrned oar then decrcageg and flael3y neaobes a ooastant ya1ue |l|hls type of reeponso ls callcQnlhe nortaleffect
lllhere are oentain neglons of the cr1rstaI horeven Chtohglve e cuJplrent flor rlrlcb gtantg out ln ono dfupectloa Justaftcn the llgpt ls turtred oa deeneasss naplclly rlth the ttne of lllrutnatloa and tben florE ln the opposlte dlneetlonEhls ls ealled the abnomal effeot It ts found that thls abnoraal effect alrays ocours rhen a polnt (srall neglon) ls tlhmlnated tbet LLog betseen tro regtons rhose nomel ounnent flors eno opBosltely dllrected Iho Buporposltlm of ths tro nomel orurncnt-ttne rosBonso onrYes glvoe a nesu1taut rhloh agneor rlth the obsenved abnomal rosponso rlthll the expenlshyuental error
A study ras uade of the verlatioa of pbotoounent dth taperature betveen 23oC end 15100 llhe crnrent ras found to hecrease rapidIy as tbe tcn1renature ras raleed fp 25oC to SOoC et rbloh point tbe orrrnent becaoe too mall to mealurolt 151oC a maII rovorro onpreat ras noted
Palntlag tbe onystal faoes drlch mede oonteot lth the eleetrodes r][th iaguidagi resuted la aa lncroase tn Bbotoshyourent
- 2 shy
The current response was studied when the crystal was examined with a light probe When the light fell on the crystal near the electrodes the response was found to be slightly less than when the light probe was used mid-waybetween the two electrodes
The fatigue effect of the crystals was examined bymeasuring the current response after comparatively longperiods ot illumination It was found that the decrease in current caused by the illumination was much greater for freshly grown crystals than for those grown several months before the test
Several theories relating to the crystal photoeffect are discussed With a alight extension the assumption of a bullconductivity axisbull or direction of max~ conductivitythe diffusion theory explains all results obtained includingthe new bullabnormal effect
IDPROVEDT
Redacted for Privacy
Xa Gbarge of ltral or
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
Ghslruea of State Collcgo
ACKNOWLEDGMENT
The author wishes to express her gratitude to
Dr James J Brady Associate Professor ot Physics
who suggested the problem and whose untiling interest
and helpful suggestions have proved invaluable for
the completion ot the work
The author also wishes to thank Dr w Weniger
Head of the Physics Department who has made the
necessary apparatus available
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
- 2 shy
The current response was studied when the crystal was examined with a light probe When the light fell on the crystal near the electrodes the response was found to be slightly less than when the light probe was used mid-waybetween the two electrodes
The fatigue effect of the crystals was examined bymeasuring the current response after comparatively longperiods ot illumination It was found that the decrease in current caused by the illumination was much greater for freshly grown crystals than for those grown several months before the test
Several theories relating to the crystal photoeffect are discussed With a alight extension the assumption of a bullconductivity axisbull or direction of max~ conductivitythe diffusion theory explains all results obtained includingthe new bullabnormal effect
IDPROVEDT
Redacted for Privacy
Xa Gbarge of ltral or
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
Ghslruea of State Collcgo
ACKNOWLEDGMENT
The author wishes to express her gratitude to
Dr James J Brady Associate Professor ot Physics
who suggested the problem and whose untiling interest
and helpful suggestions have proved invaluable for
the completion ot the work
The author also wishes to thank Dr w Weniger
Head of the Physics Department who has made the
necessary apparatus available
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
IDPROVEDT
Redacted for Privacy
Xa Gbarge of ltral or
Redacted for Privacy
Redacted for Privacy
Redacted for Privacy
Ghslruea of State Collcgo
ACKNOWLEDGMENT
The author wishes to express her gratitude to
Dr James J Brady Associate Professor ot Physics
who suggested the problem and whose untiling interest
and helpful suggestions have proved invaluable for
the completion ot the work
The author also wishes to thank Dr w Weniger
Head of the Physics Department who has made the
necessary apparatus available
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
ACKNOWLEDGMENT
The author wishes to express her gratitude to
Dr James J Brady Associate Professor ot Physics
who suggested the problem and whose untiling interest
and helpful suggestions have proved invaluable for
the completion ot the work
The author also wishes to thank Dr w Weniger
Head of the Physics Department who has made the
necessary apparatus available
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
~LE OF CONTENTS
Part Page
I Introduction bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 1
The Barrier Layer Theory bull bull bull bull bull bull bull bull bull 3
The Light Pressure Theory bull bull bull bull bull bull bull bull bull 4
The Electrochemical Theory bull bull bull bull bull bull bull bull 5
Difpoundusion Theory bull bull bull bull bull bull bull bull bull bull bull bull bull 5
II Apparatus and Material bull bull bull bull bull bull bull bull bull bull bull bull 14
III Experbnent s bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 24
A The Effect of Crystal Thicknessbullbull bull bull bull 26
B The -Effect of a Coat of Aquadag on the Crystal Surfaces in Contact with Elecshytrodes bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 28
c The Effect of Crystal Orientationbullbull bull 30bull
D The Temperature Effect bull bull bull bull bull bull bull bull bull 32
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 35
F The Fatigue Effect bull bull bull bull bull bull bull bull bull bull bull 35
IV Discussion bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 39
v Conclusions bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 48
Bibliography bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 49
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
bull bull
bull bull bull
LIST OF FIGURES
Figure Page
1 Circuit for Crystal Photoeffect (Longitudinal Ulumination) bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
2 Circuit for Crystal Photoeffect (Transverse illumination) middot bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 13
3 Energy Level Diagram for Crystals bull bull bull bull bull bull 13
4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier bull bull bull bull bull bull bull bull bull bull bull bull 16
5 General View of the Apparatus bullbullbull bull bull bull bull bull 17
6 Diagram Showing the Cross-aection of the Crystal Holder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 19
Temperature-current Curve of the CrystalHolder bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 21
a A Tartaric Acid Single Crystal bull bull bull bull bull bull bull 23
9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces bull bull bull bull bull bull bull bull bull bull bull bull 23
10 Variation of Photocurrent with Time of Illumination bull bull bull bull bull bull bull bull bull bull bull bull bull 25
11 Variation of Photocurrent with Thickness of the Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 27
12 Effect on Photocurrent Due to Aquadag LayerBetween Crystal and Electrodes bull bull bull bull bull bull bull 29
13 Change of Photocurrent ])le to IlluminatingDifferent Crystal Faces bull bull bull bull bull bull bull bull bull bull bull 31
14 Curves Showing the Relationship of Normal and Abnormal Effects bull bull bull bull bull bull bull bull bull bull bull bull bull bull 33
15 Variation of Photocurrent with Temperature bull 34
16 Effect on Photocurrent l)le to Applying the Light Probe to Different Parts of Crystal bull bull 36
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
LIST OF FIGURES
(Continued)
Figure Page
17 Variation of Photocurrent with Time or Exposshytlle bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 38
18a Two Dimensional Dia~am of a Unit Cell or Tartaric Acid Crystal When the Top of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
18b Two Dimensional Diagrwm of a Unit Cell or Tartaric Acid Crystal When the Bottom of the Crystal is Illuminated bull bull bull bull bull bull bull bull bull bull bull 41
19 tdagram of a Unit Cell or Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 44
20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal bull bull bull bull bull bull bull bull bull bull bull 44
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
THE CRYSTAL PHOTOEFFECT IN
D-TARTARIC ACID SINGLE CRYSTALS
I INTRODUCTION
The crystal photoeffect manifested by certain
crystals consists in the production of an electric curshy
rent upon illumination without the aid or an impressed
battery The electric current may be detected by conshy
necting the metal electrodes supporting the crystal to
a galvanometer or electrometer The diagram of the conshy
nections is shown in Fig 1
This phenomenon was first observed about 1844 by
Hankel (5) who called it the actinoelectrie effect
Several workers have since used this expression but it
is rapidly being replaced by The crystal photoeffect
The latter term was first used by Dember (8) in 1931 in
reference to the electron flow in the direction of the
light transmitted through single crystals of cuprous
oxide
Very little attention was paid to this crystal
photoeffect prior to 1901 when J c Bose (2) in India
observed this effect in galena (lead sulfide) He put
this effect to practical use middotror measuring light intenshy
sity by designing his Tejometer described in us patent
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
2
755840 in 1901 Since then various crystals have been
found in nature which exhibit the crystal photoetfect A
list ot these is given in Table 1
TABLE 1
A List of ~oto-crystals
Name ot crystal Investigator Year
lead sulfide J c Bose (2) 1901
argentite (~S) H H Sheldon (22) and P H Geiger (11) 1922
molybdenite w w Coblentz (5) 1924
selenium R M Holmes (12) and N L Walbridge (13 1928
cuprite H Dember (89) 1931
diamond R Robertson (21) 1932
sodium chloride St Pelz (20) 1933
potassium chloride St Pelz (20) 1933
tartaric acid r r Brady and W H Moore (3) 1939
Note Sodium chloride and potassium chloride must be colored yellow with X-rays in order to show the effect
The question ot the origin of the electromotive force
1n the illuminated crystals has proved to be very puzzling
The following theories have been proposed within the last
few years
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
3
THE BARRIER LAYER THEORY The barrier layer theory
has proved very successfUl in explaining the behavior of
the copper oxide photo-cell and was therefore suggested as
an explanation for the crystal photoeffect In the copper
oxide cell the barrier layer is a very thin layer having
a thickness or 10-6 to 10-a em at the boundary between the
crystal surface and the electrodes This layer is of pure
cuprous oxide containing no tmpurities The rest of the
cuprous oxide has an excess of oxygen atoms The excess
oxygen atoms nearest the metal remove electrons from the
metal and thus establish an electric field in the barrier
layer Any electrons that may be released in the barrier
layer by the absorption of light will be forced out of the
oxide into the metal giving rise to a current This explashy
nation is known as Schottkys (14) barrier layer theory
According to this theory the current should be greatest 1n
the neighborhood of the boundary and should become extremely
small at a short distance away from the barrier layer
H Dember (8) proved by expertment that the barrier layer
theory failed to explain the crystal photoelectric effect
He showed that photocurrents are produced when the crystal
but not the electrode is exposed to light He also obtained
a flow of current in a single crystal of cuprite which was
free from barrier layers
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
4
THE LIGHT PRESSURE THEORY In the early experiments
of Dember the light was directed on the crystal perpenshy
dicular to one of the electrodes He observed that the
photo-electric current flowed in the same direction as the
light This fact led von Laue (15) to propose that the
motion of the electrons may be due to light pressure
Maxwells electro-magnetic theory of light predicts
that light should exert a pressure on any surface on whiCh
it falls The experiment of Nichols and Hull (19) proved
the existence of this light pressure It is reasonable to
assume in the present case that the electrons are acted
upon by light pressure The fact that the electrons in
Dembers (8) experiments moved in the direction of propashy
gation of the light thus finds a ready explanation Howshy
ever R Deaglio (6) still working with cuprite crystals
(from Chessy) allowed the light to fall upon a crystal
perpendicular to the line joining the two electrodes ie
parallel to the electrode faces as shown in Fig 2 He
observed no current flow when light was directed at a point
half way between the two electrodes but did obtain a curshy
rent when the light fell slightly to the left or the right
of this point and moreover these currents flowed in
opposite directions These observations are evidently
not explained by the light pressure theory
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
5
THE ELECTROCHEMICAL THEORY Deaglio (6) attempted
to explain his results on the basis of an electrochemical
theory He assumed that although the dark conduction is
electronic the action of the light is such as to produce
electrolytic conduction He discovered a fatigue phenomeshy
non that could be explained by this theory After a crystal
has been illuminated at constant intensity for a long time
the photocurrent was observed to fall to less than half of
its initial value According to this theory au+ ions
are transported to the cathode and deposited there as
metallic coPPer Since this copper layer absorbs a conshy
siderable amount of light the current will be decreased
appreciably
G M~nch and R St~ler (17) allowed light to fall
on a crystal through a thin open ring electrode where the
light could not be absorbed by the transported copper but
the fatigue effect persisted nevertheless The fact that
a fatigued crystal will return to its original behavior by
being kept in the dark tor several hours also contradicts
this theory Cuprite crystals from Cornwall and Tsumeb
showed no fatigue effect
DIFFUSION THEORY The theory that will now be preshy
sented has proved most satisfactory thus tar It has its
origin in a new theory or solids first suggested in a
qualitative manner by M J 0 Strutt (23) He pointed out
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
6
that a solution of Schrodingers wave equation in solids should lead to a number of allowable energy bands whiCh
need not necessarily overlap or even be in contact but
might be separated by a region of forbidden energy values
The solution for individual atoms gives rise to widely
separated energy states similar to those postulated by Bohr
When these individual atoms collect to form a solid
each energy state of the individual atoms breaks up into
a band of energy states If the forbidden region has a
width corresponding to a considerable fraction of an
electron-volt of energy and the band below is completely
filled with electrons the crystal will be a good electrishy
cal insulator as an electron would be unable to gain any
energy from an applied electric field unless that field
were sufficiently intense to raise its energy to that of
the empty energy band above the forbidden region It the
crystal lattice contains impurity atoms or detecta ot any
kind such as one would expect if normal atoms became disshy
placed from their normal positions in the crystal lattice
energy states for the electrons might arise 1n the forshy
bidden region Fig 3 illustrates the relative positions
ot the energy states in a crystal of this type If an
electron leaves the filled band and locates on one of
these so-called tmpurity levels a vacancy will be left
1n the filled band This vacancy is commonly referred to
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
7
as a hole The hole may move about in the crystal and
give rise to a resultant electrical conductivity It will
behave like a positive ion 1n many respects but of course
will not account for the transport of metal
A physical picture of the motion of a hole is not
difficult to conceive The ejection of an electron from
an atom into an impurity state leaves behind a positive
ion An electric field that may be present due to any
cause Whatever either within or without the atom will make
it highly probable that some neighboring atom will lose an
electron This electron will combine with the positive
ion The former neighboring atom will now be a positive
ion This process repeated many ttmes will constitute a
moving positive charge through the crystal not accompanied
by the motion of an atomic nucleus
J Frenkel (10) was one of the first to apply these
concepts to a theory of the crystal photoeffect For the
sake of simplicity Frenkel considered the case of a crysshy
tal illuminated by a plane sheet of light He derived an
expression for the potential difference between this plane
and any other point in the crystal Let the sheet of light
be in the yz plane passing through the origin Its equashy
tion will be x = o Assume a difference in diffusion
velocities of electrons and holes This difference will
cause a potential gradient whichwill tend to retard the
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
- - -
8
faster particles (electrons or holes) and accelerate the
slower ones For a steady state the rate of change of
electron or hole concentration with respect to time will
be zero but with respect to distance x it will be for
any unit volume in the crystal
d2 n D ----plusmn =9 (ElL n e)+ dX2 dX + +
where
D+ is the diffusion coefficient for the holes
n+ is the concentration or number of holes per cc
E is the electric field strength
If+ is the mobility of the holes divided bye
e is the electronic charge
The effect of the recombination of holes and alec trona is
neglected 1n this equation and the following For the
electron concentration a similar equation holds
where D ~ and n refer to electrons On the further
assumption that the field E is constant throughout the
crystal these expressions may be written
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
9
This equation states that the poundield set up by the difrusion
process will draw the charges out of a unit volume as fast
as they accumulate by diffusion
The effect of recombination will now be considered
In the conduction of electricity through gases it is well
known that the rate of recombination of the ions varies as
the square of their concentration If this relation were
to hold for crystals the current would increase as the
square root of the light intensity However it is an
experimental fact that under uniform illumination of the
entire crystal the current is proportional to the first
power of the light intensity Hence it is evident that
the electrons and holes in a crystal do not recombine in
the same manner as the electrons and ions in a discharge
tube where the ions first attach themselves to the walls
and then recombine on the surface The electrons or holes
may become trapped on impurities or lattice defects and
the recombination may take place at these points
Taking recombination into consideration the equation
may be written
Dplusmn d2n+---=shy Ellplusmn e
dnplusmn-shy rnplusmn = 0 (1) dx2 dx
where r is the recombination coefficient
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
10
The relation of the coefficients D and ~ is expressed
by Einsteins well known equation
DftL =kT (2)
where k is Boltzmanns constant and T is absolute temperashy
ture If the same concentration be assumed for electrons
and holes n_ is the s~e as n+ ~oughout the crystal
n =n =n - +
The solution of the differential equation (1) is
(3)
where a is a constant and n is the concentration in the0
crystal plane illuminated by the plane of light Substishy
tuting the value of n from equation (3) in equation (1)
a 2
Dplusmn plusmn ecdJplusmn E - r = 0 (4)
Equation (4) may be written as two separate equations
2 a D+ + eal+E - r = 0 (5)
2a n_ - eall_E - r = 0 (6)
Subtracting (6) from (5) and solving for E
D - D - + middot E = Ct (7) e(l_ + ll+)
By means of (2) equation (7) becomes
ll - E =kT - + a (8) e ll_+IJ+
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
11
From (3) ax = 1n (n n)0
write Ex = where is the potential difference between
the illuminated plane and any point in the crystal at a
distance x from this plane
Substitute these expressions in (B) after multiplying
both sides by x
Then
(9)
Mgnch and St~ler (16 18) reported that for pure
laboratory grown cuprous oxide crystals no crystal photoshy
effect was observed but that it was found in cuprous oxide
crystals occurring in nature and containing a slight trace
of impurities Mench explained these results by the assumption that the mobilities of electrons and holes are
identical when there are no impurities This is borne out
by equation (9) for if~+=~- ~ = 0
For semi-conductors the mobility of the electrons is
much greater than that of the holes Therefore the fracshy
tion II - tJ to-_ bull + =1 Jl_+tJ+
Equation (9) then can be written
n qgt = ~ ln 2 (10)e n
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
12
It is interesting to note that except for the constant
ke this equation happens to be exactly the s~e as that
for the electromotive force of a galvanic concentration
cell
This theory shows how an electromotive force can be
set up 1n a crystal by the absorption of light It also
predicts how the crystal photoeffect should vary with
temperature The concepts used in this theory will later
be applied to the results obtained by the author 1n the
study of tartaric acid crystals
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
-------------------
13
T
Fig 1 l ~Light
Circuit for Crystal Photoeffect
(Longitudinal illumination) -E~~ ~
G
Fig 2 Circuit for
Crystal Photoeffect (Transverse illumination)
Fig 3 Energy Level Diagram
for Crystals
Emptyband
Impurity -----r------shy level
~~F~~d
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
14
II APPARATUS AND MATERIAL
The expertmental set-up used 1n this investigation
is similar to that used by Brady and Moore (3) A photoshy
graph is given 1n Fig 5 and a diagram of connections 1n
Fig 4 The amplifying circuit was originally designed by
DuBridge and Brown (4 and employs an FP-54 electrometer
tube As this tube and the amplifying circuit are extremeshy
ly sensitive to stnay fields the tube and the resistance
R are enclosed in a cylindrical brass case The rest of
the amplifying circuit and the storage battery (12 volt
Willard type Syrig are mounted in a copper box The
type HS Leeds and Northrup galvanometer G 1n the diagram)
was connected to the circuit by grounded Shielded conducshy
tors
The crystal holder H consists of two parallel brass
disks with the crystal between them all held together by
spring pressure (P Fig 6) This holder is mounted in an
insulated chamber with provision for changing the temperashy
ture from room temperature to 150degC The outer wall of the
chamber is a tin can about 5 inchamp - in diameter and the
inner wall a 3 inch brass tube The space between as
shown in Fig 6 is partly filled with an asbestos boiler
cement and partly by the heating coil packed in asbestos
The coil is in series with a rheostat an ammeter and a
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
SmboL Explapation Symbol Explanation
c crystal R1 resistance 50 ohms
E 12-volt d c source resistance 50 ohms~ G galvanometer resistance 4000 ohms~ H crystal holder R4 resistance 2000 ohms
milliammeter resistance 50 ohmsIf R5
L light source Rs galvanometer shunt resistance
R resistance 102500 megohms s1 switch
resistance 10000 ohms switchRo s2 R resistance 50 obms T FP-54 vacuum tube
0
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
T 8
s
-----~-11 I I I I ~+--- s2
E
Fig 4 A Complete Circuit for Crystal Photoeffect with FP-54 Amplifier
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
Fig 5 General View of the Apparatus
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
c
Smbol Explanation
crystal
E cement
H heating coil
M space for cooling agent
N space for water vapor absorbing agent
p spring
s sulfur
T thermometer
w water
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
T
Fig 6 Diagram Showing the Cross-section of the Crystal Holder
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
20
110 volt AC source A rough calibration curve (Fig 7)
relating ammeter readings to temperatures was obtained by
a preliminary experiment but actual temperatures were
always read on the thermometer shown in Fig 6
Provision was also made for reducing the temperature
by placing solid carbon dioxide in the space M Calcium
chloride has to be placed in the space N to absorb moisture
No data were taken below room temperature
The crystal -holder is supported on sulphur cylinders
SS placed in a brass tube extending as shown from the sides
o~ the insulating chwmber Water jackets are provided as
shown to keep the sulphur ~rom being melted by heat conshy
ducted along the tube
The light source L Fig 4 was a 150 watt spiral
filament tungsten gas filled lamp It was focused on the I
crystal by a simple lens Stray light was prevented from
reaching the crystal by a brass tube extending from the
crystal to the lens
All the crystals used in this investigation are sinshy
gle crystals artificially grown in this laboratory by the
investigator A saturated solution of cp d-tartaric
acid crystals was made in distilled water This solution
was filtered to remove excess crystals and dust particles
Beakers containing this solution were covered and placed
in a box in an unused roam in which the temperature could
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
~
~~~
Rt-4 ~~middot +~
4 ~--_
j
~_~
bull--tshy
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
22
be controlled to the extent or avoiding large or ~dden
changes A sudden change or temperature will cause the
crystals to grow 1n clusters Crystallization usually
starts at the place where the surface of the solution
touches the wall of the beaker Crystals obtained from
this region are not perfect single crystals Crystals
starting at the surface and growing downward in to the solushy
tion are generally large and fairly perfect except for the
upper race The crystals which form at the bottom or the
beaker are almost always most nearly perfect The process
must be inspected from time to time to make sure that ranshy
dom clusters are not formed A photograph of one of the
crystals is shown in Fig e From external appearances
the small crystals are more nearly perfect than the larger
ones The best ones obtained bad a thickness of from one
to two millimeters
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
23
Fig 8 A Tartaric Acid Single Crystal
I
I b-axis----shy
I
aI
a-axis
c
q
Fig 9 Diagram of a Tartaric Acid Single Crystal Showing Crystal Faces
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
24
III EXPERIMENTS
According to the observations of J J Brady and
w H Moore (3) on tartaric acid crystals when light
falls on the crystal the galvanometer deflection rises
very suddenly to the maximum value and then decreases very
rapidly at first then more and more slowly until it
approaches a steady value When the light is cut off
the galvanometer deflects in the opposite direction to
approximately the same maximum value but finally apshy
proaches the initial value If the galvanometer deflecshy
tion is plotted against the time the curve will appear
as in Fig 10 This curve is characteristic of the crysshy
tal photoelectric effect The decrease in current 1n the
first part of the curve has been explained by the investishy
gators as caused by the building up of a space charge
(or polarization) within the crystal
They observed that crystals which appeared to have
flaws behaved differently from the curve shown in Fig 10
When the light was turned on such a crystal the galvanomshy
eter derlected first in one direction then quickly reversed
and reached a maximum in the opposite direction A thorough
investigation of this peculiar phenomenon was conducted by
the author It was found that a similar behavior is also
shown by all perfect clear single crystals It will be
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
bullbullbull-+-+shy~~ ~-4
1=-~shy~~~~ -~f
~~~~bull _r---
middot _fu~ ~ 1
1 bull+
-+t
~F
~Hi]=
f l~
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
26
called the abnormal effect in this thesis In contrashy
distinction the usual effect will be referred to as
normal
A The Effect of Crystal Thickness
All the perfect single crystals exist in a definite
form as Shown in Fig 8 the crystal faces being very
distinct This definite form is shown more clearly by
means of Fig 9 In crystallographic nomenclature face
a is called the ortbopinacoid face q clinodome c basalshy
pinacoid and r orthodame The crystal is symmetrical
about the b-axis the b- and c-axes are at right angles
to each other but the a-axis is perpendicular only to
the b-axis and not to the c-axis
In order to investigate the effect of thickness of
crystal on the crystal photoelectric current a particular
face of the single crystal is chosen for illumination
Face m is chosen in this case because it exists in most
of the crystals obtained and is easily distinguished
Electrodes are placed against the orthopinacoid faces and
light falls on the m faces along the b-axis If the
maximum deflection of the galvanometer reading is plotted
against the thickness of the crystals the curve appears
to be a straight line (Fig 11) showing that the photoshy
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
Ibull
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
28
electric current varies directly as the thickness of the
crystals Of the eleven crystals studied two did not
lie on the curve the reason is not known definitely but
these crystals bad probably been previously exposed to
strong illumination for a considerable time
B The Ettect of a Coat or Asuadag on the CrystalSurfaces in Contact with Electrodes
It was attempted to increase the current flow by deshy
creasing the contact resistance between the crystal and
the electrodes Aquadag a colloidal graphite is highly
conducting and seemed to be a suitable material A paste
or aquadag obtained by mixing it with a drop of distilled
water was spread over the crystal surface a The coating
appears to be dry in one or two hours but observations are
not taken until after one or two days In most cases the
deflection or the galvanometer increases after this coatshy
ing has been applied The amount of the increase 1n the
galvanometer deflection varies for different crystals
In some cases the magnitude increases two or three fold
as shown in Fig 12 This treatment was given to many
but not all of the crystals used 1n this investigation
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
~
_ ~-
~ ~ ~ ~~-~ -~ -
_
-shy
--~-+1 ~
1
ir-
1-hpound-tplusmnrii
ir-r _-nEr_
_ -
- Llmiddot~
+shy
IHshy
=J
TtF
-
I+ It
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
30
c The Effect of Crystal Orientation
The effect of having the light fall on different faces
of the perfect clear single crystals was thoroughly invesshy
tigated Since most of the crystals obtained are thin it
is very difficult to concentrate the light on a particular
face as shown 1n Fig 9 The e face especially is so
small that the r face is also included in the Ulumination
Faces symmetrical with respect to the b-axis are
designated by unprimed and primed letters as q c and e
In this ease there are altogether six different faces
e q m qt c m
The results obt~ned show that the orientation of
the crystal 1n the light beam has a decided effect upon
the photoelectric current The current-time curves show
decided differences Fig 13 shows the values for the
six different faces of a perfect clear single crystal the
minimum thickness of which is 188mm The curves differ
not only as to the magnitude of deflection but even in
the direction of the current (curve F) Curve E shows
that the galvanometer starts middotto deflect in one direction
when face c is first illuminated then reverses in direcshy
tion reaches a maximum after a short time and gradually
decreases to a steady value This phenomenon appears in middot
all the perfect clear single cr~stals grown in this laborashy
tory Let us designate this curve as the abnormal curve
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
H
H-1
~Ril+
F
IH
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
32
This peculiar behavior was examined more closely
The face that shows the abnormal behavior and its two
neighbors were illuminated successively The deflections
for the two neighboring faces were always found to be
opposite in direction (Fig 14 A and C) The first porshy
tions of these current-time curves were plotted on an
enlarged scale The difference of these two sets of data
produce a curve having the abnormal shape B Fig 14
The experimental curve is shown in curve B These two
curves have the same shape and differ slightly in magnitude
Only one abnormality was found in each of the crystals
studied but it was not always found to occur on the same
face Other places near the intersection of the crystal
faces may show this abnormal behavior but if so it can
only be determined by building a crystal holder provided
with graduated circles and rotating the crystal through
a series of small angular steps
D The Temperature Effect
In this investigation the range of temperature extends
from 23degC to 151degC The crystal is coated with aquadag so
as to insure a low resistance contact between the crystal
surfaces and the electrodes The maximum galvanometer
reading is plotted against the temperature as shown in
Fig 15 From this curve it can be seen that the photoshy
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
+
fT +
+lili
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
35
electric current decreases rapidly with increasing temperashy
ture ~am 25degC to 50degC Above 50degC the current appears to
be zero but at 151degC there is a minute current in the opshy
posite direction This could not be traced rarther as
the crystal melts at 170degC Upon cooling the crystal
regains its original photoelectric current
E The Effect of a Light Probe Near the Electrode and at the Center of the Crystal
A thick crystal or about 388mm was chosen ror this
investigation A slit about one millimeter wide was placed
~ediately in front of the crystal Fig 16 shows that
the shape of the current-time curve is not unusual When
the light probe is near the electrode the current is
slightly less than when it is at the center of the crystal
This may be caused by a slight unavoidable illumination of
an electrode
F The Fatigue Efrect
A freshly grown crystal was used to investigate
fatigue To show this phenomenon the crystal is illumishy
nated as usual and a galvanometer reading taken The
illumination is continued for several hours and galvanomshy
eter deflections taken at varying intervals but before
each deflection the illumination is discontinued for one
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
++
~4
+-J ++
ttrt
-1
tplusmn
~Sill
plusmn_ ~ -t
~
~if
li ~
~
~ 1
~--B middot~
Jtshytplusmn
4
-r-
t
1-5
f+1irt ~12
+-dshy
t~middot ll
middot--=~ ~rmiddot
titr E ~~~~
middot---=1i +
Ibull
t -r~
bshy
~~
lff~ ~_r
r
imiddot
~
f1
p
mrr
H-
rpound_tttfi=H -middot
p +
+
l71middot~
__ jj -Hf+ _
+tl n
t-t_115- -~-
~ifj +l
tl -1
m~
+-[
q +
i~if~ ~ -
~
middot ttl
tJtplusmnt1
lgt-JH
-m
~
f+l
uiIJ
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
37
minute in order to give the space charge caused by the
light in the crystal a chance to dissipate The illumishy
nation is then resumed and a galvanometer deflection taken
immediately
Under this procedure successive galvanometer derlecshy
tions become smaller and smaller The amount of decrease
is greatest in the first hour ot exposure The curve
obtained by plotting the maximum galvanometer deflection
against the time o~ exposure is shown in Fig 17 After
this crystal had been exposed to light for several hours
and had in consequence exhibited a marked fatigue effect
it was allowed to remain in the dark for several hours in
order to determine whether or not the original sensitivity
would return After a dark period of twelve hours the
photo-current response for the same light intensity not
only exhibited no recovery but actnally showed a slight
decrease In a similar experiment with a crystal which
had been grown several months before the fatigue effect
was exhibited by a decrease of only six per cent in the
photo-current after continuous exposure to light for seven
hours This decrease is in marked contrast to that exhibshy
ited by the freshly grown crystal which showed a decrease
in photo-current of forty per cent after a six-hour exposshy
ure to the same light intensity
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
H+
Itshy
~
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
39
IV DISCUSSION
In order to correlate the observed results the varishy
ous theories which have been proposed for the crystal
photoeftect will be examined
The fact that the l~t probe when illuminating the
middle portion of the crystal but not the region near the
electrodes yielded a fairly large resultant current flow
does not support the barrier layer theory According
to this theory the current should be much greater when
the light probe illuminates the region near the electrodes
than when it strikes the middle portion of the crystal
The experfmental results indicate that the current is
greater when the middle portion of the crystal is illumishy
nated We may conclude that although the barrier layer
theory is very successfUl when applied to the cuprous
oxide photocell it cannot be used tor correlating the
results of the present experiments
The light pressure theory as proposed by von Laue
(15) is inapplicable to this experiment as the light was
incident on the crystal in a direction perpendicular to
the current flow (see Fig 2) whereas it is regarded as
parallel to the current flow in von Laues theory
The electrochemical theory of R Deaglio (8) is based
on assumptions which again are not applicable to this
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
40
exper1ment as the fatigue experiments he performed inshy
volved the passage of light parallel to the current flow
The diffUsion theory appears to be more usefUl than
any of the others which have been proposed for correlatshy
ing the data obtained in this experfment It is necesshy
sary however to add a very ~portant assumption in order
to explain the observations It must be assumed that there
is a particular direction in the crystal along which the
conductivity is a maxtmum This direction will be referred
to as the conductivity axis This important assumption
has a foundation in the experfments of J J Brady and
w H Moore (3) who discovered a series of equipotential
lines on one face of an illuminated tartaric acid crystal
The direction of maxtmum conductivity or current flow is
assumed to be perpendicular to these equipotential lines
To exhibit the crystal photoeffect electrons must
be able to gain energy from the absorbed light by the
photoelectric process This may result in the production
of the positive holes as well as in furnishing a supply
of free electrons
Let us suppose that the conductivity axis lies diagshy
onally across the unit crystal cell as represented in the
two dfmensional diagram of Fig 18 When light falls on
the top face as in case (a) the number of photoelectrons
released near the top will be greater than the number
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
41
Fig 18a Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal When the Top of the Crystal is Illuminated
1 I
Fig 18b Two Dimensional Diagram of a Unit Cell of Tartaric Acid Crystal Nhen the
Bottom of the Crystal is Illuminated
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
42
released farther down 1n the crystal due to the diminished
light intensity The concentration of electrons and holes
will then be greater near the edge of the crystal where
the conductivity axis comes closer to the upper face
A difference in the concentration of charges along
this axis will account for an electromotive force in the
crystal When the crystal is illuminated on the bottom
race or the unit cell Fig 18 case (b) the concentrashy
tion of charges along the conductivity axis will be greater
on the left side instead of on the right as in case (a)
This will result in current flows of opposite direction
in the two cases In both cases the ~ceumulation of charges
at the boundaries between the crystal and the electrodes
will result in a decrease of current with time Because
of the difference in arrangement of the atoms at opposite
ends of the conductivity axis in contact with the electrodes
it is to be expected that the variation middotor the current with
time will depend on the direction of current flow
From the X-ray analysis of tartaric acid crystals by
w T Astbury (1) a very definite picture of the unit cell
bas been obtained The crystal belongs to the monoclinic
system the unit cell has the following dfmensionss
a =770A b =604A and c =620A The axes b and c are
perpendicular to each other and a is perpendicular to b
but makes an angle of 100deg17 with c The unit cell is shown
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
43
diagrwmmatically in Fig 19 The X-ray analysis shows
that there are two molecules to a unit cell The single
crystal is composed of a large number or unit cells Fig
20 shows the unit cell properly oriented with respect to
the single crystal The face c or the single crystal is
formed by the top surfaces of a large number of unit cells
The crystal faces m mbull q and qt are not parallel to the
sides of the unit cell The a-axis lies 1n the same plane
as the q and q faces
The expertmental results indicate that the direction
of current flow is the same for illumination of faces c
q m and qt When face m is illuminated the current
flows 1n the opposite direction to that produced by the
illumination of face c The conductivity axis as already
indicated has been assumed to lie in the unit cell as
shown in Fig 19 Bearing in mind the direction of the
conductivity axis the direction of current flow may be
predicted when any particular race is illuminated When
light is sent along the c-axis toward the c face the conshy
centration of charges due to light absorption will be
greatest at one electrode while the greatest charge conshy
centration tor light sent along the b-axia is near the
other electrode The inclination of the conductivity axis
relative to the direction of light propagation is 1n opposhy
site directions in the two cases indicating that flow of
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
44
Fig 19 Diagram of a Unit Cell of Tartaric Acid Crystal
Fig 20 Diagram Showing the Unit Cell in Relation to a Tartaric Acid Crystal
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
45
the currents should also be opposite
Fig 14 illustrates how the abnormal effect results
from the superposition of two current-time curves obtained
by illuminating two crystal faces which yield opposite
currents Curve A was obtained by illuminating the c-face
Curve C was obtained by illuminating the m face and Curve
B was the observed abnormal effect obtained from the illumishy
nation of the q-face B is the resultant of curves A and
c As it is difficult to obtain accurate readings in Short
time intervals it is entirely possible that the difference
between curves B and B is due to experimental error
From these results it may be expected that there will
be an abnormal effect when the beam of light falls upon a
particular portion of the crystal lying somewhere between
two faces that yield oppositely directed currents This
was therefore sought and found experimentally The direcshy
tion of light propagation was held constant while the crysshy
tal was rotated very carefully so as to explore the region
between faces m and c
However since the crystal faces are not always formed
exactly parallel to the electrodes but may have their unit
cells tilted slightly from this condition of parallelism
thus changing slightly the direction of the conductivity
axis with respect to the crystal faces it may be and it
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
46
was so found experimentally that the abnormal effect does
not always occur at exactly corresponding points in difshy
ferent crystals
The diffusion theory in its stmplest form indicates
that there should be a decrease in the crystal photocurrent
with increase in temperature This prediction is in accord
with the experimental results from 23deg0 to 50deg0 At higher
temperatures the current becomes too small to detect It
is reasonable to suppose that the mobility of the electrons
and holes would approach each other for the higher temperashy
tures and the concentration theory indicates that the
electromotive force would be zero under these conditions
In equation (9) if~- a~+ the potential difference= 0
The fact that the initial current response increases
as a linear fUnction of the thickness of the crystal may
be explained on the basis of increased light absorption
Just as impurities in the crystal give rise to intershy
mediate energy states so also normal atoms if displaced
tram their normal positions during the growth of the crysshy
tals may be regarded as giving rise to energy states beshy
tween a filled and an empty band (impurity levels Fig 3)
The fUrther assumption is then in order that the displaced
atoms may be brought back to their normal positions by the
passage of a current through the crystal These assumptions
are sufficient to account for the results observed when
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
47
studying the fatigue effect A decrease 1n the number of
impurity levels represents a decrease in the possible numshy
ber of holes and consequently a decrease 1n the observed
current Thermal agitation at room temperature may also
aid the displaced atams to return to their normal posishy
tions this accounts for the fact that old crystals show
a much smaller fatigue effect than those freshly grown
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
48
V CONCLUSIONS
From the experimental facts and the correlation obshy
tained the following conclusions may be drawn
1 d-Tartaric acid single crystals exhibit a crystal
photoeffeet
2 Hole conductivity as well as electron conductivity
exists in the crystals
3 There is a particular direction in the unit cell
along which the conductivity is a maximum This direction
is named the conductivity axis
4 The conductivity axis is perpendicular to the equishy
potential lines reported by J J Brady and W H Moore
5 The fact that the current flow is in one direction
for the illumination of a particular face and in the opposhy
site direction for the illumination of another face is a
result of the particular direction of the conductivity
axis in the unit cell
6 The exceedingly puzzling fact that the current may
start out in one direction and then decrease to zero and
rise to a maximum in the opposite direction is due to the
superposition of the effects trom two neighboring faces
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
49
BIBLIOGRAPHY
1 Astbury w T The crystalline structure and propershyties of tartaric acid Proc Roy Soc Ser A 102506-528 1924
2 Bose J c US Patent 755840 filed Sept 30 1901 issued March 29 1904
3 Brady J J and Moore W H Actinoelectric effects in tartaric acid crystals Phys Rev 55308-311 1939
4 Brown H and DuBridge L A An tmproved dc amplishyfying circuit Rev Sci Inst 4532-536 1933
5 Coblentz w w Some new thermoelectrical and actinoshyelectrical properties of molybdenite Scientific Papers of Nat Bur of Standards No 486 April 1924
6 Deaglio R Photoelectric effect for single crystalsof cuprite Zeits bull f Phys - 83179-183 1933 (Cit) Photoelectric effect in monocrystals of cuprite Phys Zeits 36144-147 1935
7 Dember H Electron strewm produced by light Phys Zeits 33207-208 1932
8 Dember H Photoelectric emf in cuprous oxide crystals Phys Zeits 32554-556 1931
9 Dember H Crystal photoelectric cell Phys Zeits 32856-858 1931
10 Frenkel J Conduction in poor electronic conductors Nature 132312-313 1933
11 Geiger P H Spectro-raquobotoelectrical effects in argentite The production of an electromotive force by illumination Phys Rev 22461-469 1923
12 Holmes R M and Rooney A B Thermoelectric power of selenium crystals Phys Rev 311126 1928
13 Holmes R M and Walbridge N L A photo-emf in single crystals of selenium Phys Rev 32281 1929
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
50
14 Lange B Photo-elements Reinhold Publishing Corpshyoration 1938 (Cit) Schottky w Conduction and photoelectric effects 1n blocking layers Phys Zeits 32833-842 1931
15 Laue v M (Cit) Phys Zeits 32858 1931 n16 Monch G Theory of crystal photoelectric effect Zeits f Phys 91264-271 1934
n17 Monch G and Stuhler R Photoelectric effect for single crystals of cuprite Zeits f Phys 85131-134 1933
18 Monch G and Stuhler R Crystal photoelectric effect Zeits f Phys 91253-263 1934
19 Nichols E F and Hull G F Preliminary communicashytion on the pressure of heat and light radiation Phys Rev 13307-320 1901
20 Pelz s Photoelectric effect in colored rock-salt Akad Wiss Wien Ber 142509-522 1933
21 Robertson R Fox J J and Martin A E Photoshyconductivity of d~onds Nature 129579 1932 (Cit) Two types of diamond Phil Trans of Roy Soc s A 232463-535 1934
22 Sheldon H H and Geiger P H The production of an emf on closed circuit by a light effect on argentite Proc Nat middotAcad Amer 8161-163 1922
23 Strutt M J o Eddy currents in an ellipticalcylinder Ann d Phys 84485 1927
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