Defects II - RKR Point Defects2

7/30/2019 Defects II - RKR Point Defects2

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2. Point Defects

R. Krause-Rehberg

2. Point Defects

2.1 Introduction

2.2 Classification2.3 Notation

2.4 Examples

2.5 Peculiarities in Semiconductors

2.6 Determination of Structure and Concentration

2.7 Vacancies in thermodynamic Equilibrium

2.8 Irradiation-induced Point Defects

2.9 Aspects of Defect Chemistry(F-center in NaCl)


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2.1 Introduction

point defects: vacancies, interstitials, impurities, antisite

defects, and their complexes

many physical properties are governed by point defects:

Conductivity and conduction type

Color

Transparency

Diffusion

Mechanical properties

Formation of precipitation

without vacancies: with 0.001% vacancies

transparent opaque

1 defect in 100000 atoms!

Galliumphosphide1 cm


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2.2 Classification

Types of Point Defects:

Vacancies

Interstitials

wrong species at

regular lattice site

Schottky defect

Frenkel pair

self-interstitial

impurity at interstitial Position

antisite atom

impurity at regular lattice position


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Another way of Classification

point defectsnative

induced extrinsic

intrinsic

native: defects in crystal after growth (intrinsic and extrinsic defects)

induced: generated in crystal after growth (e.g. by irradiation and plasticdeformation, or diffusion, precipitation growth)

intrinsic: self-defects of crystal without impurities (e.g. VGa, GaAs, Asi inGaAs)

extrinsic: defects including impurities (e.g. B- acceptor and V-O defect in Si;SiGa-VGa in GaAs)

however, this notation is not used uniformly in literature


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Still another Classification

Point De

fec

ts

Equilibrium Defec ts Excess Defec ts

thermal

vacancies

structural

defec ts

elec tronically

induced

ir radiation plastic

deformation

vacancies

in metals close

to melting point

AsGa

in LT-GaAs

Hg vacancies

in CdHgTe

SiGa-VGa in

n-doped GaAs

electron irradiation

ion implantation

cold-rolled metals

high-T deformed Si

lubrication


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Vacancies

vacancy of Schottky type Frenkel pair (here: close Frenkel pair)

note: relaxation of lattice at vacancy vacancies: - dominating defect at high temperature

- most important (primary) irradiation defect

- generated during plastic deformation (but often not stable)

in compounds and intermetallic phases: two different types of vacancies with

different properties


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Vacancies

defect reactions lead to defect complexes:

formation of divacancies and vacancy clusters

VAl-MgAl in Al-Mg-alloys

TeAs-VGa in GaAs:Te

V-Oi in Cz-Si (so-called A center)


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Interstitials

a) and b) interstitial in octahedral and tetrahedral position in a bcc crystal

EFFERG\FHQWHUHGFXELF

c) interstitial as dumbbell (deutsch: Hantel)

interstitial atoms are often small (e.g. B, C, N, O in metals)

often built-in in octahedral position (C in Fe): lattice distortion leads to

increased hardness

H is always built-in as interstitial


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Interstitials

important defect in silicon: Oi [O] is about 1018 cm-3 in Cz-Si

Oi has six equivalent positions

during annealing: formation of O-

precipitates; important for gettering of

impurities

self-interstitials often in dumbbell

FRQILJXUDWLRQLHDPROHFXOHRIWZR

identical atoms shares a regular lattice

site

Oxygen forms varies defect complexes in Si

with Si interstitials and Si vacancies

proposed structure of the I-O2 complex in Si


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Impurities

important defect in semiconductors (but also in metals, remember C in Fe)

intentionally used as dopants for the generation of carriers in high-resistive material

(Si, GaAs)

important acceptors: B in Si Zn or C in GaAs

important donors: P and As in Si Te, Si in GaAs

effect of a donor dopant

dopant levels in bandgap of Si


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Antisite Defects

prerequisite: ordered structure

in compound semiconductors and

intermetallic compounds

antisite defects compensate partly

deviations from stoichiometry

superlattice in system Au-Cu

a) (100)-plane in ordered Cu3Au

b) same plane at T > 390C

in existence region: deviation compensated

by point defects; outside: formation of

different phases, starting with small

precipitations

maximum deviation in compound

semiconductors very small at room

temperature

in LT-GaAs (grown at 200C): up to 1% of

point defects (mainly AsGa) extremely highconcentration

0.50000 0.50004 0.50008 0.50012900

1000

1100

1200

1300

TF

Melt

GaAss

GaAss+ Ga(As)

l

GaAss+ As(Ga)

l

solidus line

liquidus line

p6As

= 0.1 1 3 6 9 12 18 barT/

oC

xAs


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2.3 Notation of Point Defects

twofold negatively charged As vacancy2AsV

0

GaAs

iSi

SiB

neutral As antisite defect

Si atom at interstitial position

negatively charged boron atom at Si position

2AsV

speciescharge

position

often used in defect chemistry: .U|JHUVQRWDWLRQ

Au A' A'' acceptor neutral, negative, twofold negative

donor neutral, positive, twofold positive DDDu

e' electron in conduction band

GHIHFWHOHFWURQRUKROHLQYDOHQFHEDQG

h


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2.4 Examples: Color Centers

DONDOLKDORJHQLGHV1D&O.&ODUHFOHDUDQGWUDQVSDUHQW

coloring is obtained by point defects: color centers

possible defects: chemical impurities, excess metallic ions (e.g. Na+ in NaCl)

so-called F-bands: optical

absorption as function of wave

length; a part of optical

spectrum is cut, so the crystal

appears colored

the simple anion vacancy with a bound electron is the

F-center (absorption in UV region)

absorption: electric dipole transition to a bound exited

state of the defect

missing anion acts as positive charge and binds a

valence electron (which was delocalized before)


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other Color Centers

the FA-center in KCl; one of six K+

ions is replaced by another alkali ion(here Na+)

the M-center consists of two F-centers

the R-center consists of three F-centers

which are in an [111] plane of the NaCl

structure


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EL2 in GaAs: important antisite defect

probably the most frequently studied point defect in semiconductors: EL2 in GaAs

EL2 = electrical active defect II (as found in DLTS measurements)

used to obtain semi-insulating GaAs (auto-compensation of unwanted impurities)

self-compensation works only when [EL2] > [shallow acceptors] > [shallow donors]

VWHSQHHGVWRRKLJKWHPSHUDWXUHWKXVDOOFDUULHUVDUHFRPSHQVDWHGDWQRUPDOWHPSHUDWXUHV

condition can be fulfilled in pure semi-LQVXODWLQJ*D$VE\GRSLQJZLWK&


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EL2 in GaAs: important Antisite Defect

interesting feature: EL2 exhibits metastability

illumination at low temperature oproperties changes (e.g. no IR absorption any more)

many structural models were discussed

Dabrowski/Scheffler and Chadi/Chang: EL2 is isolated AsGa and in metastable state the

antisite atom moves outward and leaves a VGa Metastability is lost during warming-up to 115 K


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EL2 in GaAs: important Antisite Defect

positron annihilation is a method to detect

vacancy-type defects in solids

before annihilation, diffusing positrons can be

trapped by such defects

as a consequence: positron lifetime increases due

to the reduced electron density in the vacancy

experiment shows the existence of a Ga vacancy

in the metastable state of GaAs, which does not

exist in stable ground state

was prove of AsGa model of EL2

R. Krause, K. Saarinen, P. Hautojrvi, A. Polity, G. Grtner, and C. Corbel

Observa tion of a monovacancy in the metastablesta te of the E L2 defect

in GaAs by positron annihilation

Phys. Rev. Lett. 65 (26), 3329-32 (1990).


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DX Center in GaAlSb

defect appears in doped quasi-ternary III-V compound

semiconductors (e.g. AlxGa1-xAs, AlxGa1-xSb)

is complex: donor-? (so-called DX center)

also shows metastable state at low temperatures

model of Dabrowski/Scheffler predicted vacancy in

stable state and the disappearance of this vacancy in

metastable state

also proved by positron annihilation

Ga GaAl Al

Te Te

Sb Sb

metastable stable

Illumination

Illumination

10 2

10 3

10 4

10

5Photoconductivity[S]

279

278

277

276

275

274Averagepo

sitronlifetime[ps]

20 40 60 80 100 120Annealing temperature [K]

GaAlSb:Te

R. Krause-Rehberg et al., Phys. Rev. B 48 (1993) 11723


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Compensating Defects in GaAs:Te

Te is typical donor in GaAs

is built-in only as TeAs experimental finding: with increasing

donor doping concentration

acceptor density simultaneously

increases

VHOI-FRPSHQVDWLRQ

degree of compensation about 25%

confirmed model:

donor acceptor

TeAs

+

VGaTeAs

-

driving force for generation of defect

clusters: so-FDOOHG)HUPL-OHYHOHIIHFW

it is energetically favorable to form

additional acceptors in n-type GaAsresult of Hall-effect measurements


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Compensating Defects in GaAs:Si

Si is also often used as donor in GaAs

Si is built-in as SiGa+ and also as SiAs

-

(amphoteric behavior)

thus: situation is different from GaAs:Te

degree of compensation not constant, butgrowing

result: doping only possible up to 1019 cm-3

at higher Si content: almost complete auto-

compensation

model for additional compensating center(acceptor): VGaSiGa-

result of positron annihilation spectroscopy (by K. Saarinen et. al, Helsinki UT)


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Compensating Defects in GaAs:Si

model was proven by correlated STM and positron experiments

STM shows at cleavage planes of GaAs:Si the VGaSiGa- defect (but possibly formed

during cleavage)

positron annihilation found the same number of vacancies in the volume of the identical

crystals

conclusion: both methods detect the identical defects

J. Gebauer et al.

Phys. Rev. Lett. 78 (1997) 3334


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22

1 2 3 4 5 6 7 8 90.00.1

0.2

1 2 3 4 5 6 7 8 9

lattice spacing in [110] direction

Heigh

t[nm]

-2.0 V +1.4 V

occupied empty states

Scanning tunneling microscopy at GaAs (110)-

cleavages planes (by Ph. Ebert, Jlich)

Defect complex identified as VGa-SiGa

1018

1019

1017

1018

1019

Si concentration (cm-3)

Positrons - cvac

STM - [SiGa

-VGa

]

Defectconcentration(cm

-3)

Quantification o Agreement

Mono-vacancies in GaAs:Si are VGa- SiGa-complexes

Identification of VGa-SiGa-Complexes in GaAs:Si

Gebauer et al., Phys. Rev. Lett. 78 (1997) 3334


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two-zone-furnace: Control ofsample temperature and Aspartial pressure in quartz tube

TAs: determines As-partialpressure

navigate freely in phase diagram(existence area of compound)

Tsample: 1100 C

GaAs: annealing under defined As-partial pressure

Jurisch, Wenzl; 2002

0.50000 0.50004 0.50008 0.50012

900

1000

1100

1200

1300

TF

Melt

GaAss

GaAss+ Ga(As)

l

GaAss+ As(Ga)

l

solidus line

liquidus line

p6As

= 0.1 1 3 6 9 12 18 barT/

oC

xAs

Equilibrium Phase Diagram of GaAs


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0,01 0,1 1 10

1017

GaAs:Si

Linear fit

Vacancyc

oncen

tra

tion

(cm

-3)

Arsenic pressure (bar)

0,1 1 10

1016

1017

1018

[Te] in cm-3

9x1016

4x1017

6x1018

2x1018

231

GaAs:Te

250

235

240

245

Wav

at550K(ps)

Vacancyconcentration(cm

-3)

Arsenic pressure (bar)

SiGa-VGa

TeAs

-VGa

Fit: [VGa-Dopant] ~ pAsn

o n = 1/4

Thermodynamic reaction:1/4 As4

gaslAsAs + VGa

Mass action law:

[VGa] = KVG upAs1/4

J. Gebauer et al.,Physica B 273-274, 705 (1999)

GaAs: Annealing under defined As pressure


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Thermodynamic reaction:AsAs l VAs + 1/4As4

gas

Mass action law:

[VAs] = KVAs upAs-1/4

Fit: [V-complex] ~ pAsn

o n = -1/4

undoped GaAs: As vacancy

Comparison of doped and undoped GaAs

Bondarenko et al., 2003


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2.5 Peculiarities in Semiconductors

defects in semiconductors can be

charged (e.g.: +, 0, -)

charge depends on position of

Fermi level

electronic configuration and

structure of a defect depend on

charge state a different charge leads to

different lattice distortions

is so-FDOOHGJahn-Teller Effect

thus: distortion energy depends

on charge state influence may be so strong that

normal charge sequence (2-, -, 0,

LVFKDQJHGnegative-U

behavior

electron configuration of V0 in Si


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negative-U behavior

example: theoretical calculations of

ionization levels

a) to c) are calculated without lattice

relaxation

calculations g) to h): lattice distortion

was taken into account

Jahn-Teller Effect is frequently foundin semiconductors

Defec ts in InP

GaAs in Ga As

relaxedunrelaxed

relaxed


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2.6 Determination of structure and concentration

range of concentration: about 1010 cm-3 (metallic impurities in Si)

> 1020 cm-3 (some dopants in Si, AsGa in LT-GaAs)

defect identification difficult due to large variety of species

in GaAs: 6 intrinsic defects in many charge states; they form defect complexes; in

addition: they can form complexes with impurities

there is no universal method many methods give information about ionization levels in

band gap, but no structural information (e.g. DLTS, Hall, IR absorption)

other methods have structural information, but can only be applied to a restricted number

of defects or materials (e.g. EPR, Positron Annihilation)

topic of lec tures in next course!


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2.7 Vacancies in thermodynamic equilibrium

VVV STWNF ''

!)!(

!

!

)1()1(

VVV

V

NNN

N

N

NNNNG

!)!(

!lnln

VV

BBVNNN

NkGkS

'

statistical considerations change of free enthalpy during formation of NV Schottky-type vacancies (N .. number of

atoms; WV YDFDQF\IRUPDWLRQHQHUJ\

(positive energy term can be compensated by gain of entropy!)

'SV is entropy gain; is calculated in the following (from statistics: S= kB ln G):

probability Gto form NV vacancies in N atoms is equal to probability to

choose NV atoms out of N atoms (numerator):

The factor NV! (speak: factorial) in the denominator excludes those cases which differ onlyby the different order of pick-out of atoms.

using the Boltzmann-Equation and the Stirling approximation:

xxxx # ln!ln


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!)!(

!lnln

VVBBV

NNN

NkGkS

' xxxx # ln!ln

Tk

W

NN

N

B

V

V

V

ln

]ln)ln()(ln[ VVVVBV NNNNNNNNkS '

0ln

w

'w

V

VBV

TV N

NNTkW

N

F

it follows:

in thermal equilibrium: 'F is extreme value (minimum)

in the lattice: NV 103)

Tk

WNN

B

VV exp

thus: vacancies must exist in an ideal crystal at T>0 !

[1]

VVV STWNF ''

!


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example: T=1000K and WV = 1 eV NV/N 10-5

T=1000K and WV = 3 eV NV/N 10-15

not detectable

real example: vacancies in Au: WV = 0.98 eV, but in Si: WV > 3.6 eV

vacancy concentration is slightly larger compared to Eq. [1]

further factors to be taken into account:

- interaction of vacancies

- influence of point defects to 'S

- volume work for dilatation of lattice

- electronic effects

defect density often much larger: crystal far from being in thermal equilibrium

excess vacancies due to e.g. irradiationby fast particles

also: vacancies can be quenched-inby very fast quenching

quenching rate must be about 104 Ks-1, then a large fraction of thermal vacancies remain

during slow warming-up: vacancies become mobile (migration energy required 0.5mm)

ions produce extended defect cascades; energy large enough for 104 displacement events

however: only a few defects survive (stationary state reached after 1 ps)

also larger point defect clusters are generated

computer-simulated defect cascade in {100} plane of Cu. T=250 eV, ta = 0.06 ps, tb = 0.35 ps, tc = 1.5 psstationary result after 1.5 ps: 5 vacancies and 5 interstitials


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ion implantation

important dopant species in Si are As and B

in order to obtain homogenous doping depth profiles: multiple implantation steps with

different energy

depth distribution of implanted B

(As) atoms in silicon

depth distribution of displaced

atoms in B-implanted Si

when implantation dose large enough: lattice becomes amorphous

amorphisation dose is function of ion mass, target species, and temperature

6LPXODWLRQZLWKIUHHFRGH65,0ZZZVULPRUJ 7KH6WRSSLQJDQG5DQJHRI,RQVLQ

0DWWHU

projected range Rp


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Example of SRIM simulation


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temperature dependence of amorphisation

dose for different ions in Si

Doping by ion-implantation

KDVPDQ\DGYDQWDJHVEXW

defects must be annealed

temperature dependence ofamorphisation dose is strong

at elevated temperature:

defects anneal during

irradiation

at room temperature: boron

implantation will not lead to

amorphisation at all

in technology: defects must be

annealed

often: rapid thermal annealing

(RTA) in Si: 30s at 950C

done by light illumination by

strong halogen lamps (few

kW)


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Rutherford Backscattering

classical method to investigate ion implantation defects:

Rutherford Backscattering

probe atoms (H, He) penetrate into the sample into low-

index directions (channels)

defects which are present scatter the probe atoms and raise

the backscattered intensity

defect depth profiles can be determined


41/53

41

FLA = Flash Lamp Annealing

short light pulses of Xe flash lamps may melt surface of Si

heating period some ms

RTA-Annealing (Rapid thermal annealing) of semiconductors after ionimplantation

Problem: measurement of temperature

P h ti f s l b h l l s d th


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42

Pre-heating of sample by halogen lamps and then:light pulse by flash lamps

Pulse-forming network (PFN).

Ground switch

Xenon flash-lampsPulse-forming network (PFN).

Ground switch

Xenon flash-lamps

Temperature up to 2000C electrical power: 12 MW (for 20ms)

Pre-heating necessary

temperature gradient: 5105 K/s


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2.8.2 Annealing of excess point defects

irradiation defects far from thermal equilibrium but still stable (frozen-in)

increasing temperature: defects start migration

energymigration...exp0 mB

m ETk

ENN

electri

calresistance

annealing of irradiation defects in Cu

electrical residual resistance at low temperature: sensitive for defects (electrons are

scattered during movement in electric field)


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Annealing of excess point defects

annealing starts at very low temperatures (in metals: interstitials have smallest migration energy)

many annealing stages; during annealing: defect reaction (e.g. formation of vacancy clusters)

often: several mechanisms lead to

disappearance of same defect: vacancies

vanish due to migration of interstitials and

vacancies itself

several stages (A-E) for interstitials: close

Frenkel pairs (A-C) and separated interstitials

(D+E)

curve b: electron irradiation

curve k: plastic deformation

curve a: quenched sample

stage I + II: interstitial annealing stage III: vacancy annealing

isochronal annealing curve of Cu after 3-

MeV-electron irradiation (Tirr=4.5 K)


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Annealing of excess point defects

example: defects after electron irradiation in

Ge (Ee-=2 MeV, Tirr=4K)

distinct annealing stage at 200K

sample with highest dose: formation of

divacancies during annealing (they anneal at

about 400K)

formation of divacancies prove: it is nomovement of interstitials but vacancies

this is further supported by the fact that the

vacancies disappear completely in this stage;

interstitial stage always incomplete

(Polity et al., 1997)

Defect annealing in electron irradiated Si


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Positron study of defect annealing after 4K-

electron irradiation of Cz-Si

Monovacancies disappear around room

temperature and divacancies are formed

Annealing is more complex: several stages

in intensity

Cz-Si contains about 1018 cm-3 oxygen Oxygen-vacancy complexes are formed

which can be transferred into more

complex defects during course of annealing

Defect reactions occur

(Polity et al., 1998)

Defect annealing in electron irradiated Si

f


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2.8.3 Defect reactions

defect reactions during annealing sequence is a normal

effect

defect complexes could be rather complicated

typical example: defect annealing in Cz-Si after low-

temperature electron irradiation

Cz-Si contains about 1018 cm-3 oxygen

many different oxygen-vacancy complexes are formed

most simple defect is theso-called A-center (VO)

during annealing:

sequence of different

VxOy complexes are

formed

defects stable up to

800C, although an

isolated monovacancy

anneals at about 200K

oxygen stabilizes the

defects

V-O complex (A-center)


48/53

2.9 Aspects of defect chemistry

chemical or defect reaction

i

DCBA DCBA

:indexreaction

molesofQXPEHU

DCO

prior to reaction: O = 0 ; complete reaction O = 1

in thermodynamic equilibrium: 0 < O < 1

equilibrium condition:

T,p

G0 minimum of free entalphy G

w

w

reaction runs spontaneously only when:

0

,

w

w

pT

G


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The mass action law

DCBA mo chemical or defect reactionk1

k2

ki ... reaction velocity coefficientsci ... concentrations

BABA

cckdt

dc

dt

dc 1 DC

DCcck

dt

dc

dt

dc 2and for return reaction:

in case of thermodynamic equilibrium: velocity in both directions identical

dt

dc

dt

dc CA and thus: mequilibriuinionconcentrat...2

1i

BA

DCck

k

k

cc

cc

equation is called mass action law not only for chemical reactions: intrinsic conductivity in semiconductors

kN

pnpn

m

o :lawactionmass0 N ... number of all electrons

and thus: 'kpn


50/53

Example: Defect chemistry in HgCdTe

HgCdTe is used as infrared detector; dominating defect is VHg2- (twofold ionized acceptor)

vacancies are in equilibrium with vapor pHg over crystal

HgHg HggasHghV

he

l

l

)(2

0

2

electrical conductivity is sum of intrinsic

conduction and ionization of VHg acceptors

QQXPEHURIIUHHHOHFWURQV

KQXPEHURIIUHHKROHV

mass action laws:

(1)][ v

22kphV

khn

HgHg

i

(2)0][22

HgVhn

neutrality condition: intrinsic part

extrinsic part (3)][2 2 hVHg

ratures)high tempe(athn

technical use at T < 100K (no intrinsic conduction); combination of (1) to (3) gives:

(4)02

22

v77

2

77

v

2

3

77

Hg

KiK

Hgi

Kp

khkh

k

pkh


51/53

Defect chemistry in HgCdTe

is equation which defines

correlation between Hg partial

pressure and concentration of

Hg vacancies in crystal(because h77K= 2 [VHg])

constants ki and kv were

determined by electrical

measurements (Hall effect)

lines in figure: result ofsimulation by eq. (4);

measured points: experimental

data of Hg vacancy

concentration obtained by

positron annihilation

(4)02

22

v77

2

77

v

2

3

77

Hg

KiK

Hgi

K

p

khkh

k

pkh

f h


52/53

Defect chemistry

treatment of quasi-ternary compounds

becomes rather difficult

very large number of intrinsic defects

but in special regions: only a few

defects dominate

calculation of the dominating defects

requires the knowledge ofthermodynamic constants which are

usually only roughly known

diagram only valid for a constant

temperature

CuInSe2


53/53

References

1. &K:HLPDQWHO&+DPDQQ*UXQGODJHQGHU

Festkrperphysik

2. %HUJPDQQ6FKlIHU/HKUEXFKGHU

([SHULPHQWDOSK\VLN%G)HVWN|USHU

3. -%RXUJRLQ0/DQRR3RLQW'HIHFWVLQ

6HPLFRQGXFWRUV6SULQJHU-Verlag, Teil II

4. 0$UQROG3K\VLNDOLVFKH&KHPLHGHU+DOEOHLWHU

Akademie-Verlag Berlin 1978

5. )9ROOHUWVHQ69RJHO:HUNVWRIIHLJHQVFKDIWHQXQG0LNURVWUXNWXU+DQVHU6WXGLHQEFKHU0QFKHQ

1989

6. 50%DUUHU'LIIXVLRQLQDQGWKURXJK6ROLGV

Cambridge Univ. Press, 1951

7. R. Krause-5HKEHUJ+6/HLSQHU3RVLWURQ$QQLKLODWLRQLQ6HPLFRQGXFWRUV6SULQJHU-Verlag,

Berlin 1999

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Defects II - RKR Point Defects2