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Slide 1EE40 Fall 2007 Prof. Chang-Hasnain
EE40Lecture 31
Prof. Chang-Hasnain
11/19/07
Reading: Supplementary Reader
Slide 2EE40 Fall 2007 Prof. Chang-Hasnain
Week 13
• OUTLINE
– Basic Semiconductor Materials
– n and p doping
– Bandgap
– Gauss’s Law
– Poisson Equation
– Depletion approximation
– Diode I-V characteristics
– Lasers and LEDs
– Solar Cells
• Reading
– Supplementary Notes Chap 3
2
Slide 3EE40 Fall 2007 Prof. Chang-Hasnain
Conductors, Insulators and Semiconductors
• Solids with “free electrons” – that is electrons notdirectly involved in the inter-atomic bonding- arethe familiar metals (Cu, Al, Fe, Au, etc).
• Solids with no free electrons are the familiarinsulators (glass, quartz crystals, ceramics, etc.)
• Silicon is an insulator, but at highertemperatures some of the bonding electrons canget free and make it a little conducting – hencethe term “semiconductor”
• Pure silicon is a poor conductor (and a poorinsulator). It has 4 valence electrons, all ofwhich are needed to bond with nearestneighbors. No free electrons.
Slide 4EE40 Fall 2007 Prof. Chang-Hasnain
The Periodic Table
III IV V
3
Slide 5EE40 Fall 2007 Prof. Chang-Hasnain
Unit Cell of Crystalline Silicon
• Si (1s2 2s2 2p6 3s2
3p2 )
22 3
3 8 3
0
1 18 6 4# 88 2 5.00 10(5.43 10 )
Atomscm
Volume a cm
!
!
" + " +
= = = ""
Slide 6EE40 Fall 2007 Prof. Chang-Hasnain
Electronic Bonds in Silicon
2-D picture of perfect crystal of pure silicon; double line is a Si-Sibond with each line representing an electron
Two electrons in each bond
Si ion(charge+4 q)
Actual structure is 3-dimensional tetrahedral- just like carbonbonding in organic and inorganic materials.
Essentially no free electrons, and no conduction - insulator
4
Slide 7EE40 Fall 2007 Prof. Chang-Hasnain
Bandgap
• Electrons are mobile in the conduction band, while holesare mobile in the lower energy valence band.
• The excited electrons move from the valence band intothe conduction band, leaving holes in the valence band– when the crystal is illuminated with photons whose energy is
larger than the bandgap energy
– or when the crystal is sufficiently heated.
Valence Band
E
Conduction Band
Band gap, E g
e-
Ef
Slide 8EE40 Fall 2007 Prof. Chang-Hasnain
Bandgap for Insulator and Metal
• Insulators have alarge band gap,usually 3.5 electron-volts (eV) or greater,preventing substantialamounts of chargecarriers from flowing.
• Metals are goodconductors, withelectrons filling upinto the conductionband.
Conduction Band
E Small band
gap, Eg
E
f
Valence Band
Electrons fill into
conduction
band
Large bandgap, Eg
Valence Band
E
Conduction Band
E
f
5
Slide 9EE40 Fall 2007 Prof. Chang-Hasnain
If the lower floor is full and top one is empty, no traffic ispossible. Analog of an insulator. All electrons arelocked up.
Shockley’s Parking Garage Analogy for Conduction in Si
Two-story parking garage on a hill:
Slide 10EE40 Fall 2007 Prof. Chang-Hasnain
If one car is moved upstairs, it can move AND THE HOLEON THE LOWER FLOOR CAN MOVE. Conduction ispossible. Analog to warmed-up semiconductor. Someelectrons get free (and leave “holes” behind).
Shockley’s Parking Garage Analogy for Conduction in Si
Two-story parking garage on a hill:
6
Slide 11EE40 Fall 2007 Prof. Chang-Hasnain
If an extra car is “donated” to the upper floor, it can move.Conduction is possible. Analog to N-type semiconductor.
(An electron donor is added to the crystal, creating freeelectrons).
Shockley’s Parking Garage Analogy for Conduction in Si
Two-story parking garage on a hill:
Slide 12EE40 Fall 2007 Prof. Chang-Hasnain
If a car is removed from the lower floor, it leaves a HOLEwhich can move. Conduction is possible. Analog to P-type
semiconductor. (Acceptors are added to the crystal,“consuming” bonding electrons,creating free holes).
Shockley’s Parking Garage Analogy for Conduction in Si
Two-story parking garage on a hill:
7
Slide 13EE40 Fall 2007 Prof. Chang-Hasnain
Fermi-Dirac Distribution
• Fermi-Dirac function provides the probability that anenergy level is occupied by a fermion which is underthermal equilibrium. Electrons as well as holes areFermions and hence obey Fermi-Dirac statistics.
Fig. 5. Fermi function plots at absolute zero, mid-range, and high temperature.
Slide 14EE40 Fall 2007 Prof. Chang-Hasnain
Electron and Hole Densities
, ,
( )
( )
( ) ( ) ( )
1
( )/1
11
( )/1
f c
v f
f i c v f i gv c
E E kT
c cf
c
E E kT
v vf
v
E E kT E E kT E kTE E kT
c v c v c v
n N N eE E kT
e
p N N eE E kT
e
np N e N e N N e N N e
!
!
! ! !!
=!
+
" #= !$ %!$ %+& '
= = =
!
!
2
g
i i
i i i
E kT
i c v
n p
n p n
n N N e!
=
=
=
For instrinsic (i.e.
undoped Si),
8
Slide 15EE40 Fall 2007 Prof. Chang-Hasnain
How to get conduction in Si?
For the first approach controlled impurities, “dopants”, are added toSi:
or
We must either:
1) Chemically modify the Si to produce free carriers (permanent) or
2) Electrically “induce” them by the field effect (switchable)
(Extra electrons produce “free electrons” for conduction.)
Add group V elements (5 bonding electrons vs four for Si),such as phosphorus or arsenic
Deficiency of electrons results in “free holes”
Add group III elements (3 bonding electrons), such as boron
Slide 16EE40 Fall 2007 Prof. Chang-Hasnain
Doping Silicon with Donors (n-type)
Donors donate mobile electrons (and thus “n-type” silicon)
Example: add arsenic (As) to the silicon crystal:
Immobile (stuck) positively charged arsenic ion after 5th electron left
As
Mobile electrondonated by As ion
The extra electron with As, “breaks free” and becomes a freeelectron for conduction
9
Slide 17EE40 Fall 2007 Prof. Chang-Hasnain
Doping with Acceptors (p-type)
B
Mobile hole con-tributed by B ionand later path
Immobile (stuck) negative boron ion after accepting electron from neighboring bond
Group III element (boron, typically) is added to the crystal
The “hole” which is a missing bonding electron, breaks free fromthe B acceptor and becomes a roaming positive charge, free tocarry current in the semiconductor. It is positively charged.
Slide 18EE40 Fall 2007 Prof. Chang-Hasnain
Doping
• Typical doping densities:1016~1019 cm-3
• Atomic density for Si: 5 x1022 atoms/cm3
• 1018 cm-3 is 1 in 50,000
– two persons in entireBerkeley wearing a greenhat
• P-n junction effect is like
10
Slide 19EE40 Fall 2007 Prof. Chang-Hasnain
EE40Lecture 32
Prof. Chang-Hasnain
11/21/07
Reading: Supplementary Reader
Slide 20EE40 Fall 2007 Prof. Chang-Hasnain
Electron and Hole Densities in Doped Si
( )
2
v fE E kT
a v
i a
p N N e
p n N
!
= =
=
• Instrinsic (undoped) Si
• N-doped Si– Assume each dopant contribute to one electron
• p-doped Si– Assume each dopant contribute to one hole
( )
2
f cE E kT
d c
i d
n N N e
p n N
!
= =
=
2
i
i
n p n
np n
= =
=
11
Slide 21EE40 Fall 2007 Prof. Chang-Hasnain
Summary of n- and p-type silicon
Pure silicon is an insulator. At high temperatures it conductsweakly.
If we add an impurity with extra electrons (e.g. arsenic,phosphorus) these extra electrons are set free and we have apretty good conductor (n-type silicon).
If we add an impurity with a deficit of electrons (e.g. boron) thenbonding electrons are missing (holes), and the resulting holescan move around … again a pretty good conductor (p-typesilicon)
Now what is really interesting is when we join n-type and p-typesilicon, that is make a pn junction. It has interesting electricalproperties.
Slide 22EE40 Fall 2007 Prof. Chang-Hasnain
Junctions of n- and p-type Regions
A silicon chip may have 108 to 109 p-n junctions today.
p-n junctions form the essential basis of all semiconductor devices.
How do they behave*? What happens to the electrons and holes?What is the electrical circuit model for such junctions?
n and p regions are brought into contact :
n p
aluminum aluminum
wire
?
*Note that the textbook has a very good explanation.
12
Slide 23EE40 Fall 2007 Prof. Chang-Hasnain
The pn Junction Diode
Schematic diagram
p-type n-typeID
+ VD –
Circuit symbol
Physical structure:(an example)
p-type Si
n-type Si
SiO2SiO2
metal
metal
ID+
VD
–
net donor
concentration ND
net acceptor
concentration NA
For simplicity, assume that
the doping profile changes
abruptly at the junction.
cross-sectional area AD
Slide 24EE40 Fall 2007 Prof. Chang-Hasnain
• When the junction is first formed, mobile carriers diffuseacross the junction (due to the concentration gradients)
– Holes diffuse from the p side to the n side,leaving behind negatively charged immobile acceptorions
– Electrons diffuse from the n side to the p side,leaving behind positively charged immobile donor ions
!A region depleted of mobile carriers is formed at the junction.
• The space charge due to immobile ions in the depletion regionestablishes an electric field that opposes carrier diffusion.
Depletion Region Approximation
+++++
––
–––
p n
acceptor ions donor ions
13
Slide 25EE40 Fall 2007 Prof. Chang-Hasnain
Summary: pn-Junction Diode I-V
• Under forward bias, the potential barrier is reduced, sothat carriers flow (by diffusion) across the junction– Current increases exponentially with increasing forward bias
– The carriers become minority carriers once they cross thejunction; as they diffuse in the quasi-neutral regions, theyrecombine with majority carriers (supplied by the metal contacts)
“injection” of minority carriers
• Under reverse bias, the potential barrier is increased, sothat negligible carriers flow across the junction– If a minority carrier enters the depletion region (by thermal
generation or diffusion from the quasi-neutral regions), it will beswept across the junction by the built-in electric field
“collection” of minority carriers ! reverse current ID (A)
VD (V)
Slide 26EE40 Fall 2007 Prof. Chang-Hasnain
quasi-neutral p region
Charge Density Distribution
+++++
––
–––
p n
acceptor ions donor ions
depletion region quasi-neutral n region
charge density (C/cm3)
distance
Charge is stored in the depletion region.
14
Slide 27EE40 Fall 2007 Prof. Chang-Hasnain
Two Governing Laws
2
2
( ) ( ) ( )d x dE x x
dx dx
! "
#= $ = $
00
1( ) ( ) ( )
x
x
E x E x x dx!"
# = $dE
dx
!
"=
1 encl
S V
QE dA dV!
" "# = # =$ $!!
" "
Gauss’s Law describes the relationship of charge (density) andelectric field.
Poisson’s Equation describes the relationship between electricfield distribution and electric potential
00( ) ( ) ( )
x
x
x x E x dx! !" = "#
Slide 28EE40 Fall 2007 Prof. Chang-Hasnain
Depletion Approximation 1
0 ( ) ( ) ( 0)a
po po
s
qNE x x x x x
!
"= + " < <
( )( )( )
( ) ( )000
0
0
0 , 0 and 0
0 np
nd
paxxxxx
xxqN
xxqNx >!<=
"#$
%%
%%!!& ''
xno x
x
-xpo
_o(x)
-qNa
qNd
xno x
x
-xpo
E0(x)
s
nod
s
poa xqNxqNE
!!
"=
"=)0(0
00 0
0
( )( ) ( ) ( ) 0
( ) ( )
(0 )
nox dno no
xs s
dno
s
no
x qNE x dx E x x x
qNE x x x
x x
!" "
"
#= # = # #
= #
< <
$Gauss’s Law
p n
p n
15
Slide 29EE40 Fall 2007 Prof. Chang-Hasnain
Depletion Approximation 2
p n
P=1018
n=104
n=1017
p=105
x
E0(x)
s
nod
s
poa xqNxqNE
!!
"=
"=)0(0
xno-xpo
22
22 pos
a
nos
dx
qNx
qN
!!+
#0(x)
xxno-xpo
Poisson’s Equation
Slide 30EE40 Fall 2007 Prof. Chang-Hasnain
EE40Lecture 33
Prof. Chang-Hasnain
11/26/07
Reading: Supplementary Reader
16
Slide 31EE40 Fall 2007 Prof. Chang-Hasnain
Depletion Approximation 3
0 0 0( ) ( ) ( ) ( ) 0po po
po po
x xa
po pox x
s
x xa
pox x
s
qNx E x dx x x x dx
qNxdx x dx
! !"
"
# #
# #
= # + # = + +
$ %= +& '
( )
* *
* *
2
0 ( ) ( ) ( 0)2
a
po po
s
qNx x x x x!
"= + # < <
( )
2
0 0 00 0
2
0 0
( ) ( ) (0) ( ) (0 )2
2
x xd a
no po
s s
x xd a
no po
s s
qN qNx E x dx x x dx x
qN qNxdx x dx x
! !" "
" "
= # + = # # + +
= # + +
$ $
$ $
2 2
0 ( ) (2 ) (0 )2 2
d ano po no
s s
qN qNx x x x x x x!
" "= # + < <
Slide 32EE40 Fall 2007 Prof. Chang-Hasnain
Effect of Applied Voltage
• The quasi-neutral p and n regions have low resistivity,whereas the depletion region has high resistivity. Thus,when an external voltage VD is applied across thediode, almost all of this voltage is dropped acrossthe depletion region. (Think of a voltage dividercircuit.)
• If VD > 0 (forward bias), the potential barrier to carrierdiffusion is reduced by the applied voltage.
• If VD < 0 (reverse bias), the potential barrier to carrierdiffusion is increased by the applied voltage.
p n
+++++
––
–––
VD
17
Slide 33EE40 Fall 2007 Prof. Chang-Hasnain
Depletion Approx. – with VD<0 reverse bias
p n
P=1018n=1017
x
E0(x)
s
nod
s
poa xqNxqNE
!!
"=
"=)0(0
xno-xpo
22
22 pos
a
nos
dx
qNx
qN
!!+
#0(x)
xxno-xpo
#bi
Built-in potential #bi=
-xp xn
-xp xn
#bi-qVD
Higher barrier and few holes in n-type lead to little current! p=105
n=104
Slide 34EE40 Fall 2007 Prof. Chang-Hasnain
Depletion Approx. – with VD>0 forward bias
Poisson’s Equation
p n
n=104
n=1017
p=105
x
E0(x)
s
nod
s
poa xqNxqNE
!!
"=
"=)0(0
xno-xpo
22
22 pos
a
nos
dx
qNx
qN
!!+
#0(x)
xxno-xpo
#bi
Built-in potential #bi=
-xp xn
#bi-qVD
Lower barrier and large hole (electron) densityat the right places lead to large current!
-xp xn
P=1018
18
Slide 35EE40 Fall 2007 Prof. Chang-Hasnain
Forward Bias
• As VD increases, the potential barrier to carrierdiffusion across the junction decreases*, andcurrent increases exponentially.
ID (Amperes)
VD (Volts)
* Hence, the width of the depletion region decreases.
p n
+++++
––
–––
VD > 0The carriers that diffuse across the
junction become minority carriers in
the quasi-neutral regions; they then
recombine with majority carriers,
“dying out” with distance.
D( 1)qV kT
D SI I e= !
Slide 36EE40 Fall 2007 Prof. Chang-Hasnain
Reverse Bias
• As |VD| increases, the potential barrier to carrierdiffusion across the junction increases*; thus, nocarriers diffuse across the junction.
ID (Amperes)
VD (Volts)
* Hence, the width of the depletion region increases.
p n
+++++
––
–––
VD < 0A very small amount of reverse
current (ID < 0) does flow, due to
minority carriers diffusing from the
quasi-neutral regions into the depletion
region and drifting across the junction.
19
Slide 37EE40 Fall 2007 Prof. Chang-Hasnain
• Light incident on a pn junction generates electron-hole pairs
• Carriers are generated in the depletion region as well as n-doped and p-doped quasi-neutral regions.
• The carriers that are generated in the quasi-neutral regionsdiffuse into the depletion region, together with the carriersgenerated in the depletion region, are swept across thejunction by the electric field
• This results in an additional component of current flowing inthe diode:
where Ioptical is proportional to the intensity of the light
optical
kTVq
SD IeII !!= )1( D
Optoelectronic Diodes
Slide 38EE40 Fall 2007 Prof. Chang-Hasnain
Example: Photodiode
• An intrinsic region is placedbetween the p-type and n-typeregions
$ Wj % Wi-region, so that most of theelectron-hole pairs are generatedin the depletion region
! faster response time (~10 GHz operation)
ID (A)
VD (V)
with incident light
in the dark
operating point
20
Slide 39EE40 Fall 2007 Prof. Chang-Hasnain
Planck Constant
• Planck’s constant h = 6.625·10-34 J·s• E=h&=hc/'=1.24 eV-µm/'(µm)• C is speed of light and h& is photon energy• The first type of quantum effect is the quantization of
certain physical quantities.• Quantization first arose in the mathematical formulae of
Max Planck in 1900. Max Planck was analyzing how theradiation emitted from a body was related to itstemperature, in other words, he was analyzing theenergy of a wave.
• The energy of a wave could not be infinite, so Planckused the property of the wave we designate as thefrequency to define energy. Max Planck discovered aconstant that when multiplied by the frequency of anywave gives the energy of the wave. This constant isreferred to by the letter h in mathematical formulae. It isa cornerstone of physics.
Slide 40EE40 Fall 2007 Prof. Chang-Hasnain
Bandgap Versus Lattice Constant
Si
21
Slide 41EE40 Fall 2007 Prof. Chang-Hasnain
Solar cell: Example of simple PN junction
• What is a solar cell?– Device that converts
sunlight into electricity
• How does it work?– In simple configuration, it is a
diode made of PN junction
– Incident light is absorbed bymaterial
– Creates electron-hole pairs thattransport through the materialthrough
• Diffusion (concentration gradient)
• Drift (due to electric field)PN Junction Diode
Slide 42EE40 Fall 2007 Prof. Chang-Hasnain
optical
kTVq
SD IeII !!= )1( D
Photovoltaic (Solar) Cell
ID (A)
VD (V)
with incident light
in the dark
Operating pointThe load line a simple resistor.
22
Slide 43EE40 Fall 2007 Prof. Chang-Hasnain
I-V characteristics of the device
• I-V characteristics of a PNjunction is given by
where Is is the saturation intensity
depending on band gap and dopingof the material and IL is thephotocurrent generated due to light
• Efficiency is defined as
Voc
Isc
(Vm, Im)
LSI
kT
eVII !"#
$%&
'!= 1)exp(
IntensityLight
IVFF
IntensityLight
VI scocmm **.==!
Voc - Open circuit voltage
Isc - Short circuit current
Imp , Vmp- Current and voltage
at maximum powerFF is the Fill Factor
Slide 44EE40 Fall 2007 Prof. Chang-Hasnain
Architecture and PV
Isofotón: aUPM spin-off
IES-UPM
23
Slide 45EE40 Fall 2007 Prof. Chang-Hasnain
A technology for solidarity...and a goodbusiness
Total MWp 9.51
Individual investors 752
Cost 7 kWp !53000
Slide 46EE40 Fall 2007 Prof. Chang-Hasnain
Space
• Efficiency &Reliability critical
• Multi-junction – 80%market
• Two players– Emcore –
125kW/year
– Spectrolab (Boeing)– 600kW/year
• Up to $40/W
• $30M/year market
Boeing 702Sojourner 16W
24
Slide 47EE40 Fall 2007 Prof. Chang-Hasnain
Portable Electronics
• US PP $7.6b in 2004
• PV? Power!– Rechargeable (LiIon)
– Fuel cells (2013)
• TI’s Voltage Booster– Efficient sub 0.3V
step-up converter
• ULP & Low PowerElectronics?
Slide 48EE40 Fall 2007 Prof. Chang-Hasnain
Transportation
MIT
Venturi – AstrolabTBR Jan. 2008$120k
Pathfinder
MW-Line$560kAtlantic
Pathfinder, 75% wing cover, 8kW
25
Slide 49EE40 Fall 2007 Prof. Chang-Hasnain
Off-Grid Small Scale
Telecommunicationtower in Australia
Railroad crossingin Georgia
Most off-shore oil rigs
Arizona, 500W
Austria
•Lighting•Communications•16% market
(PV 2010)
Slide 50EE40 Fall 2007 Prof. Chang-Hasnain
Electrifying the Unelectrified
Subsahara – power for light and water pumps
Panels in French Polynesia
Los Uros, Peru Southern India
26
Slide 51EE40 Fall 2007 Prof. Chang-Hasnain
Solarizing the Electrified
Residential (grid) – 40% market
• Fastest growth (33% US)
• Typical Cost– Non-battery $6-8/W-DC
– Battery $8–12/W-DC
California $6.5/W after rebatesor $20,000 for 2,500ft2
home
Installations (2006)
1) Germany – 960MWp
2) Japan – 300MWp
3) US – 140MWp
Total World 1744MWp
Modules on apartment complexrooftops (Bremen, Germany)
Marketbuzz 2007
Slide 52EE40 Fall 2007 Prof. Chang-Hasnain
Utility Scale
• US Total Power Plant Capacity 600GW(28% of world) and will grow 30% by2030
• Largest PV– Gut Erlasee Solar Park(12MWp)
• PV cells - $0.25-0.39/kWhr• Coal plant - $0.06/kWhr• PV < $0.10/kWhr to be competitive!
EIA, DOE
Tucson, AZ, 4.6 MWp
NUON rooftop, Netherlands, 2.3MWp
27
Slide 53EE40 Fall 2007 Prof. Chang-Hasnain
Example 2: Photodiode
• An intrinsic region is placedbetween the p-type and n-typeregions
$ Wj % Wi-region, so that most of theelectron-hole pairs are generatedin the depletion region
! faster response time (~10 GHz operation)
ID (A)
VD (V)
with incident light
in the dark
operating point
Slide 54EE40 Fall 2007 Prof. Chang-Hasnain
Photodetector Circuit Using Load Line
I
V
load line
VTh
VTh/RTh
operatingpoints underdifferent lightconditions.
As light shines on the photodiode, carriersare generated by absorption. These excesscarriers are swept by the electric field at thejunction creating drift current, which is samedirection as the reverse bias current andhence negative current. The current isproportional to light intensity and hence canprovide a direct measurement of lightintensity ! photodetector.
- What happens when Rth is too large?- Why use Vth?
VTh
+" +
V
–
RThI
As lightintensityincreases.Why?