Photodetectors and Solar Cells
In this lecture you will learn:
• Photodiodes
• Avalanche Photodiodes
• Solar Cells
• Fundamentals Limits on Solar Energy Conversion
• Practical Solar Cells
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Photodiodes
Consider the standard pn diode structure:
1 (p doped)
I
-Wp
+ +
+ +
+ +
- - - -xp
xn

+
V
2 (n doped)
Wn
x
-
 qV

I  Io  e KT  1




The pn diode can be used as a photodiode
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
1
Photogeneration in the Quasineutral Region
Consider an unbiased photodiode with light shining on the p quasineutral region:
Light
IL
-Wp
+ +
+ +
+ +
- - - -
1 (p doped)
-xp
2 (n doped)
xn

Wn
x
We need to compute the current IL in the external circuit
Start from:
Generation term
due to light
n 0 1 

J e  x   Ge  x   Re  x   GL  x 
t q x
Assumptions:
n  x 
 minority carrier current by diffusion only
x
n x   n po 
Ge  x   Re  x   
J e  x   qDe 1
 e1
GL  x   constant  GL
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Shockley’s Equations for Photodiodes: Electron Density
Light
We get for the minority carrier density:
 nx 
2
x
2

n x   n po 
L2e 1
- - ++
- - ++
- - ++
1 (p doped)

GL
De 1
IL
-Wp
-xp

2 (n doped)
xn
Wn
x
Boundary conditions:
n x   x p   n poe qV
n x  W p   n po
Solution:
n  x   n po
KT
 n po
At depletion region edge
At the left metal contact

 x  xp 
 Wp  x 

  sinh
 sinh
L
Le 1  
e1 



 GL e 1  GL e 1


 Wp  x p 

sinh


 Le 1 


Solution in the short base limit is:
n  x   n po 
2
Wp  x p 
G 
GL  W p  x p 

  L  x 

D
2De 1 
2
2
2
e1 


2
Le 1  W p  x p 
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
2
Shockley’s Equations for Photodiodes: Electron and Hole Currents
n  x   n po  G L e 1

 Wp  x 
 x  xp 
  sinh
 
 sinh
Le 1 

 Le 1  

 G L e 1


 Wp  x p 

sinh


 Le 1 


n(x)
npo
-Wp
Electron Current:
Electron (minority carrier) current flows by diffusion:

-xp
xn
Wn
x

 Wp  x 
 x  xp 
  cosh
 
 cosh
n
 Le 1 
 Le 1  
Je  x   q De 1
 qGL Le 1 


x
 Wp  x p 

sinh


L
e1





W
x

p
p

 Short base limit
 qGL  x 
2


ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Shockley’s Equations for Photodiodes: Electron and Hole Currents
Total Current:
Total current is due to the electrons that reach the
depletion region edge

 Wp  x p  
 cosh
  1
 Le 1  
JT  J e  x p   qG L Le 1 

 Wp  x p  
 
 sinh
 Le 1  

 Wp  x p 

 qG L 
2


n(x)
npo
-Wp
-xp

xn
Wn
x
 Short base limit
Hole Current:
Jh  x   JT  Je  x 
Je(x)
Jh(x)=0
0
JT
Je(x)=JT
Jh(x)
-Wp
-xp

xn
Wn
x
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
3
Shockley’s Equations for Photodiodes: Hole Currents
Quasineutrality implies:
n(x)
p x   n x 
npo
-Wp
Hole Diffusion Current:
 p
J h,diff  x   q Dh1
x
D
 n
 q Dh 1
  h1 J e  x 
x
De 1
-xp

xn
Wn
x

xn
Wn
x
p(x)
ppo
-Wp
-xp
Hole Drift Current:
J h  x   JT  J e  x 
 J h ,drift  x   J h ,diff  x   JT  J e  x 
 J h ,drift  x   JT  J e  x   J h ,diff  x 
 D 
 J h ,drift  x   JT  1  h1  J e  x 
 De 1 
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
External Circuit Current
Light
1 (p doped)
IL
-Wp
+ +
+ +
+ +
- - - -xp

2 (n doped)
xn
Wn
x
I L   AJT

 Wp  x p  
  1
 cosh
 Le 1  
I L  qGL ALe 1 

 Wp  x p  
 
 sinh
 Le 1  

 Wp  x p 

 qG L A 
2


 Short base limit
Even if one ignores recombination inside the quasineutral region (short base limit),
the circuit current corresponds to only half the total number of electron-hole pairs
generated by light inside the detector (why?)
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
4
Photogeneration in the Depletion Region
Light
IL
-Wp
+ +
+ +
+ +
- - - -
1 (p doped)
-xp
2 (n doped)
xn

Wn
x
Electron Current:

1 Je  x 
 GL
q x
 Je  x p   Je  x n   q xxn GL dx  qGL x n  x p 
p
Hole Current:
1 J h  x 
 GL
q x
 J h  x n   J h  x p   q xxn GL dx  qGL x n  x p 
p
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Electron, Hole, and Total Currents
Light
IL
-Wp
+ +
+ +
+ +
- - - -
1 (p doped)
-xp

2 (n doped)
xn
Wn
x
Electron and Hole Current:
The electric field inside the depletion region sweeps the electrons towards the n-side
and the holes towards the p-side. Consequently, it must be that:
Je  x p   0
Jh x n   0
Therefore,
Jh  x p   Je  x n   qGL x n  x p 
Total Current:
JT  Je  x n   J h  x n   Je  x p   J h  x p 
 qGL x n  x p 
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
5
Electron, Hole, and Total Currents
Je(x)=0
0
Jh(x)=0
JT
Jh(x)=JT
-Wp
Je(x)=JT
xn

-xp
Wn
x
External Circuit Current
Light
IL
+ +
+ +
+ +
- - - -
1 (p doped)
-Wp
-xp
2 (n doped)
xn

Wn
x
I L   AJT  qG L x n  x p 
The circuit current corresponds to the total number of electron-hole pairs generated
by light inside the detector!
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Photodetector Circuits: Electrical Characteristics
V
+
- - - -
1 (p doped)
I
-Wp
-xp
R
-
+ +
+ +
+ +

VR
2 (n doped)
xn
Wn
+
x
Photodetectors are operated in reverse bias (why?)
The circuit current I has two components:
i) The current due to the biased pn junction given as:

I o e qV
KT

1
ii) The current IL due to photogeneration
These two components can be added together (why?) to give the total current:

I  Io e qV
KT

 1  IL
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
6
Photodetector Circuits: Electrical Characteristics

V
+
We had:
I  Io e qV
KT

 1  IL
(1)
1 (p doped)
I
-Wp
Kirchhoff’s Voltage Law gives:
IR  VR  V  0
-
- - ++
- - ++
- - ++
-xp
R
2 (n doped)
xn

Wn
-V +
R
(2)
x
I
The solution of these two equations
gives the circuit current and the
junction voltage
(2)
-VR
Open circuit voltage (R = ∞):
V  Voc 
(1)

KT  I L
ln  1
q  Io

Voc
V
Isc = -( Io + IL )
Increasing R
Short circuit current (R = 0): :
I  I sc   Io  I L 
Current due to photogeneration
Current due to thermal generation
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Common Photodetector Structures
AR coating
Light
Passivation
p+ doped
0
Front side illuminated
homojunction photodetector
I  x   Ioe x
Metal
contacts
x
n doped substrate
GL  x   R  R


I x 

Ioe x

Front side illuminated
homojunction pin
photodetector
Light
Passivation
AR coating
0
p+ doped
intrinsic
Metal
contacts
x
n doped substrate
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
7
Common Photodetector Structures
Light
AR coating
Passivation
Front side illuminated
heterojunction pin
photodetector
(used for 1550 nm fiber optic
communications)
p+ doped (InP)
0
Intrinsic In0.53Ga0.47As
Metal
contacts
x
n doped substrate (InP)
Photogeneration only in the
intrinsic region!
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Figures of Merit of Photodetectors
Responsivity (units: Amps/Watt):
R
IL
Pinc
W
External Quantum Efficiency:
ext 
IL q
 I L



R
Pinc 
q Pinc
q
External quantum efficiency measures the fraction of photons incident on the
photodetector that ended up producing an electron in the external circuit
Internal Quantum Efficiency:
int 
IL q
 I L

Pabs 
q Pabs
Internal quantum efficiency measures the fraction of photons that caused
photogeneration and also ended up producing an electron in the external circuit
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
8
Figures of Merit of Photodetectors
Dark Current:
The dark current of a photodetector is the
current present even if there no light and
limits the detector sensitivity
When VR=0:
I  Io  I L 
Recall that:
Current due to thermal
generation → dark current
Eg


2
2 kT

where
n
N
N
e

i
c v

I o  An i2
 Small bandgaps and high temperatures
increase dark current
Device leakage current also contributes
to dark current
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Photodetector Bandwidth
We assume that the optical
power incident of the photodiode
is time dependent:

Pinc t   Po  Re P f e j 2ft
Pinc t 

Suppose the current I t  in the
external circuit is:

I t   Io  Re I f e
j 2ft

I t 
We know that: Io  R Po
But how do we relate I(f ) to P(f )?
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
9
Photodetector Bandwidth: Small Signal Model
I(f)
Cd
Cj
R h(f ) P(f )
Rd
Rext
Rd  Differential resistance of the pn junction 
C j  Diode junction capacitance
kT qV
e
qIo
KT

kT qVR
e
qIo
KT
Cd  Diode depletion capacitance due to charge storage in the quasineutral regions
and can be ignored in a reverse biased pn junction
hf   A frequency dependent function that describes the intrinsic frequency response
of the photogenerated carriers inside the photodiode
I f   RP f h f 
Rd
1
 RP f h f 
Rd  Rext  j 2f C j Rd Rext
1  j 2f C j Rext
The RC limit of the detector bandwidth
hf  0  1
Limiting behavior of h(f ):
hf    0
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Intrinsic Frequency Limitations of Photodetectors: h(f )
V
+
2 (n-doped)
1 (p-doped)
I
-Wp
-xp
-
Wn
xn

x
VR
+
x
Consider an electron generated at point x inside the junction at time t=0
Ramo-Shockley Theorem:
As the electron and hole move inside the depletion region under the influence of the
electric field, there is current flow in the external circuit due to image charges (or
capacitive coupling)
I xe t 
I xh t 
x  x p 
x n  x 
e E


q e E
x n  x p 
 I xe t   I xh t  dt  q
o
hE
t

e E
x n  x p  
t
q h E
x n  x p 
x n  x   q
e E
hE
x n  x p  
x  x p 
hE
 q
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
10
Intrinsic Frequency Limitations of Photodetectors: h(f )
The actual detector current consists of
photogenerated pairs at all locations inside the
depletion region. So the average current waveform
due to one photogeneration event is:
I t  
xn
1
q
x n  x p   x pI xe t   I xh t  dx    e
I xe t 
I xh t 

e


t 
 1  
 e 
 0  t  e
q 
t 
 1  
h  h 
 0  t h
h
t
q
e
t

q
h
Electron and hole transit times through the entire depletion region are:
e 
x n  x p 
h 
e E
x n  x p 
hE
The above transients can be approximated as:
t
I t   
t
q  e
q h
e

e
2 e
2 h
t  0
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Intrinsic Frequency Limitations of Photodetectors: h(f )
The average current waveform due one
photogeneration event is:
t
t
q  e
q h
I t   
e

e
2 e
2 h
t  0
This is the impulse response h(t ) of the detector:
h t  
I t 
q
The Fourier transform of the impulse response will give h(f ):
Describes the frequency
limitations due to the


12
12

h f    
electron and hole

 1  j 2f e 1  j 2f h 
transit times through
the depletion region
Finally we have:
I f   Rh f P f 
1
1  j 2f C j Rext
Describes the frequency
 limitations due both


12
12
1
  RP f 




 1  j 2f e 1  j 2f h   1  j 2f C j Rext  intrinsic and extrinsic
(circuit level) factors
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
11
Avalanche Photodiodes (APDs): Basic Principle
Photomultiplier tubes:
 Provide high sensitivity for light detection even
at the single photon level
 Employs electron multiplication to increase the
charge output per photon
Impact Ionization in Semiconductors:
Highly energetic electrons and holes in semiconductors can create
electron-hole pairs via impact ionization

me 
Emin electron  E g  1 

m

e  mh 

mh 
Emin hole  E g  1 

m

e  mh 
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Modeling Impact Ionization in Semiconductors
Electrons and holes in high electric fields gain enough energy
to cause impact ionization
Ec
Ev
Impact Ionization Coefficients:
e  The electron ionization coefficient (units: 1/cm) defined
as the number of electron-hole pairs created by one
electron in unit distance of travel
 h  The hole ionization coefficient (units: 1/cm) defined as the
number of electron-hole pairs created by one hole in unit
distance of travel
e  Aee Ce
E
 h  Bhe Ch
E
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
12
Avalanche Photodiodes
Light
Avalanche pin photodiode
-qV
-xp
x
xn

The equation for the electron current is:
Je  x 
 q Ge  x   GL  x    e Je  x    h Jh  x   qGL  x 
x
J  x 
 e
  e Je  x    h Jh  x   qGL  x 
x

The equation for the hole current is:
J h  x 
 q Gh  x   GL  x    e Je  x    h J h  x   qGL  x 
x
J  x 
 h
  e Je  x    h J h  x   qGL  x 
x
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Avalanche Photodiodes
Light
Total current is:
JT  Je  x   Jh  x 
-qV
The equation for the electron current
becomes:
-xp

xn
x
J e  x 
  e   h Je  x    h JT  qGL  x 
x
Solution, assuming uniform illumination, is:
Je  x n   Je  x p e
e  h xn  x p 
e e  h xn  x p   1


 qGL   h JT  
 e   h 
Boundary conditions:
J e  x p   0
Jh x n   0
Total current is:
JT  Je  x n   J h  x n   Je  x n 
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
13
Avalanche Photodiodes
Light
Total current is:
JT  Je  x n   J h  x n   Je  x n 
-qV
 e e  h x n  x p   1


 JT  qGL
 e   h    h  e e  h xn  x p   1


-xp
x
xn

The multiplication gain M of the photodetector is:
 e e  h xn  x p   1
JT
1



M
qGL x n  x p  x n  x p         e e  h x n  x p   1
e
h
h


ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Avalanche Photodiodes
Light
AR coating
Passivation
Front side illuminated
heterostructure avalanche
photodiode with separate
photogeneration and
multiplication layers
p+ doped (InP)
Intrinsic In0.53Ga0.47As (Light absorption)
n- doped InP (Multiplication layer)
Metal
contacts
n+ doped InP
n doped substrate (InP)
 Avalanche photodiodes are good for high sensitivity but low speed applications
 Most avalanche photodiodes have separate regions for light absorption and
carrier multiplication.
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
14
Solar Cell Basics
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Solar Cell Basics
Light
 qV

I  Io  e KT  1  I L




1 (p doped)
I
-Wp
IR  V  0
Pinc
+ +
+ +
+ +
- - - -xp
2 (n doped)
xn

Wn
x
R
+
V
How to deliver the maximum power to
the resistor R?
  qV


Pout  I o  e KT  1  I L   V 





 

qV




d    KT

 1  I L   V    0
 Io  e

dV  




 
-
I
I
V
R
 qV

I  Io  e KT  1  I L




Voc
V
Isc = -( Io + IL )
Increasing R
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
15
Maximizing Output Power of Solar Cells
Vm = Voltage at maximum
output power
Im = Current at maximum
output power
Light
I
-Wp
qVm
 e KT
+ +
+ +
+ +
- - - -
1 (p doped)
qV




d    KT

I
e
 1  I L   V    0
 o

dV  




 
Pinc
-xp
2 (n doped)
xn

Wn
x
R
+
-
V
 qVm  I L
1
  1
KT  Io

I
 qVm

 I m  Io  e KT  1  I L




I
 qV

I  Io  e KT  1  I L




V
R
Vm
Area of rectangle = -ImVm = Pout =
Power delivered to the resistor R
Isc = -( Io + IL )
Voc
V
Im
Increasing R
Pout   I mVm  I scVoc
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Resistance Matching in Solar Cells
Light
What value of the resistor R lets one
achieve the maximum output power?
1 (p doped)
I
qVm
qIo KT
e
1

R KT

1
-Wp
Wn
x
R
-
V
I
 I mVm
 I scVoc
 I mVm
Pinc
2 (n doped)
xn

+
Solar Efficiency:

-xp
Rdm
Solar cell Fill Factor (FF):
FF 
Pinc
+ +
+ +
+ +
- - - -
I
 qV

I  I o  e KT  1  I L




V
R
Vm
Isc = -( Io + IL )
Voc
V
Im
Increasing R
Solar cells are always operated in forward bias!
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
16
Black Body Radiation
Solar radiation spectrum near Earth can be very well approximated as that of a black
body at temperature Ts = 5760K
Consider a point P at a distance r from a
black body at temperature T
z
T
P


r
We need to calculate the photon flux and
the radiation power at the point P

Each mode of radiation emitted from the black body with wavevectior q will
have photon occupancy given by:

n q  
1
e

 q  KT 1
The total photon flux per unit area at P can then be written as an integral:
o
 2
FN  2   sin cos  d 
0
0
q 2dq
2 3
c nq   c
sin2 o 
 d g p   n 
4 0
Where the photon density of states in free space is:
g p   
2
 2c 3
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Black Body Radiation
T
z
r


P
The energy flux at the point P is:
FE  c
sin2o 
 2 KT 4
2
 sin2 o  T 4
 d  g p   n   sin  o
4 0
60 c 2  3

  Stephan  Boltzmann constant  5.67  10 8

Watts
m2 - K 4
Radiation at the surface of the Earth:
s
Sun
Ts
 s  0.267 degrees
FE  1350 Watts/m2
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
17
Fundamental Limits to Solar Energy Conversion Efficiency
A device at temperature Tc absorbs solar energy,
radiates a part of it away, and then converts the rest
into useful work W by an ideal heat engine operating
between the temperature Tc and the ambient
temperature on Earth Ta = 300K
Net radiative energy absorbed by the device (and
which is available for useful work):
2

sin  s 
Ts4
 
Sun
Device
Carnot
engine
Earth
Tc4
Energy conversion efficiency of an ideal heat engine (Carnot engine):
1  Ta
Tc 
Energy conversion efficiency of the device:
sin2 s  Ts4    Tc4  1 TTa 

c

sin2 s  Ts4 
But the above expression does not consider the fact that solar energy can be
concentrated!
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Solar Energy Concentration and Energy Conversion Efficiency
One can increase the efficiency by focusing or concentrating sunlight
Focusing can increase the effective half-angle s of the Sun from 0.267 degrees to the
maximum possible value of 90 degrees
Light concentration is
measured in units of the
parameter X:
X
Sun
Ts
1 X 
1
sin2 s
Tc
Device
sin2  actual
sin2  s
s
Lens
Sun
Ts
Device
Tc
 4.6  104
actual
With full concentration, the maximum efficiency for solar energy conversion is:
sin2 s  Ts4    Tc4  1 TTa   T 4  T 

c
  1  c4  1  a 


Ts  Tc 
sin2 s  Ts4 

A maximum efficiency of close to 85% is achieved for Tc = 2450K
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
18
Fundamental Energy Conversion Efficiency of a Photodiode
Consider a solar cell made from a
semiconductor with a bandgap Eg
at temperature Ta = 300K
Assumption: The solar cells
absorbs all photons whose energies
are larger than the bandgap
We know from Chapter 3 that in the spontaneously emitted radiation by a forward
bias junction the occupancy of a radiation mode of frequency  is:
1
n     qV  KT
a 1
e
Sunlight
General expressions for emitted photon number and energy
fluxes:
FN T ,V , min  
c 
1
 d g p    qV  KT
4 min
e
1
FE T ,V , min  
c 
1
 d  g p    qV  KT
4 min
e
1
SPE
Ta
Cell
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Fundamental Energy Conversion Efficiency of a Photodiode
Sunlight
SPE
Photodiode
Sun
s
Ts
Ta
Ta
Cell
A
The radiation power per unit area incident on the cell from the Sun is:
c 
1
A sin2 s FE Ts ,0,0  A sin2 s
 d  g p    KT
s 1
4 Eg 
e
The photon flux per unit area incident on the cell from the Sun and absorbed by the
cell is:
c 
1
A sin2 s FN Ts ,0, E g    A sin2 s
 d g p    KT
s 1
4 Eg 
e
The photon flux per unit area incident on the cell from the surrounding ambient and
absorbed by the cell is:



A 1  sin2 s FN Ta ,0, E g    A 1  sin2 s
The photon flux per unit area emitted by the cell is:
AFN Ta ,V , E g    A
c4

 d g p  
Eg 
1
e
 KTa
1
c 
1
 d g p    qV  KT
a 1
4 Eg 
e
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
19
Fundamental Energy Conversion Efficiency of a Photodiode
Sunlight
SPE
Photodiode
Sun
s
Ts
Ta
Ta
Assumption: The internal quantum efficiency of the cell is
100% and each photon absorbed by the cell results in one
electron flow in the external circuit:

Cell
I
R
+

A
-
V
I  qA sin  s FN Ts ,0, E g    A 1  sin  s FN Ta ,0, E g    AFN Ta ,V , E g  
2
2
The energy conversion efficiency of the cell is:


IV
A sin  s FE Ts ,0,0
2




qA sin2  s FN Ts ,0, E g    1  sin2  s FN Ta ,0, E g    FN Ta ,V , E g   V
A sin  s FE Ts ,0,0
2
To find the maximum value of  one must maximize the above w.r.t. to the voltage V
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Shockley–Queisser Limit
Sunlight
No Concentration (s = 0.26o):
A maximum efficiency of ~31% is reached at
a bandgap of ~1.27 eV
SPE
Ta
Full Concentration (s = 90o):
A maximum efficiency of ~41% is reached at
a bandgap of ~1.1 eV.
Cell
I
R
+
A
V
-
Why is there an optimal bandgap?
Bandgap too small  Output voltage too small
qV  qVoc  E g
Bandgap too large  Low energy photons do
not get absorbed
Shockley–Queisser result
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
20
Energy Conversion Efficiencies of Some Common Solar Cells
Typical Performances of Semiconductor Photocells
(Green at al., Prog. Photovolt: Res. Appl., 17, 85 (2009))
Material
Crystalline Si
Crystalline GaAs
Poly-Si
a-Si
CuInGaSe2 (CIGS)
CdTe
Voc (V)
0.705
1.045
0.664
0.859
0.716
0.845
Jsc (Amp/cm2)
42.7
29.7
38.0
17.5
33.7
26.1
FF (%)
82.8
84.7
80.9
63.0
80.3
75.5
Efficiency (%)
25.0
26.1
20.4
9.5
19.4
16.7
Shockley–Queisser result
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Design of Silicon Solar Cells
The PERL Si solar cell
(Green et al., 1994)
Efficiency ~25%
Light trapping by a top lambertian
surface and bottom reflector can
increase the optical path length by ~4n2
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
21
Design of Solar Cell Modules
The IV characteristics of pn junctions
connected in series must identical (or
nearly so)
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Improving Efficiencies of Photodiode Solar Cells
Energy loss
Energy Loss Pathways:
Ec
ii) Photons with energies much larger
than the bandgap generate electrons
(holes) with energies much above
(below) the band edge. This extra
energy is lost to phonons and does
not contribute to output electrical
power. Recall that:
qV  qVoc  E g
Efe
Light
qV
Efh
Eg
X
Ev
1.2
1
Solar Spectrum
i) Photons with energies smaller than
the bandgap are not absorbed
Ts = 5760K
0.8
0.6
0.4
0.2
0
0
1
2
3
Energy (eV)
4
5
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
22
Improving Efficiencies of Solar Cells: Tandem Cells
Eg1 > Eg2 > Eg3
Eg1
Eg2
Light
Eg3
A three junction tandem cell
A three junction tandem cell with spectral filtering
Light
Eg1
Eg2
Eg3
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
Improving Efficiencies of Solar Cells: Tandem Cells
InGaP/GaAs two-junction tandem cell with
a reversed biased Esaki tunnel junction
and an efficiency of 30.3% (w/o
concentration) (Takamoto et al., 1997).
ECE 407 – Spring 2009 – Farhan Rana – Cornell University
23