solar cells lecture 2: physics of crystalline solar cells
DESCRIPTION
Mark Lundstrom (2011), "Solar Cells Lecture 2: Physics of Crystalline Solar Cells," http://nanohub.org/resources/11890.TRANSCRIPT
Prof. Mark Lundstrom
[email protected] and Computer Engineering
Purdue UniversityWest Lafayette, Indiana USA
Solar Cell Physics:recombination and generation
NCN Summer School: July 2011
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copyright 2011
This material is copyrighted by Mark Lundstrom under the following Creative Commons license.
Conditions for using these materials is described at
http://creativecommons.org/licenses/by-nc-sa/2.5/
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acknowledgement
Dionisis Berdebes, Jim Moore, and Xufeng Wang played key roles in putting together this tutorial. Their assistance is much appreciated.
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solar cell physics
A solar cell is a simple device – just a pn junction with light shining on it.
To maximize efficiency, we must maximize the generation of e-h pairs and minimize the recombinationof e-h pairs.
This lecture is a short introduction to the physics of crystalline solar cells – specifically Si.
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outline
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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dark current and recombination
AV− +
+
s.s. excess holes
hole-injecting contact
N P
electron-injecting contact
-
s.s. excess electrons
DI
6
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recombination in the N-type QNR
PN -
+
Anytime an electron and hole recombine anywhere within the diode, one electron flows in the external circuit.
-
AV− +
hole-injecting contact
electron-injecting contact
7
DI
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Shockley-Read-Hall recombination
minority carriers injected across junction
nF PFAqV
AV− +
DI
TE
SRH recombination
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recombination at a contact
minority carriers injected across junction
nF PFAqV
AV− +
DI
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light-current and generation
FE“base”
“emitter”
(absorbing layer)bi AV V−
AV− +
Every time a minority electron is generated and collected, one electron flows in the external current.
0DI <
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light-current and recombination
“emitter”
Every time a minority electron is generated and recombines before being collected, the solar cell current suffers.
3 e-h pairs generated
1 e in external circuit
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solar cells and recombination
• Carrier recombination lowers the short-circuit current and reduces the open-circuit voltage.
• To optimize solar cell performance, we need a clear understanding of how many carriers are recombining and where they are recombining.
• Then we need to establish a quantitative relation between recombination and solar cell performance.
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solar cells and recombination
DI
N P
x0 L
( ) ( )( )D A TOT A TOTJ V q R V G= −
( ) ( ) ( )0
0Lp n
TOT
J J LR R x dx
q q= − −∫
( )0
L
TOT opG G x dx= ∫
( )nJ L( )0pJ
For a formal derivation of this result, see the appendix.
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outline
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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n+ “emitter” (0.3 μm)
p-type “base”
(198.9 μm)
p+ “Back Surface Field” (BSF) (0.8 μm)
200
um
15
generic crystalline Si solar cell
key device parameters
base doping: NA = 1016 /cm3
emitter doping ND = 6 x 1019 /cm3
minority carrier lifetime τn = 34 μs (base)
base thickness W = 198.9 μm
front junction depth xjf = 0.3 μm
back junction depth xjb = 0.8 μm
SF = 1000 cm/s
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light-generated current
n+ “emitter” (0.3 μm)
p-type “base”
(198.9 μm)
p+ “Back Surface Field” (BSF) (0.8 μm)
200
um
1) What is GTOT?
2) How is GTOT spatially distributed?
3) What is RTOT?
4) How is RTOT spatially distributed?
5) How do things change if we remove the BSF?
( ) ( )( )0 0D TOT TOTJ q R G= −SF = 1000 cm/s
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n+ “emitter” (0.3 μm)
p-type “base”(198.9 μm)
p+ “Back Surface Field” (BSF) (0.8 μm)
200
um
17
light-generated current: numbers
( ) ( )0SC D A TOT TOTJ J V q R G= = = −
( )2
17 -2 -1
0
2.79 10 cm sL
TOT opG G x dx= = ×∫
( ) 17 -2 -1
0
2.97 10 cm sMAX opG G x dx∞
= = ×∫
217 -2 -139.4 mA/cm 2.46 10 cm sSCJ
q q= = ×
( ) 16 -2 -10 3.31 10 cm sTOTR = ×
0.3 mDW µ≈
320nL mµ≈
0.88CE =
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light-generated current: understanding
entire device near surface
jx j Dx W+
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light-generated current: summary
low lifetime (Auger recombination)surface recombination
good collection minority carrier lifetime
BSF
( )2
17 -2 -1
0
2.79 10 cm sL
TOT opG G x dx= = ×∫( ) 17 -2 -1
0
2.97 10 cm sMAX opG G x dx∞
= = ×∫
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recombination at short circuit
entire device near surface
jx j Dx W+
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recombination at short circuit: summary
low lifetime (Auger recombination)surface recombination
good collection
minority carrier lifetimeBSF
(0.49)
(0.37)
(0.14)
217 -2 -139.4 mA/cm 2.46 10 cm sSCJ
q q= = × ( ) 16 -2 -10 3.31 10 cm sTOTR = ×
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about recombination in the base
expect: ( ) ( )n
n xR x
τ∆
≈
We find the excess minority electron profile by solving the minority carrier diffusion equation:
( )nd J q Rdx
− = −
n nd nJ qDdx∆
≈
2
2 0n
d n ndx L∆ ∆
− = n n nL D τ=
x
n∆
jx W+ L
( ) ( )n backJ L q s n L′ ′= ∆
( ) ( )0 0n jJ q s n′ ′= ∆BSFL L x′ = −
0 jx W′ = +
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Adept simulation results
( )n x∆
( ) ( )n
n xR x
τ∆
≈
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the BSF
EC
CE
IE
EI
EF
FE
VE
EV
Sback ≈ υthe−∆E kBT
; 0.6 ×107 cm s
Sback ≈ υth
; 1×107 cm s
What happens if we remove the BSF?
0.13 eVE∆ =
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without the BSF
239.4 mA/cmSCJ =
25.3 mA/cmTOTqR =
0.88CE =
With BSF238.2 mA/cmSCJ =
26.5 mA/cmTOTqR =
0.85CE =
Without BSF
BSF
no BSF
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internal quantum efficiency
With BSF
No BSF
( )( )
0,D
inc
J VIQE
Fλ
λ=
=
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questions
1) Can you determine a way to find the actual back surface recombination velocity from the Adept simulation results. (Hint: Use plots of n(x) and Jn(x).)
2) How much could the performance improve if the back surface recombination velocity could be reduced to zero?
3) With the original BSF, how much would the performance increase if the minority carrier lifetime was 10 times longer?
4) In the original design, how would the short-circuit current change if the base was twice as thick?
5) Since most of the recombination loss occurs in the emitter, why not just make the emitter junction depth a lot smaller?
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2D effects
DI ( )I xDV ( ) DV x V<
SdxdRW
ρ=
1S
j D n jx N q xρρ
µ= =
jx
distributed series resistance
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outline
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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dark I-V
( ) ( )( )D A TOT A TOTJ V q R V G= −
( )( )0 TOT A OC TOTq R V V G= = −
Under open circuit conditions:
( )TOT A OC TOTR V V G= =
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illuminated at VOC:
( )lightTOT OC TOTR V G=
( )( )
darkD OC SC
darkTOT OC SC
J V J
R V J q
=
=
superposition:
31
superposition
AV
DJ
( )0 1D BqV nk TDJ J e= −
dark IVSCJ
OCV
?
0LJ <SCJ−
( ) ( )( )D A TOT A TOTJ V q R V G= −
dark:
( ) ( )dark darkD A TOT AJ V q R V=
illuminated:
( ) ( )( )light lightD A TOT A TOTJ V q R V G= −
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dark current characteristics (sketch)( ) ( )0 1A BqV nk Tdark
D AJ V J e= −
( ) ( ) ( )201 021 1A B A BqV k T qV k Tdark
D AJ V J e J e= − + −
AV
10log darkDJ
n = 2
n = 1
series resistance or…
shunt resistance or…
32
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dark current characteristics (Adept)
( ) ( )0 1A BqV nk TdarkD AJ V J e= −
( ) ( ) ( )201 021 1A B A BqV k T qV k Tdark
D AJ V J e J e= − + −
33
n = 1
n ≈ 2
n > 1
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what determines J0 and n?
( ) ( )0 1A BqV nk TdarkD AJ V J e= −
Answer:
Electron-hole recombination determines I0.
The location of recombination within the solar cell determines the ideality factor, n.
( ) ( )dark darkA A TOT AJ V q R V=
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recombination in the dark (VA = 0.7 V)
Emitter Base
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recombination summary: (VA = 0.7 V)
VA = 0.7 V recombination
( ) 20.7 465 mA/cmTOT
darkqR =
Short-circuit recombination
( ) 20 5.3 mA/cmTOT
lightqR =
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what happens if we remove the BSF? (VA = 0.7 V)
( ) 20.7 1372 mA/cmDJ =
With BSF Without BSF
( ) 20.7 644 mA/cmDJ =
~70%~85%
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2) Electrons and holes can also recombine within the SCR of the junction.
38
dark current physics (n = 1)
FB: minority carriers injected across junction
nF
0DI >
PF
( ) ( )D A TOT AI V qR V=
AqV
1) Recombination in QNRs:
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n = 1 device physics
( ) ( )D A TOT AI V qR V=
nFPF
( )bi Aq V V−
( ) 00 A BqV k TP Pn n e′ ≈
( ) nTOT A
n
QqR V
t=
20P i An n N≈
Recombination in quasi-neutral regions gives rise to n = 1 currents.
( )2
1A BqV k Tin
A
nQ e
N∝ −
: minority carier lifetimeor base transit time
nt
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dark current characteristics (sketch)( ) ( )0 1A BqV nk Tdark
D AJ V J e= −
( ) ( ) ( )201 021 1A B A BqV k T qV k Tdark
D AJ V J e J e= − + −
AV
10log darkDJ
n = 2
n = 1
series resistance or…
shunt resistance or…
40
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recombination in the dark (VA = 0.2 V)
emitter region base region
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recombination summary: (VA = 0.2 V)
VA = 0.2 V recombination
( ) 6 20.7 8.4 10 mA/cmTOT
darkqR −= ×
VA = 0.7 V recombination
( ) 20.7 465 mA/cmTOT
darkqR =
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2) Electrons and holes can also recombine within the SCR of the junction.
43
dark current physics
FB: minority carriers injected across junction
nF
0DI >
PF
( ) ( )D A TOT AI V qR V=
AqV
1) Recombination in QNRs:
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recombination in SCRs
( ) ( )darkD A TOT AJ V qR V=
nF PF
( )bi Aq V V− Maximum recombination occurs when n(x) ≈ p(x)
( )2A BqV k T
dark iTOT A
eff
qn eqR V
τ∝2 A BqV k T
inp n e=
Recombination in space-charge regions gives rise to n = 2 currents.
2ˆ ˆ A BqV k Tin p n e≈ ∝
( ) ( ) 2 A BqV k Tin x p x n e=
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recombination in SCR
( ) ( )D A TOT AJ V qR V=
2ˆ ˆ A BqV k Tin p n e≈ ∝
( )/ 2ˆˆ
A BqV k Ti
Aeff eff
n enR Vτ τ
= =
( ) ˆD A effJ V q R W=
ˆB
effk T qW =E
11 nmˆB
effk T qW = ≈E
4ˆ 2.3 10 V cm×E =
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dark IV
( ) ( ) ( ) ( )2 102 01 01 1 1A B A B A BqV k T qV k T qV nk T
D AJ V J e J e J e= − + − = −
Recombination in depletion regions
/ 202
G BE k TiJ n e−∝ ∝
large bandgaps and low temperatures
Recombination in neutral regions
/201
G BE k TiJ n e−∝ ∝
small bandgaps and high temperatures
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questions
1) What do you expect to happen if the BSF were removed? Run an Adept simulation to confirm.
2) What do you expect to happen if the minority carrier lifetime were reduced to 0.1 microseconds? Run an Adept simulation.
3) Why is recombination in the emitter so important under short-circuit conditions, but not under FB in the dark?
4) How much could VOC be increased if a BSF with near-zero surface recombination velocity could be achieved?
5) Series resistance affects the dark current, but it has no effect at open-circuit. What are the implications?
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outline
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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reducing recombination
higher material quality (longer lifetimes)
thinner base layer (but optically thick)
built-in fields
back-surface-fields / minority carrier mirrors
reducing contact areas
….
( ) ( )( )D A TOT A TOTJ V q R V G= −
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high-efficiency Si solar cells
24.5% at 1 sun
Martin Green Group UNSW – Zhao, et al, 1998
50
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how good is superposition?
0.62 V V= - Dark 0.62 OCV V= - Illuminated
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how good is superposition? (ii)
JdarkdarkDJ
lightDJ
( )0lightD
darkD JJ V+ =
superposition
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outline
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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summary1) Diode current = q times (total recombination – total
generation)
2) At VOC, recombination = optical generation
3) At V = 0, recombination lowers the collection efficiency
4) Dark current tells us much about the internal recombination mechanisms
5) Solar cell design is all about maximizing total generation and minimizing total recombination.
6) Simulations can be useful for understanding –especially if you look “inside” and not just at the IV.
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questions
1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary
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Appendices
1) Formal derivation of the relation between current and recombination/generation.
2) Mathematical justification of superposition
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Appendix 1: current and recombination
DI
N P
x0 L
( ) ( )D TOT TOTJ V q R G= −
( ) ( ) ( )0
0Lp n
TOT
J J LR R x dx
q q= − −∫
( )0
L
TOT opG G x dx= ∫
( )nJ L( )0pJ
Formal derivation of the relation between current and recombination/generation.
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continuity equation for electrons
Rate of increase ofwater level in lake = (in flow - outflow) + rain - evaporation
nt
∂∂ ( )nJ q−∇• −
G+ R−
WabashRiver
=
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solar cell physics
( ) ( )
( ) ( )
n op
p op
D
J q G R
J q G R
ρ∇• =
∇• − = −
∇• = −
Conservation Laws:
( )0 0
( , )optical generation rate
etc.
D A
n n n
p p p
op
D E V
q p n N N
J nq E qD n
J pq E qD pR f n pG
κε κε
ρ
µ
µ
+ −
= = − ∇
= − + −
= + ∇
= − ∇
==
Relations:
(steady-state)
“semiconductor equations”
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diode current and recombination
( ) ( )n opJ q G R∇• − = −
ID
DI
N P
x0 L( ) ( )
0 0
L L
n opdJ q R x G x dx = − ∫ ∫
( ) ( ) ( ) ( )0
0L
n n opJ L J q R x G x dx − = − ∫
( )n opd J q G Rdx
− = − (1D)
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current and recombination-generation
DI
N P
x0 L
( ) ( ){ } ( ) ( ) ( ) ( ) ( )0
0 0 0L
n p D op n pJ J J V q R x G x dx J L J − + = = − − − ∫
( ) ( ) ( ) ( ) ( ) ( )0
0 0 0L
n n op p pJ L J q R x G x d xJ J − = − + − ∫
( ) ( )D TOT TOTJ V q R G= −
( ) ( ) ( )0
0L
TOT n pqR q R x dx J L J= − −∫
( )0
L
TOT opG G x dx= ∫
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current and generation-recombination
The diode current is q times the total recombination minus the total generation.
The total recombination is the integrated recombination rate within the device plus the flux of minority carriers into each contact.
62
( ) ( )( )D A TOT A TOTJ V q R V G= −
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Appendix 2: justifying superposition
( ) ( )( )D A TOT A TOTJ V q R V G= − (valid in light or dark)
( ) ( )dark darkD A TOT AJ V qR V= (dark current)
( ) ( )( )0 0light lightD TOT TOTJ q R G= − (short circuit current)
( ) ( )superD 0dark light
A D DJ V J J= + (principle of superposition)
( ) ( ) ( )( )superD 0dark light
A TOT A TOT TOTJ V qR V q R G= + − (How does this compare to the exact answer?)
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mathematical justification for superposition
JD VA( )= q RTOT VA( )− GTOT( ) (valid in light or dark)
JD
super VA( )= qRTOTdark VA( )+ q RTOT
light 0( )− GTOT( ) JD
light VA( )= q RTOTlight VA( )− GTOT( )
(principle of superposition)
RTOT
light VA( )= RTOTdark VA( )+ RTOT
light 0( )?? (criterion to justify superposition)