solar cells lecture 2: physics of crystalline solar cells

64
Prof. Mark Lundstrom [email protected] Electrical and Computer Engineering Purdue University West Lafayette, Indiana USA Solar Cell Physics: recombination and generation NCN Summer School: July 2011

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Mark Lundstrom (2011), "Solar Cells Lecture 2: Physics of Crystalline Solar Cells," http://nanohub.org/resources/11890.

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Page 1: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

Prof. Mark Lundstrom

[email protected] and Computer Engineering

Purdue UniversityWest Lafayette, Indiana USA

Solar Cell Physics:recombination and generation

NCN Summer School: July 2011

Page 2: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

Lundstrom 2011 2

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/

Page 3: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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.

Page 4: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

Lundstrom 2011 4

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.

Page 5: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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outline

1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary

Page 6: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 7: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 8: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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 <

Page 11: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 12: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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.

Page 13: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 15: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 16: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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+

Page 19: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 26: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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internal quantum efficiency

With BSF

No BSF

( )( )

0,D

inc

J VIQE

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 =

Page 37: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 40: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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

Page 41: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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 =

Page 43: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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 =

Page 46: Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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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)