1

Lecture 5Physics of Organic Solar Cells

M. A. Alam and B. Ray

alam@purdue.eduElectrical and Computer Engineering

Purdue UniversityWest Lafayette, IN USA

NCN Summer School: July 2011Notes on the Fundamental of Solar Cell

2

copyright 2011

This material is copyrighted by M. Alam under the following Creative Commons license:

Conditions for using these materials is described at

http://creativecommons.org/licenses/by-nc-sa/2.5/

Alam 2011

33

Outline

1) Introduction: Rationale of organic solar cells

2) Planar Heterojunction OPV

3) Checkerbox Heterjunction OPV

4) Bulk Heterojunction devices

5) Percolation, fluctuation, and efficiency limits

6) Conclusions

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Different types of solar cells

4

Crystalline Silicon Flexible organicAmorphous silicon

*Google Images

p-n p-i-n m-i-m

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Economics of solar cells

5

C-Si CdTe a-Si CIGS OPV

Material/m2 207 50-60 64 100-125 37

Process/m2 123 86 73 130 23-37

Total/m2 350 130 138 230 50-80

Cost/W 1.75 0.94 -1.2 0.9-1.4 1.63 1-1.36

• All costs are approximate• J. Kalowekamo/E. Baker, Solar Energy, 2009.• Goodrich, PVSC Tutorial, 2011.

If efficiency exceeds 15% and lifetime 15 years, $/W ~0.36

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66

Outline

1) Introduction: Rationale of organic solar cells

2) Planar Heterojunction OPV

3) Checkerbox Heterjunction OPV

4) Bulk Heterojunction devices

5) Percolation, fluctuation, and efficiency limits

6) Conclusions

Alam 2011

Basics: Excitons, electrons, and holes

7

4

2 2 2 2 20

mqE = eV

32 01

1 113.6 mmπ ε κ κ

= ×

m= 0.1m , =10

E ~13.6 meV0

1 ~ 53Si SiBr A

κ

m= 0.1m = 3

E ~151 meV0

1 ~ 15poly polyBr A

κ Charge neutral excitons happily diffusing around …

H atomBr

20

B 2

4πr =

mq00.53

mA

mε

κ κ ×

=

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Basics: Excitons, electrons, and holes

8

E ~151 meV1 ~ 15poly polyBr A

Heterojunctions takes the exciton apart, Build-in field sweeps electrons/holes away

Aχ Bχ

MχMχ Mχ

Mχ

Band-diagram

DonorAcceptor

Bilayer Plastic Solar Cells

Side view

Exciton recombination before dissociation at the junction makes it a poor cell …

9Alam 2011

Photocurrent in bilayer cells

10

~ τex exD

/4, 1 e exWL exexex

ex ex ex

JJqG qG

D τ

− = = −

≡

, (0)L n n rec nE Sγ µ γ δ τ= = ≡

(0)(0)

ph n

ex n

J EJ E S

µµ

=+

0

nex

n

SJ

E Sµ

µ +exJ

,,

, , , ,

ph L pL n

ex L n R n rec L p R p rec

J

J

γγγ γ γ γ γ γ

= −

+ + + +

(0) bi

n

V VE

W−

===

≫≪

24 2

ex ex ex

ex ex

J qG WJ qG W W

Photocurrent in bilayer cells

11

,,

, , , ,

ph L pL n

ex L n R n rec L p R p rec

J

J

γγγ γ γ γ γ γ

= −

+ + + +

2 2(0) (0) (0) (0)ex n TJ n S E n n nγ µ γ υ = + + ≡ +

Interface recombination a key challenge

2 4

2T T ex

ph T

JJ

υ υ γυ

γ

− + + =

Defective interface

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Dark current in bilayer organic PV

12

// 2,0

( )/ 2,0

(0) (0)p Bn B

bi B

d

qEW K TqEW K TL R i

q V V K TL R i

J n p

n e p e n

n p e n

γ

γ

γ

−−

− −

≈

≈ × − = −

0 0.5 1

10-10

100

Voltage (V)

J (m

Acm

-2)

Exact

Approx.

Defective interface

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Summary: Total current in bilayer organic PV

13

( )/ 2,0

bi Bq V V K Td L R iJ n p e nγ − − = −

2 4

2T T ex

ph T

JJ

υ υ γυ

γ

− + + =

/21 e exWexex

JqG

− = −

T ph dJ J J= + -0.2 0 0.2 0.4 0.6-10

-8

-6

-4

-2

0

Voltage (V)

J (m

Acm

-2)

μ =10-4 cm2/V.s

JT,approxJT,anall

JT,num

Jd

Anomalously low fill factor!

Current collection and charge pileup

14

V=0.0V=0.6

0

2

3

4

5

6

7

8

9x 10

V=0.6

V=0.2

V=0.4E-

field

En

ergy

Position

(0)(0)

ph n

ex n

J EJ E S

µµ

=+

(0) bi

n

V VE

W−

<

The electrons stay too long close to a dangerous region …

-0.2 0 0.2 0.4 0.6-10

-8

-6

-4

-2

0

Voltage (V)

J (m

Acm

-2) JT,num

Jd

JT,anall

-0.2 0 0.2 0.4 0.6-10

-8

-6

-4

-2

0

Voltage (V)

J (m

Acm

-2)

Better mobility improves Fill factor

15

-0.2 0 0.2 0.4 0.6-10

-8

-6

-4

-2

0

Voltage (V)

J (m

Acm

-2)

μ =1e-4 μ =1e-3

JT,num

JT,anall

JT,num

JT,anall

Higher mobility improves Fill factorNonlinear series resistance ….

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The problem with planar heterojunction …

Making such thin film is essentially difficult, the layers will short out …

:ex ex exL D τ

:ex ex exL D τ

16

1717

Outline

1) Introduction: Rationale of organic solar cells

2) Planar Heterojunction OPV

3) Checkerbox Heterjunction OPV

4) Bulk Heterojunction devices

5) Percolation, fluctuation, and efficiency limits

6) Conclusions

Alam 2011

Checkerboard organic solar cellsDecoupling exciton and electron-hole paths

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/2, 2 1 e s exWL exexex

JJN

qG qG− = = × −

:ex ex exL D τ

McGehee, MRS Bulletin, Feb. 2009A. Javey, Nature Materials, July 2009

the balancing act …

2 2F FN ~1 2S V = WS

Finger density …

2ex ex

ex ex

F(S) ~ 4S × D 2S

= 2 D S

τ

τ

Fraction of the charge collected/finger …

ex F F

ex ex

J = qG ×V ×F(S)×N

~ qG ×W D Sτ

Total charge collected …

S

Two blocks

19

W

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20

Photo and dark currents (like a p-i-n diode)

20

,,

0, , , ,( )

Wph L pL n

ex L n R n L p R p

Jdx

J R V

γγγ γ γ γ

= −

− + + ∫

0Lγ υ=

( )/0

E W xR e θγ υ − −=

2 2log cosh coth

2 2D D

D D

L LW WW W

W L W L

= × ≅ −

Sokel and Hughes, JAP, 53(11), 1982.

S

W

W

( )/

( ) /1

1B

bi B

qV nk Tn bid q V V k T

V V dJ A e

e

µ+ −

− = − +

Photocurrent with distributed recombination

Dark current with distributed recombination

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meso-structured organic solar cells

Mixed Layersbilayer

21

checkerboard

/2, 2 1 e

2

2

s exWL exexex

s

s

JJN

qG qGAW NW WN A W

− = = −

==

2222

Outline

1) Introduction: Rationale of organic solar cells

2) Planar Heterojunction OPV

3) Checkerbox Heterjunction OPV

4) Bulk Heterojunction OPV

5) Percolation, fluctuation, and efficiency limits

6) Conclusions

Alam 2011

Processing of a plastic bulk heterojunction cell

23

Polymer-A(Donor)

SolventPolymer-B(Acceptor)

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

X (nm)

Y (

nm

)

0 50 100

100

50

0

Phase Separation occurs through Spinodal Decomposition

Anneal for a certain duration at moderate temperature

Cahn-Hilliard Eq:

2 40 2ϕ κ ϕ

ϕ ∂ ∂

= ∇ − ∇ ∂ ∂

fM

t

Nature Materials, 2009

Process model for phase segregation

24

Free energy:

Cahn-Hilliard Eq:

Surface tension

Energy ofmixing

free energy contains polymer details

EntropyEnthalpy

2 40 2ϕ κ ϕ

ϕ ∂ ∂

= ∇ − ∇ ∂ ∂

fM

t

= −mixf U TS

0 0.5 1

-0.5

0

0.5

ØA ØB

Ø0

Volume fraction, Ø (x,y)

Free

ene

rgy,

f(a.u

)

Ray et al., Solar Energy Mat and Solar Cells, 2011

Demixing and self-organization in thin films

Anneal time (sec)

Gra

in-s

ize

W(t

)

( )1 3at

/~

Anneal time

25

1/3atW(t)~

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Response of BHJ cells to light pulses

Electron

Holes

26

Movie: How excitons are taken apart by the heterojunction

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Photocurrent in BHJ OPV

W(tArea

L(t)× =)2

Anneal time

27

W(ta)L(ta)

1/3a

AreaL(

2 tt)~

×

1/3atW(t)~

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ex ex aQ = q D ×L(t )τEx

cito

nflu

x (a

.u)

Anneal time (a.u.)

28

W(ta)

L(ta)

Form defines function ….Should we anneal at all ?

1/3a

AreaL(

2 tt)~

×

exex

e/

ex1

x3

a

DQ 1=

tJ :

τ τ

Photocurrent and exciton flux

Photocurrent and annealing timeEx

cito

nFl

ux

Anneal time (a.u.)

1/R

29101 102

2

4

6

8

10

Anneal Time (min)

J SC(m

A/c

m2 )

ta(opt)

Ray et al., Solar Energy Mat and Solar Cells, 2011

How do they compare ?

30

0 0.2 0.4 0.6

-15

-10

-5

0

5

10

15

Voltage (V)

Curr

ent (

mA

/cm

2 )

Bi-layerη= 3.56 %Jsc = 6.6 mAcm-2

Voc = 0.66VFF = 81.5 %

Typical BHJη= 5.5 %Jsc = 14.6 mAcm-2

Voc = 0.63VFF = 59.5 %

Ordered BHJη= 6.1 %Jsc = 15.2 mAcm-2

Voc = 0.66VFF = 63.3 %

Bi-layer Typical BHJ

Ordered BHJ

Bilayer Ordered BHJ

Typical BHJ

Ray et al., PVSC, 2011

Low currentPoor fill factor

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Outline

1) Introduction: Rationale of organic solar cells

2) Planar Heterojunction OPV

3) Checkerbox Heterjunction OPV

4) Bulk Heterojunction devices

5) Percolation, fluctuation, and efficiency limits

6) Conclusions

Alam 2011

The challenge of a 15% cell …

32

New polymers with smaller bandgap

Change solvent and mixing ratio

Optimize anneal time Regularize morphology

Percolation dictates ~1:1 volume ratio

Solubility issues

Very limited play Random close to optimal

Conflicting system requires constraints the design, Need to consider all improvement within this context

0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

1

Fraction of P3HT

Con

nect

ed V

olum

e 100 nm200 nm

Mixing ratio and percolation

100 102 1040

0.2

0.4

0.6

0.8

1

Anneal Time (s)C

onne

cted

Vol

ume

Fluctuation and Mixing Ratio

1:11:2

1:3

Moving away from 1:1 ratio is challenging ….

Ordered vs. Disordered Morphology

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5 10 15 20 25

0.58

0.6

0.62

0.64

0.66

0.68

0.7

<WD>

FF

5 10 15 20 250.6

0.61

0.62

0.63

0.64

0.65

0.66

<WD>

V OC (V

)

5 10 15 20 253

3.5

4

4.5

5

5.5

6

6.5

<WD>

Effic

ienc

y (%

)

5 10 15 20 2560

80

100

120

140

160

180

<WD>

J SC (m

A/cm

2 )

Regular BHJ

Random BHJ

Regular BHJ

Random BHJ

Regular BHJ

Random BHJ

Regular BHJ

Random BHJ

Reduced variability, optimal for a range of anneal conditions

Ray et al., PVSC, 2011

35

Fundamental constraint of reliability

(i) ta = 0 s (ii) ta = 102s (iii) ta = 103s

(i) ts = 104 s (ii) ts = 105s (iii) ts = 106s

(i) ts = 104 s (ii) ts = 105s (iii) ts = 106s

(i) ts = 104 s (ii) ts = 105s (iii) ts = 106s

(a) Ta =1200C(ProcessingTemperature)

Stre

ss T

empe

ratu

re ,T

S

(d)

T S=

120

0 C

(

c) T

S=

100

0 C

(b

) T S

= 80

0 C

102 104 106

10

20

50

WC~ tSn

Stress Time (s)Cl

uste

r Siz

e, W

C(n

m) TS= 800, 1000, 1200 C

Continued coarseningwith anneal time

n

C a a eff a aW (t ,T ) D (T )t ∝ A a-E / kT

eff a 0D (T )= D e

The difference between Arizona sun and an oven is negligible

Derivation of the reliability formula

36

exSC

C

LJ

W (t)∝

A S

SC 0 s C 0

SC 0 C 0 s

n

eff 0 0

n

eff 0 0 eff s s

-n

-E / kT s

eq

J (t + t ) W (t )=

J (t ) W (t + t )

D (T )t=

D (T )t + D (T )t

t= 1+ e

t

ts = 10 hrs

Operating T (0C)Li

fetim

e (d

ays)

20 30 400

100

200

300

400

500JSC (deg) = 10, 20, 30%

Ea = 1.2 eVn = .25

100 hrs

103 104 105 106

0.2

0.4

0.6

0.8

1

Ts= 800, 1000, 1200 C

Anneal Time (s)

J SC

(nor

m)

102 104 106

10

20

50

WC~ tan

Anneal Time (s)

Clus

ter S

ize,

WC

(nm

) Ts= 800, 1000, 1200 C

Ray et al., APL, 2011 Lifetime less than a year!

ordered vs. spinodal films

Bulk Heterojunction Checkerboard Double Gyroid

Good … Best …

37

better …

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3838

Conclusions

Organic solar cells promises a low cost PV technology, lightweight, easy to install. Also, a beautiful physics problem with biomimetic transport.

Theory explains optimum of anneal time, the rationale of 1:1 mixing ratio, the fundamental constraints of reliability, limits of Voc and FF.

Reliability, variability, and efficiency are important concerns. Self assembled regularized structure, new class of optics, lower bandgap materials, may help us reach 15% efficiency targets.

Alam 2011