Muhammad A. Alam (2011), "Solar Cells Lecture 5: Organic Photovoltaics," http://nanohub.org/resources/11950.

1. NCN Summer School: July 2011
Notes on the Fundamental of Solar Cell
Lecture 5
Physics of Organic Solar Cells
M. A. Alam and B. Ray
alam@purdue.edu
Electrical and Computer Engineering
Purdue University
West Lafayette, IN USA
1

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/
2 Alam 2011

3. 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 3

4. Different types of solar cells
p-n p-i-n m-i-m
Crystalline Silicon Amorphous silicon Flexible organic
Alam 2011 4
*Google Images

5. Economics of solar cells
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
If efficiency exceeds 15% and lifetime 15 years, $/W ~0.36
• All costs are approximate
• J. Kalowekamo/E. Baker, Solar Energy, 2009.
• Goodrich, PVSC Tutorial, 2011.
Alam 2011 5

6. 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 6

7. Basics: Excitons, electrons, and holes
H atom
rB
m = 0.1m0 , κ =10
mq4 1 1  m 
E1 Si ~13.6 meV rBSi ~ 53 A E1 = = 13.6 × 2   eV
32π  ε 0 κ
2 2 2 2
κ  m0 
4πε 0  2 m 
rB = κ = 0.53 × κ  0  A
mq 2  m 
m = 0.1m0 κ = 3 Charge neutral excitons happily
E1 poly ~151 meV rBpoly ~ 15 A diffusing around …
Alam 2011 7

8. Basics: Excitons, electrons, and holes
E1 poly ~151 meV rBpoly ~ 15 A
χB χM
χM χA χM
χM
Heterojunctions takes the exciton apart,
Build-in field sweeps electrons/holes away 8

9. Bilayer Plastic Solar Cells
Side view Band-diagram
Acceptor Donor
Exciton recombination before dissociation
at the junction makes it a poor cell …
Alam 2011 9

10. Photocurrent in bilayer cells Jex
µn S
µn E + S
Jex
~ Dexτ ex
0
J ph  γ L ,n γ L ,p 
=  − 
Jex  γ L ,n + γ R ,n + γ rec γ L ,p + γ R ,p + γ rec 
 
Jex JL ,ex
= =  ex 1 − e −W /4  ex 
 
qG qG = µn E(0) = δ τ n ≡ S
γ L ,n γ rec
 ex ≡ Dexτ ex
J ph µn E(0) Vbi − V
= E(0) =
Jex = qG  ex W 2 ≫  ex Wn
Jex µn E(0) + S
Jex = qG W 4 W 2 ≪  ex
10

11. Photocurrent in bilayer cells
Defective interface
J ph  γ L ,n γ L ,p 
=  − 
Jex  γ L ,n + γ R ,n + γ rec γ L ,p + γ R ,p + γ rec 
 
Jex γ n(0)2 + S + µn E  n(0) ≡ γ n(0)2 + υT n(0)
=  
 −υ + υ 2 + 4γ J 
J ph =  T T ex
 υT
 2γ 
 
Interface recombination a key challenge
Alam 2011 11

12. Dark current in bilayer organic PV
Defective interface
0 Approx.
10
J (mAcm -2)
Exact
-10
Jd ≈ γ n(0)p(0) 10
0 0.5 1
≈ γ nL e − ni2,0 
− qEWn / KB T − qEWp / KB T
× pR e Voltage (V)
 
γ nL pR e − q(Vbi −V )/ KBT − ni2,0 
 
Alam 2011 12

13. Summary: Total current in bilayer organic PV
Jex μ =10-4 cm2/V.s
=  ex 1 − e −W /2  ex 
 
qG 0
 −υ + υ 2 + 4γ J  -2 Jd
J ph =  T  υT JT,num
J (mAcm -2)
T ex
 2γ  -4
 
-6
Jd γ nL pR e − q(V

bi −V )/ KB T
− ni2,0 
 -8 JT,approx JT,anall
-10
-0.2 0 0.2 0.4 0.6
= J ph + Jd
JT Voltage (V)
Anomalously low fill factor! 13

14. Current collection and charge pileup
V=0.6
Energy
V=0.0
J ph µn E(0) Vbi − V
= E(0) <
Jex µn E(0) + S Wn
x 10
9
8
0 7
V=0.2
-2 Jd
JT,num
6
J (mAcm )
-2
E-field
5
-4
4 V=0.4
-6 3
-8
JT,anall 2
-10 V=0.6
-0.2 0 0.2 0.4 0.6 0
Voltage (V) Position
The electrons stay too long close to a dangerous region … 14

15. Better mobility improves Fill factor
μ =1e-4 μ =1e-3
0 0
-2 JT,num -2 JT,num
J (mAcm -2)
J (mAcm )
-2
-4 -4
-6 -6
JT,anall
-8 -8 JT,anall
-10 -10
-0.2 0 0.2 0.4 0.6 -0.2 0 0.2 0.4 0.6
Voltage (V) Voltage (V)
Higher mobility improves Fill factor
Nonlinear series resistance ….
Alam 2011 15

16. The problem with planar heterojunction …
Lex : Dexτ ex
Lex : Dexτ ex
Making such thin film is essentially difficult,
the layers will short out …
16

17. 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 17

18. Checkerboard organic solar cells
Decoupling exciton and electron-hole paths
Lex : Dexτ ex
McGehee, MRS Bulletin, Feb. 2009
Jex JL ,ex
= = N ×  ex 1 − e −Ws /2  ex 
2  
A. Javey, Nature Materials, July 2009
qG qG 18

19. the balancing act …
Finger density …
S
NF ~1 2S 2 VF = WS 2
Fraction of the charge collected/finger …
F(S) ~ 4S × Dexτ ex 2S 2
= 2 Dexτ ex S
Two blocks
W Total charge collected …
Jex = qG ×VF × F(S)× NF
~ qG ×W Dexτ ex S
Alam 2011 19

20. S Photo and dark currents (like a p-i-n diode)
Photocurrent with distributed recombination
J ph W  γ L ,n γ L ,p 
=
Jex − R(V ) ∫
0
dx  − 
 γ L ,n + γ R ,n γ L , p + γ R , p 
 
W
2 LD W  2 LD W 
=
W× log cosh ≅W − coth 
γ R = υ0 e − E(W − x )/θ W W 2 LD  W 2 LD 
γ L = υ0
Dark current with distributed recombination
 µn (V − Vbi ) / d  qV
= A  + q(V −V )/ k T  e
Jd nkB T
− 1
e bi B
+ 1  
Sokel and Hughes, JAP, 53(11), 1982.
Alam 2011 20

21. meso-structured organic solar cells
bilayer checkerboard Mixed Layers
Jex JL ,ex
= = 2N ex 1 − e −Ws /2  ex 
 
qG qG
AW = NWs 2W
2N = A Ws
21

22. 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 22

23. Processing of a plastic bulk heterojunction cell
Solvent Nature Materials, 2009
Polymer-A Polymer-B
(Donor) (Acceptor)
100
Y (nm)
50
0
0 50 100
X (nm)
Anneal for a certain duration Cahn-Hilliard Eq:
at moderate temperature
∂ϕ  ∂f 
Phase Separation occurs = M0  ∇ 2 − 2κ∇ 4ϕ 
∂t  ∂ϕ 
through Spinodal Decomposition 23

24. Process model for phase segregation
Free energy:
f mix= U − TS
Ø0
Free energy, f(a.u)
0.5
Enthalpy Entropy
Cahn-Hilliard Eq: 0
∂ϕ  2 ∂f 4 
= M0  ∇ − 2κ∇ ϕ 
∂t  ∂ϕ  ØA ØB
-0.5
0 0.5 1
Surface
Energy of
mixing
tension Volume fraction, Ø (x,y)
free energy contains polymer details
24
Ray et al., Solar Energy Mat and Solar Cells, 2011

25. Demixing and self-organization in thin films
Anneal time
Grain-size W(t)
~ ( ta )
1/ 3
1/ 3
W(t) ~ t
a
Anneal time (sec)
Alam 2011 25

26. Response of BHJ cells to light pulses
Electron
Movie: How excitons are taken
Holes apart by the heterojunction
Alam 2011 26

27. Photocurrent in BHJ OPV
Anneal time
1/ 3 L(ta)
W(t) ~ t a W(ta)
Area
L(t)× W(t) =
2
Area
L(t) ~
2 × t1/ 3
a 27
Alam 2011

28. Photocurrent and exciton flux
Q Dex 1
Exciton flux (a.u)
Jex = :
τ ex τ ex t1/ 3
a
Anneal time (a.u.)
L(ta) Area
L(t) ~
2 × t1/ 3
a
W(ta) Q = q Dexτ ex × L(ta )
Form defines function ….
Should we anneal at all ? 28

29. Photocurrent and annealing time
Ray et al., Solar Energy Mat and Solar Cells, 2011
10
Exciton Flux
JSC (mA/cm2)
8
1/R 6 ta(opt)
4
2 1 2
Anneal time (a.u.) 10
Anneal Time (min)
10
29

30. How do they compare ?
Bilayer Typical BHJ Ordered BHJ
Ray et al., PVSC, 2011
15 Bi-layer Typical BHJ Ordered BHJ
η = 3.56 % η = 5.5 % η = 6.1 %
10 Jsc = 6.6 mAcm -2 Jsc = 14.6 mAcm -2 Jsc = 15.2 mAcm -2
Voc = 0.66V Voc = 0.63V
Current (mA/cm2)
Voc = 0.66V
5 FF = 81.5 % FF = 59.5 % FF = 63.3 %
Low current
0 Bi-layer Typical BHJ Poor fill factor
-5
-10
-15 Ordered BHJ
0 0.2 0.4 0.6
Voltage (V)
Alam 2011 30

31. 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 31

32. The challenge of a 15% cell …
New polymers with Change solvent
smaller bandgap and mixing ratio
Solubility issues Percolation dictates
~1:1 volume ratio
Optimize anneal time Regularize morphology
Very limited play Random close to optimal
Conflicting system requires constraints the design,
Need to consider all improvement within this context 32

33. Mixing ratio and percolation
Fluctuation and
1
Mixing Ratio
Connected Volume
100 nm
0.8 1
200 nm
1:1
Connected Volume
0.6
0.8 1:2
0.6
0.4
0.4
0.2
0.2
0 1:3
0 0
0.2 0.4 0.6 0.8 10 10
2
10
4
Fraction of P3HT Anneal Time (s)
Moving away from 1:1 ratio is challenging ….

34. Ordered vs. Disordered Morphology
Ray et al., PVSC, 2011
6.5 180
6
160
Regular BHJ
5.5
Efficiency (%)
140
(mA/cm 2)
5 Regular BHJ
120
4.5 Random BHJ
Random BHJ
SC
100
J
4
3.5 80
3 60
5 10 15 20 25 5 10 15 20 25
<W D> <W D>
0.66 0.7
0.65 Regular BHJ 0.68
Regular BHJ
0.66
0.64
(V)
0.64
Random BHJ
FF
0.63
OC
0.62 Random BHJ
V
0.62
0.6
0.61 0.58
0.6
5 10 15 20 25 5 10 15 20 25
<W D> <W D>
Reduced variability, optimal for a range of anneal conditions 34

35. Fundamental constraint of reliability
(i) t a = 0 s (ii) t a = 10 2 s (iii) t a = 10 3 s
Continued coarsening
with anneal time
(a) Ta =120 0 C n
(Processing
Temperature) WC (ta ,Ta ) ∝  Deff (Ta )ta 
 
(i) t s = 10 4 s (ii) t s = 10 5 s (iii) t s = 10 6 s
Deff (Ta ) = D0 e -EA / kTa
(b) TS = 80 0 C
TS= 800, 1000, 1200 C
Cluster Size, WC (nm)
Stress Temperature ,TS
(i) t s = 10 4 s (ii) t s = 10 5 s (iii) t s = 10 6 s 50
(c) TS = 100 0 C
W C~ tSn
20
(i) t s = 10 4 s (ii) t s = 10 5 s (iii) t s = 10 6 s
(d) TS = 120 0 C
10
2 4 6
10 10 10
Stress Time (s)
The difference between Arizona sun and an oven is negligible 35

36. Derivation of the reliability formula
Lex JSC (t0 + t s ) WC (t0 )
JSC ∝ =
ts = 10 hrs 100 hrs WC (t) JSC (t0 ) WC (t0 + t s )
n
 Deff (T0 )t0 
 
= n
 Deff (T0 )t0 + Deff (Ts )t s 
 
-n
 -E A / kTS
 ts 
= 1+ e  
  teq 
  
500
Ts= 800, 1000, 1200 C 1 JSC (deg) = 10, 20, 30%
Cluster Size, WC (nm)
Lifetime (days)
400
50
JSC (norm)
0.8
300
WC~ tan Ea = 1.2 eV
0.6
200 n = .25
20
0.4
100
10 0.2 Ts= 800, 1000, 1200 C
0
2 4 6 3 4 5 6 20 30 40
10 10 10 10 10 10 10
Anneal Time (s) Anneal Time (s) Operating T (0C)
Ray et al., APL, 2011 Lifetime less than a year! 36

37. ordered vs. spinodal films
Bulk Heterojunction Checkerboard Double Gyroid
Good … better … Best …
Alam 2011 37

38. 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 38