The document discusses how trap-assisted recombination influences polymer-fullerene solar cells. It finds that: 1) Recombination in annealed P3HT:PCBM solar cells is reduced Langevin or higher order than second order, indicating the influence of traps. 2) Transient absorption measurements of P3HT also show recombination orders higher than second order at low temperatures, consistent with photo-CELIV results. 3) The disorder in pristine samples leads to even higher recombination orders, showing the influence of morphological factors like phase separation on recombination.

1. Influence of
Trap-Assisted Recombination on
Polymer–Fullerene Solar Cells
C. Deibel, J. Lorrmann, A. Baumann, J. Gorenflot,
A. Wagenpfahl, J. Rauh,* V. Dyakonov
Julius-Maximilians-University of Würzburg, Germany
SPIE Optics+Photonics
* formerly known as Julia Schafferhans :-) 25th August 2011 in San Diego

2. Recombination Mechanisms: Overview
PP diss V
P
Photo-!
extract current
P rec
PEDOT
bulk rec P surface!
rec
glass
Surface! ‣ geminate recombination
loss (PRL 103, 036402 (2009))
‣ nongeminate recombination
internal external ‣ surface recombination
(PRB 82, 115306 (2010))
‣ extraction at wrong
electrode due to diffusion
P = Polaron; PP = Polaron Pair (PRL 105, 266602 (2010)) 2

3. Nongeminate Recombination
Disordered System: all charges localised, hopping
Energy concentration: free << trapped
LUMO trapped charges are immobile
Etransport
Etailstate traps
ECT
Edeep traps
Etailstate traps
Etransport
HOMO
a) b) c) d) e)
DOS no recombination Trapped with Trapped (a)
But: Free with Trapped Charges (b,c) , Free with Free (e) , or SRH (d)
3

4. Recombination Order
Geminate Recombination:
concentration independent lifetime
1st order
Nongeminate Recombination: bimolecular
concentration dependent (effective) lifetime
2nd order
typical for photogeneration w/out traps
1st order
asymmetric doping or deep traps 4

5. Nongeminate Recombination
Langevin recombination
(1)
(2)
(1)
V
RLangevin = np
q
= (µe + µh )
PEDOT ⇥
• 2nd order recombination?
glass • Langevin? reduced?
• influence of traps? 5

6. Experimental Method
short
Photo-CELIV
delay
1.2
Photo-CELIV
‣ ns laser pulse delay dependent @ T=150 K
1.0
‣ delay time / P3HT:PCBM 1:0.8
j [x10 A/cm ]
2
recombination at V=Voff 0.8
‣ charge extraction
-3
0.6 delay time tdelay between
laser and voltage pulse
0.4
‣ mobility and
‣ carrier concentration 0.2
simultaneously 0.0 0.4 0.8
long -3
t [x10 s]
delay
and transient absorption for comparison 6

7. Bulk Recombination
P3HT:PCBM (annealed) measured by photo-CELIV
125 K
22
RLangevin = np
10
q
= (µe + µh )
⇥
n [m ]
-3
21 300 K
10
‣ temperature dependence
same as for mobility
P3HT:PCBM 1:0.8
20 annealed
10 ‣ typical for Langevin
recombination
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s]
Andreas Baumann 7

8. Analysis: Fitting to the Continuity Equation
P3HT:PCBM (annealed) measured by photo-CELIV
5
4
T=150K
3
2
P3HT:PCBM 1:0.8
22
10
next [m ]
-3
6 experiment
5
4
3
2
21
10
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s] 8

9. Analysis: Fitting to the Continuity Equation
Monomolecular Recombination? dn n
=
dt ⌧
5
4
T=150K
3
2
P3HT:PCBM 1:0.8
22
10
next [m ]
-3
6 experiment
5 -4
4 MR: τ = 6.6·10 s
3
2
21
10
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s]

10. Analysis: Fitting to the Continuity Equation
Langevin Recombination? dn q 2
= · µ ·n
dt ✏r ✏0
| {z }
L
5
4
T=150K
3
2
P3HT:PCBM 1:0.8
22
10
next [m ]
-3
6 experiment
5 -4
4 MR: τ = 6.6·10 s
3
Langevin
2
21
10
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s] 10

11. Analysis: Fitting to the Continuity Equation
Reduced Langevin Recombination! dn q 2
= ⇣· · µ ·n
dt ✏r ✏0
| {z }
L
5
4
T=150K
3
2
P3HT:PCBM 1:0.8
22
10
next [m ]
-3
6 experiment
5 -4
4 MR: τ = 6.6·10 s
3
Langevin
2 red. Langevin: ζ = 0.057
21
10
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s] 11

12. Analysis: Fitting to the Continuity Equation
Recombination Order > 2 ? dn +1
= k +1 ·n
dt
5
4
T=150K
3
2
P3HT:PCBM 1:0.8
22
10
next [m ]
-3
6 experiment
5 -4
4 MR: τ = 6.6·10 s
3
Langevin
2 red. Langevin: ζ = 0.057
λ+1
21 kλ+1n with λ+1=2.41
10
-7 -6 -5 -4 -3 -2
10 10 10 10 10 10
tdelay [s] 12

13. Recombination Order
P3HT:PCBM measured by photo-CELIV
3.4
recombination order λ+1
P3HT:PCBM 1:0.8
3.2
pristine ‣ 2nd order or higher
3.0 annealed
‣ bimolecular
2.8 recombination
2.6
2.4 ‣ the more disordered
2.2 pristine sample:
BR
2.0 ‣ higher rec. order
150 200 250 300
T [K]
Andreas Baumann 13

14. For Comparison: Transient Absorption
P3HT:PCBM (annealed) measured by transient absorption
7 ‣ P3HT:PCBM,
Order of Decay λ+1
6 similar results as
compared to
5
photo-CELIV
4
3 ‣ P3HT >140K due
to polarons;
2
P3HT second order
1 P3HT:PCBM recombination!
50 100 150 200 250 300 ‣ neat P3HT: „no“
Temperature [K] phase separation
Julien Gorenflot 14

15. Similar for „Intercalating“ Materials!
5.0 pBTCT-C 12:PC61BM
photo-CELIV 1:1
4.5 1:4
TRMC 1:1
recombination order
4.0 1:4
3.5
or films of pure pATBT, pBTTT,
BM 8annealed at 120 °C. For
1000 3.0
ling at 165 °CpBTCT-C12:PC61BM
6
is also presented.
4 1:0
are given on the right.
2
1:1
1:4
2.5
100
ential of the polymer. Increas-
8
6
the polymeric donor is one
4
2.0
circuit voltage of the 2.0 nm
2 bulk
related to the energy offset
108 1.5
ecular orbital (HOMO) of the
6
180 200 220 240 260 280 300
4
d molecular orbital (LUMO)
2.8 nm
M.13,14 The polymers of interest
2
T/K
2,5-bis(3-alkylthiophen-2-yl)-
2 3 4 5 6
an unsubstituted thieno[3,2-b]-
2Θ/°
Adv. Funct. Mater. 21, 1687 (2011) 15
into the polymer backbone.

16. Causes for High Recombination Order?
carrier concentration dependent mobility
Shuttle et al, Adv. Funct. Mater 20, 698 (2010)
influence of trapping
Zaban et al, Chem. Phys. Chem. 4, 859 (2003)
Nelson, PRB 67, 155209 (2003)
influence of phase separation
idea, but without change of order: Koster et al, APL 88, 052104 (2006)
qualitatively: Baumann et al, Adv. Funct. Mater. 21, 1687 (2011)
16

17. Concentration Dependent Mobility?
P3HT:PCBM (annealed) measured by photo-CELIV
4
3
2
-9
10
µ [m /Vs]
6
5 ‣ at least, not for annealed
2
4 P3HT:PCBM 1:0.8
3 annealed P3HT:PCBM solar cells
2
125 K
-10 150 K
10 175 K
200 K
6 300 K
5
20 21 22
10 10 10
-3
n [m ]
Andreas Baumann 17

18. Concentration Dependence of Rec. Prefactor
P3HT:PCBM (annealed) measured by photo-CELIV
-17
10
‣ fit:
-18
10
kBR [m /s]
‣ if it were pure Langevin:
3
-19
10
P3HT :PCBM 1:0.8
annealed
-20 fit Langevin
10
125 K
175 K n and μ(n) from CELIV
300 K
λ and kλ from fitting CELIV
20 21 22
10 10 10
-3
n [m ]
Andreas Baumann 18

19. Concentration Dependence of Rec. Prefactor
P3HT:PCBM (annealed) measured by photo-CELIV
-17
10
‣ consequence:
-18
10 is not universal
kBR [m /s]
3
-19
10 ‣ High recombination
P3HT :PCBM 1:0.8
order in part due to
annealed not all carriers being
-20 fit Langevin
10
125 K
able to recombine with
175 K one another (no nt2)
300 K
20 21 22
10 10 10
-3
n [m ]
Andreas Baumann 19

20. Trapping?
P3HT:PCBM (annealed) by Thermally Stimulated Currents
21
6x10 T2 P3HT:PC61BM Trap density (Lower Limit)
T1 PC61BM
trap density (lower limit) [m ]
-3
5 P3HT P3HT:PCBM: 6-8⋅1022 m-3
4 P3HT: 1⋅1022 m-3
3 T3
‣ trapping in extrinsic traps
2 does occur
1
‣ generally: in a hopping
0 system, trapping also within
100 200 300 400 intrinsic density of states
activation energy [meV]
APL 93, 093303 (2008), Org. Electron. 11, 1693 (2010),
Julia Rauh Adv. Ener. Mater. 1, 655 (2011) 20

21. Phase Separation?
Scenario Modelling
Polymer
et
Fullerene but !
cannot be extracted
delayed recombination
due to emission from trap
solving the continuity equation
• trapping and release
et • exponential DOS (intrinsic)
=> recombination order >2
• here: R ∝ nfree pfree
Jens Lorrmann due to phase separation
et
21

22. Recombination Order λ+1
even without phase separation ... but stronger with it!
>10.0
   

 
Jens Lorrmann 22

23. Impact on Current–Voltage Characteristics
free–free recombination free–free and free–trapped
recombination
150 150
illum. σ dark illum. σ dark
100 25 meV 100 25 meV
50 meV 50 meV
Current density [A/m ]
Current density [A/m ]
75 meV
2
2
75 meV
50 100 meV 50 100 meV
125 meV 125 meV
0 0
disorder
-50 -50
disorder
disorder
-100 -100
-0.4 0.0 0.4 0.8 -0.4 0.0 0.4 0.8
Voltage [V] Voltage [V]
unfortunately, probably a mixture of both in real devices:
Alexander Wagenpfahl pure and intermixed phases 23

24. Conclusions: Nongeminate Recombination
carrier concentration dependent mobility
- CELIV: order > 2 also for cases with μ(n) = const
- part of concentration dependence from R ≠ f(nt2)
influence of trapping
- significant trap concentration, nt >> nc
=> multiple-trapping-and-release
influence of phase separation
- 2nd order recombination in neat polymer indicates:
phase separation plays role in blends‘ high order
order > 2 from delayed bimolecular recombination
due to trapping
24

25. Acknowledgments
Thank You!
deibel@physik.uni-wuerzburg.de Bayerische
Akademie der Wissenschaften
www.disorderedmatter.eu
EP VI
25