langevin recombination in regioregular poly(3-hexylthiophene)

8/10/2019 Langevin Recombination in Regioregular Poly(3-Hexylthiophene)

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Two dimensional Langevin recombination in regioregular poly(3-hexylthiophene)

Gytis Juka, Kristijonas Geneviius, Nerijus Nekraas, Gytis Sliauys, and Ronald sterbacka

Citation:Applied Physics Letters 95, 013303 (2009); doi: 10.1063/1.3141513

View online: http://dx.doi.org/10.1063/1.3141513

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Two dimensional Langevin recombination in regioregularpoly3-hexylthiophene

Gytis Juka,1,a Kristijonas Geneviius,1 Nerijus Nekraas,1 Gytis Sliauys,1 andRonald sterbacka21Department of Solid State Electronics, Vilnius University, Saultekio 9 III k., 10222 Vilnius, Lithuania2Department of Physics and Center for Functional Materials, bo Akademi University, Porthansgatan 3,FI-20500 Turku, Finland

Received 26 January 2009; accepted 3 May 2009; published online 7 July 2009

In this work, it is shown that recombination in regioregular poly3-hexylthiophene:6,6-phenyl-C61-butyric acid methyl esterRRP3HT:PCBMbulk-heterojunction solar cells is caused bythe two dimensional2DLangevin recombination in the lamellar structures of RRP3HT, which areformed after annealing process. Due to 2D Langevin process, bimolecular recombination coefficientis reduced in comparison with three dimensional Langevin case, and bimolecular recombinationcoefficient depends on the density of charge carriers n1/2. Data obtained from the differentexperimental techniquescharge extraction with linearly increasing voltage, integral time of flight,double injection current transients and transient absorption spectroscopy confirms 2D Langevinrecombination in RR3PHT. 2009 American Institute of Physics. DOI:10.1063/1.3141513

One of the main factors limiting conversion efficiency inorganic solar cells is the recombination of the charge carri-ers. In low mobility materials bimolecular Langevin-type re-combination is usually observed.1,2 Langevin recombinationis caused by the probability for electrons and holes to meet incoordinate space, and therefore depends on the transportproperties of the charge carriers.

We have previously shown that in bulk heterojunctionsolar cells made from blends of regioregular poly3-hexylthiophene with 6,6-phenyl-C61-butyric acid methylesterRRP3HT:PCBM, the bimolecular recombination is re-duced by approximately 103 times with respect to the Lange-vin recombination.1 Using different experimental methods:double injection DoI current transient,3 integral time-of-flight TOF method,4 transient absorption spectroscopy,5

charge carriers extraction with linearly increasing voltageCELIV,3,6 it was obtained that bimolecular recombinationcoefficientdepends on the density n of the charge carriers.This dependence is observed only in annealed samples,where lamellar structures are formed.6,7 It was explained bythe trimolecular recombination.4

In this work, we are explaining that the reduction inbimolecular recombination coefficient and its dependenceon charge carriers density as being caused by the two dimen-sional2DLangevin recombination.

The time needed for charge carriers to meet in the coor-dinate space under influence of Coulomb interaction can beexpressed as

tm= 0

rm dr

n+ pEr, 1

where

Er= e40r

2 , 2

n, pare the mobilities of the electrons and holes, and 0is the dielectric permittivity. In the three dimensional 3Dcase, the interaction radius rm is determined by the 4rm

3/3

= 1 / n, so that the Langevin recombination probability,

f3D= 1

tm=

en+ pn

0

. 3

Sirringhaus et al.8 showed that the mobility across andalong the lamellar structure differs more than 100 times,

which means that the recombination of charge carriers ismainly taking place in the 2D lamellar structure. When spac-ing between lamellas lrm,rmis determined by rm

2 l= 1 / n,then the recombination probability becomes

f2D= 1

tm=

34

en+ p

0

ln3/2 = 2Dn3/2, 4

where2Dis 2D recombination parameter. Hence in 2D case,the bimolecular recombination coefficient will be reduced incomparison with the 3D case with

2D

3D=

34

l3/2n1/2. 5

For RRP3HT l1.6 nm Ref. 8 and, for example, whenn= 1016 cm3, 2D /3D = 610

3, and that is close to ex-perimental observation.1,6

In the case of 2D, using Eq. 4 the equation governingthe decay of the charge carriers is

dn

dt =G 2Dn

5/2, 6

where G is the rate of the photogeneration or DoI. Similardependencies were observed experimentally dn /dtn2.6.9

According to Eq. 6 in the case of 2D, after excitationwith short light pulse the decay of the density of charge

carriers,

aAuthor to whom correspondence should be addressed. Electronic mail:

[email protected].

APPLIED PHYSICS LETTERS 95, 0133032009

0003-6951/2009/951/013303/3/$25.00 2009 American Institute of Physics95, 013303-1This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP

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nt= 1n0

3/2 + 322Dt

2/3

t2/3n0. 7

Here n0 is initial density of photogenerated charge carriers.Similar dependence is observed with photo-CELIVtechnique.1,6

In the case of 3D Langevin recombination nt t1.It is worth to notice that slower than nt t1 dependencecan be observed due to the mobility dependence on timestochastic transport, as it was shown in regiorandompoly3-hexylthiophene.10 However, it is established byphoto-CELIV that in the RRP3HT:PCBM bulk heterojunc-

tion solar cells the mobility does not depend on the delaytime after exitation.1 That is why this explanation is not validfor the blends of RRP3HT and PCBM.

Another technique which allows determination of re-combination process is DoI current transient technique.11 Inthe case of 3D Langevin recombination, volt-ampere charac-teristics and DoI current transients correspond to the sum ofthe space charge limited currents of electrons and holes be-cause the injected charge carriers will recombine completelywithin the interelectrode distance. In Fig. 1a numericallycalculated DoI current transients are shown for the both 3Dand 2D Langevin recombination cases for different distancesl and ratios between fast and slow charge carrier mobilities

f/sl.In the case of 2D Langevin recombination the current-

voltage characteristics can be obtained from Eq. 6 in the

same way as in Ref. 11: jU9/5 /d13/5, while the saturationtime of the DoI current transient is trU

6/5. The observedexperimental results4 are very close to these dependencies.Using the following expression, which was obtained analyti-cally, from measured initial currentj0and saturated DoI cur-rent jstvalues, the spacing distancel could be estimated,

l=169

n2p

2

n+ p4

ed2

0U1/32j0

jst5/3. 8

The comparison of experimentally obtained inRRP3HT:PCBM and numerically calculated using n= 102 cm2 /V s, p =2.510

3 cm2 /V s,11 and l=1.6 nmobtained from x-rays studies8DoI current transients is pre-sented in Fig.1b. The ratio between initial and stationarycurrents is in good agreement with experiment giving the

same l value. Discrepancy in current rise times could beexplained by the dispersivity of the transport which was nottaken into account in the simulations.

So, the observed increase in DoI current inRRP3HT:PCBM bulk heterojunction and TiO2 / RRP3HTstructures and good agreement of experimental data with nu-merical modeling in RRP3HT:PCBM proves that recombina-tion takes place in RRP3HT. The slower current rise inTiO2 /RRP3HT structureis caused by the lower electron mo-bility and deep trapping.3

By the integral mode TOF method, where the RC timeconstant of the measurement setup is much larger than thetransit time of the charge carriersRC ttrwe can determine

the 2D recombination parameter 2D in lamellas and theirtemperature dependencies in more convenient7,12 andstraightforward way because it is independent on materials

0.0 0.1 0.20

1x10-3

2x10-3

j[A/cm

2]

t [ms]

tex

a)

1

2

3

4

10-5 10-4 10-3 10-2 10-1 100

10

100

1000

tex

~jex

-1/2

TiO2/RRP3HT

RRP3HT:PCBM

tex

[s]

jex

[A/cm2]

tex

~jex

-3/5

b)

FIG. 2. aCharge carriers extraction observed by the integral TOF methodin TiO2 / RRP3HT1drift current of the small charge and2photocurrentsaturated on light intensity; RRP3HT:PCBM bulk heterojunction 3driftcurrent of the small charge and 4photocurrent saturated on light intensity.Estimation of extraction time is indicated. b Extraction time dependenceon the extraction current density in RRP3HT:PCBM bulk heterojunction andTiO2 /RRP3HT structures.

0.1 1 10

1

10

j/j

SCLC

t/ttr

a)

1

2

3tr/ttr

4

10-3

10-2

10-1

10-2

10-1

100

PCBM:RRP3HT

TiO2/RRP3HT

j[A/cm

2]

t[s]

b)

10-6

10-4

10-2

FIG. 1. a Simulated DoI current transients in the case of 3D Langevinrecombination 1 and 2D Langevin recombination for 2 l=10 nm, 3l =1 nm and f/sl =10,4l =1 nm andf/sl = 1; time scale is normal-ized to the faster charge carriers transit time ttrand current is normalized tospace charge limited current of faster charge carriers. b Solid linesexperimental DoI transients in RRP3HT:PCBM bulk heterojunction d=1.4 m , U= 9 V and TiO2 /RRP3HT d=0.6 m , U= 4 V struc-tures; dashed linenumerically calculated DoI current transient forRRP3HT:PCBM structure n = 10

2 cm2 / Vs, p =2.5103 cm2 /Vs, l

=1.6 nm.

013303-2 Juka et al. Appl. Phys. Lett. 95, 013303 2009


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parameters. In the case of 3D Langevin recombination, thecurrent transients saturate as a function of light intensity andthe amount of extracted charge slightly exceeds CU whend1 ,Qex= CU, thereforetex= 0. In the case of 2D Lange-vin recombination saturated charge carriers extraction timetexis estimated in the similarway as in the case of reducedbimolecular recombination,12

tex = 232D2/5 ed

jex3/5 jex3/5, 9

where jex is extraction current which could be varied bychanging loading resistance or applied voltage. To experi-mentally determine tex see Fig. 2a, the difference in thetime at high and low light intensities when the TOF tran-sients have been decreased to half of their initial value isused.7 In the case of the reduced bimolecular recombinationtexjex

1/2. Therefore, texjex dependence can show which

mechanism, 2D Langevin or reduced bimolecular recombi-nation is valid and allows evaluation of the recombinationparameter 2D.

In Fig.2bthe extraction time as a function of the den-sity of extraction current in different structures containingRRP3HT is shown. Sincetexis much larger than the RC-timeconstant of the system and shows the same dependence on

the extraction current density jex, it can be concluded that therecombination is taking place in RRP3HT and it is governedby the 2D Langevin recombination.

Figure 3 demonstrates temperature dependence of 2DLangevin recombination parameter 2D, which is propor-tional to sum of the mobilities in the lamellar structure.

In conclusion, we have used photo-CELIV, DoI currenttransients and integral TOF mode experiments to show that

the decay of the density of photogenerated charge carriers inannealed samples of RRP3HT and bulk heterojunction solarcells of RRP3HT:PCBM can be explained using a 2D Lange-vin recombination in the lamellar structure.

We acknowledge financial support from the LithuanianState Science and Studies Foundation through Contract No.C-19/2008, the Academy of Finland through the Project No.118097; Dr. G. Dennler, Dr. J. H. Smtt, and Dr. M. Lindnfor the help with the samples preparations.

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3.0 3.2 3.4 3.6 3.8 4.0

3x10-20

1x10-20

2D

[cm

9/2/s

]

1000/T [1/K]

3x10-21

FIG. 3. Temperature dependence of the 2D Langevin recombination param-eter 2D.

013303-3 Juka et al. Appl. Phys. Lett. 95, 013303 2009


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langevin recombination in regioregular poly(3-hexylthiophene)

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