Charge Carrier Dissociation and Recombination in Polymer Solar Cells
CCharge Carrier Dissociation and Recombination in Polymer Solar Cells
C. Deibel a Experimental Physics VI, Julius-Maximilians-University of W¨urzburg, D-97074 W¨urzburg
In polymer:fullerene solar cells, the origin of the losses in the field-dependent photocurrent is still controver-sially debated. We contribute to the ongoing discussion by performing photo-induced charge extraction mea-surements on poly(3-hexylthiophene-2,5-diyl):[6,6]-phenyl-C butyric acid methyl ester solar cells in order toinvestigate the processes ruling charge carrier decay. Calculating the drift length of photogenerated charges, wefind that polaron recombination is not limiting the photocurrent for annealed devices. Additionally, we appliedMonte Carlo simulations on blends of conjugated polymer chain donors with acceptor molecules in order togain insight into the polaron pair dissociation. The dissociation yield turns out to be rather high, with only aweak field dependence. With this complementary view on dissociation and recombination, we stress the im-portance of accounting for polaron pair dissociation, polaron recombination as well as charge extraction whenconsidering the loss mechanisms in organic solar cells. PACS numbers: 71.23.An, 72.20.Jv, 72.80.Le, 73.50.Pz, 73.63.BdKeywords: organic semiconductors; polymers; photovoltaic effect; charge carrier recombination
The performance of polymer based solar cells has increasedsteadily over the years, culminating in 6% power conversionefficiency achieved recently . For a further optimization, amore fundamental understanding of the recombination pro-cesses in these devices is necessary, but a unified model hasnot been presented yet. Indeed,the dominant loss mechanismof the photocurrent remains a controversially debated issue.In order to understand the importance of loss mechanisms,we briefly describe the steps taken from absorbed light toflowing photocurrent, as shown in Fig. 1. For details, we re-fer to the book by Brabec et al. Light transmitted through thetransparent anode of the solar cell, typically indium tin oxideon glass, is absorbed mainly in one constituent of the pho-toactive organic semiconductor blend, the conjugated poly-mer. Singlet excitons are generated. These neutral excita-tions can move by diffusion, but due to their high bindingenergy cannot be separated spontaneously at room tempera-ture. If they do not reach a donor–acceptor interface withintheir lifetime, they will recombine radiatively (a), sending outphotoluminescence. Reaching the heterointerface, however,an electron transfer to the acceptor molecular yields a polaronpair with almost 100% yield (b), which can be separated—assisted by processes discussed later in the text—with a highyield. On the way of the separated charge carriers to theirrespective electrodes, charges can be trapped , or bimolecu-lar recombination (c) can take place, although usually with alow rate . Also, the extraction of the photogenerated chargesis influenced by the selectivity of the electrodes, namely thesurface recombination velocity for electrons and holes .Coming back to the discussion on the dominant loss mech-anism, polaron pair dissociation or polaron recombination. In2004, Mihailetchi et al. described the experimental photocur-rent of a bulk heterojunction solar cell completely by polaronpair dissociation, applying the Braun–Onsager model , alsoconsidering a minor contribution of diffusion . The field-dependence of the photocurrent was described relative to the a Electronic address: [email protected] F u ll e r e n e CathodeTransparent Anode P o l y m e r (a)(b) (c) FIG. 1: The steps from light absorption to the flow of photocurrentin a polymer solar cell, and some loss mechanisms: (a) Photolumi-nescence due to excitons not reaching the dono–acceptor interfaceduring their lifetime. (b) Polaron pair dissociation or geminate re-combination, respectively. (c) Bimolecular polaron recombination. voltage V , where the photocurrent becomes zero. As theproperties of organic semiconductors under dark and illumi-nation are not identical, this is not a physically well-definedquantity. Last year, Ooi et al. presented investigations of thephotocurrent of polymer based solar cells by a pulsed tech-nique. They found a point of optimum symmetry, V pos , rel-ative to which the field dependence of the photocurrent is al-most identical in forward and reverse voltage direction. Theyassigned this voltage to the built-in voltage. Although notperforming a quantitative fit to the photocurrent, they assignthe shape of the field dependent photocurrent to the importantprocess of charge collection, implying a field independent po-laron pair dissociation, which is in contrast to the results ofMihailetchi et al. . In both publications , the influence of a r X i v : . [ c ond - m a t . m t r l - s c i ] J u l polaron recombination is neglected. Indeed, recent measure-ments of charge carrier loss processes in bulk heterojunctionsolar cells, applying the versatile Photo-CELIV technique,photo-induced charge extraction by linearly increasing volt-age , show that the recombination rate is very low .The charge carrier dynamics are found to follow the temper-ature dependence of the bimolecular Langevin theory , butwith a reduced prefactor . Other reports point out that theorder of the decay is larger than two, which is expected forbimolecular processes, but between 2.5 and 3.5 . Expla-nations for this behaviour are still debated , but the ex-perimental findings agree that the recombination rates foundin bulk heterojunction solar cells are low. Nevertheless, thequestion wether the photocurrent in bulk heterojunctions canbe described by one dominant process of polaron pair disso-ciation, polaron recombination, and polaron extraction, or ifa combination of all three is necessary, has not yet been ad-dressed.In this paper, we will present experiments and simulationson polaron pair dissociation and polaron recombination, in or-der to contribute to this issue. We find that a unified modelwill have to consider dissociation, recombination as well ascharge extraction simultaneously, although polaron recombi-nation can be mostly neglected for annealed state-of-the-artbulk heterojunction solar cells.Polymer based solar cells where processed by spin coat-ing poly(3-hexylthiophene-2,5-diyl) (P3HT):[6,6]-phenyl-C butyric acid methyl ester (PCBM) blends made from a so-lution of (20mg P3HT+20mg PCBM) per ml chlorobenzene,on poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)covered indium tin oxide/glass substrates. The active layerwas about 105nm thick. Aluminum anodes were evaporatedthermally. The annealed samples were subsequently treatedfor 10 minutes at 140 ◦ C. P3HT was purchased from RiekeMetals, PCBM from Solenne. All materials were used with-out further purification.The preparation steps were done in anitrogen glovebox with attached thermal evaporation cham-ber.The samples were characterized in a He contact gas cryostatby current–voltage measurements as well as the photo-CELIVmethod. After a nanosecond laser pulse, the solar cell beingheld at the built-in voltage, the photogenerated charge carriersare extracted after a given delay time by an extraction voltage.The details of this method are described in Ref. . The inset ofFig. 2 shows the schematic measurement cycle. The sampleis held at the built-in potential. A nanosecond laser pulse isabsorbed in the sample, generating excitons, and from thesepolaron pairs are formed due to the highly efficient chargetransfer. During a variable delay time, the charge carriers canrecombine, reducing the carrier concentration within the de-vice. After the delay time, two consecutive triangular volt-age extraction pulses—in reverse bias direction—are appliedin superposition of the built-in potential, separated by a shortwaiting time. The first voltage pulse extracts all remainingphotogenerated charge carriers, plus charges from doping andinjection. As the latter two mechanisms are not in the focusof our investigations, the second voltage pulse helps to dis-criminate them from the photogenerated charges, which have j [ x - A / c m ] -3 s] tlaser extraction pulses0-t d V bi -V delay time t d µ s 100ms T=260K FIG. 2: Photo-CELIV measurement of a P3HT:PCBM solar cell at260K with variable delay between laser pulse and charge extraction.For longer delay times, loss mechanisms reduce the signal magni-tude. The right extraction signal was recorded without laser pulse, itshows the contribution of injected charge carriers. The inset showsthe schematic Photo-CELIV experiment: laser pulse, and–after a de-lay time t d —two voltage pulses in reverse bias direction for chargeextraction. In the experiment, the extraction pulse length was µ s,and the waiting time between the two consecutive extraction pulses µ s. already been drawn from the sample during the first pulse.By changing the delay time between laser pulse and chargeextraction voltage pulses, a time resolution in analogy to apump–probe experiment can be achieved, yielding the car-rier concentration vs. time dependence. Another outstandingfeature of photo-CELIV is the simultaneous determination ofcharge carrier mobility and concentration of the extracted car-riers. Its almost only drawback is that, in contrast to transientphotoconductivity , electrons and holes cannot be discrimi-nated.Retracing the derivation of the photo-CELIV analysis aspublished by Juska et al. in 2000 due to the authors ofRef. , and comparing it to the original result for the mobility µ (Ref. , Eqn. (5)), we found a somewhat different outcome.Solving the Riccatti equation numerically, we find µ = 23 L At max (1 + 0 . j/j (0)) , (1)with the original factor . replaced by . . L is the devicethickness, A is slope of the extraction pulse, and ∆ j/j theheight of the current extration peak relative to the dielectriccontribution. In the normalised parameter space At max vs. ∆ j/j , the error of Eqn. (1) is below for ∆ j/j < ,whereas the original evaluation is only in the range of < .Thus, we use Eqn. (1) for the evaluation of all our CELIVmeasurements.An exemplary photo-CELIV measurement with variabledelay time between laser pulse and charge extraction for anannealed solar cell at 260K is shown in Fig. 2. The evalua-tion of the extracted charges over delay time yields the time-dependent carrier concentration n ( t ) , which we could fit withthe carrier continuity equation, dndt = G − R = G − ζγnp. (2)Here, the spatial derivative of the current is expected to bezero at the built-in potential. G is the generation term; withthe laser pulse at t = 0 , it is zero thereafter. We have shownhere only a bimolecular recombination rate R , also assum-ing the electron and hole concentrations n resp. p to be equal. γ = q/(cid:15) · µ is the Langevin recombination parameter, with theelementary charge q , the effective dielectric constant (cid:15) , andthe sum of electron and hole mobility µ . ζ is a correctionfactor: We found that polaron losses in the solar cells can bedescribed only by a reduced Langevin recombination. Thisworks well for pristine devices; for annealed samples, a car-rier concentration dependent prefactor leads to an even betteragreement, yielding a third order decay. The latter is probablyrelated to delayed recombination due to trapping , however,it makes a difference only for long decay times not that rele-vant to steady-state solar cell operation, we concentrate on thereduced bimolecular recombination here. We found ζ to bebetween . and − , the details of which are described inRef. . At temperatures above 260K, the evaluation was madedifficult by charge carrier injection, which can already be seenin Fig. 2 for the right extraction peak, which was recordedwithout laser excitation.In order to consider how relevant polaron recombinationis for a working solar cell, we evaluate the mobility–lifetimeproduct µτ . It is a measure of how efficiently charges can beextracted before recombination. It is used to calculate the driftlength d c , which should exceed the device length in order toyield an efficient charge extraction. The drift length is givenas d c = µτ F, (3)where F is the electric field acting on the charges. In order tocalculate an effective lifetime, the recombination rate has tobe reshaped to R = n/τ , τ = ( ζγn ) − . (4)We point out that this effective lifetime depends on the car-rier concentration. Now, the mobility–lifetime product can beeasily derived, µτ = (cid:16) ζ q(cid:15) n (cid:17) − . (5)From the experimental photo-CELIV data, n , µ and ζ candirectly be extracted. Thus, using the experimental data, thetemperature dependent µτ product can be calculated accord-ing to Eqn. (5). The data for temperatures above 260K couldnot be used due to dark injection currents disturbing the dataanalysis. Generally, the carrier concentration—needed for the -142468 -132468 -12 M ob ili t y x L i f e t i m e [ m / V ] FIG. 3: The µτ product for the pristine and annealed bulk hetero-junction solar cells. calculation of the effective lifetime—was taken at the mini-mum delay time of 5 µ s. For the annealed sample, the carrierconcentration has its maximum at these short times. This isalso true for the pristine sample at 180K, but for higher tem-peratures, the carrier concentration is already decreased some-what at the minimum delay time. The resulting underesti-mated concentration (factor 2 at 260K) yields a correspondingoverestimation of τ . However, as the laser used in the photo-CELIV experiment generally leads to clearly higher light in-tensities as compared to solar radiation, a solar cell under op-erating conditions will have lower steady state carrier concen-trations, and the resulting lifetimes could even be longer. InFig. 3, the µτ product for the pristine and annealed sample isshown.In order to estimate the collection distance, the extractionfield F = ( V bi − V ) /L still needs to be determined. L isthe sample thickness, V the applied voltage. The compen-sation voltage of photo-CELIV measurements, at which thetransient photocurrent becomes zero, corresponds to the built-in potential V bi . For the pristine sample we determine a com-pensation voltage of 0.95V, for the annealed sample of 0.85V.From the current–voltage characteristics under illuminationof 100mW/cm (Fig. 4), the corresponding open circuit volt-ages can be determined. At room temperature, they are 0.74Vand 0.62V, respectively, and higher at lower temperatures asshown in Fig. 5. Therefore, we estimate an internal voltage V bi − V of approx. 0.2V at open circuit for both samples, and0.95 resp. 0.85V at short circuit for the pristine and the an-nealed sample. The resulting collection distance, calculatedusing Eqn. (3), is shown in Fig. 6. Generally, d c is larger thanthe device thickness L = 105 nm at temperatures above 200K,except for the pristine cell at open circuit conditions. This im-portant result is in agreement with our published macroscopicsimulation of the influence of the charge carrier mobility onthe solar cell performance , and also with the carrier concen- -8-40 C u rr en t D en s i t y [ m A / c m ] FIG. 4: Current–voltage characteristics of (a) pristine and (b) an-nealed P3HT:PCBM solar cell in dependence on temperature. tration evaluated in Ref. . Thus, we find that in state-of-the-artpolymer solar cells, the nongeminate, bimolecular recombi-nation of electrons and holes is not limiting the performanceunder most conditions.In order to achieve a complementary view on the limitingfactors in polymer solar cells, we also consider polaron pairdissociation. This was done by performing Monte Carlo sim-ulations of hopping transport in a gaussian density of stateswithin a cubic lattice of × × sites (with one hop-ping site per cubic nm). Some sites are considered electron,some hole transporting, in order to simulate a blend system.The width of the gaussian density of states distribution ofthe polymer donor was set to 75meV, and to 60meV for thefullerene acceptor, according to experimental results of ours.The dielectric constant of the blend was chosen to be 3.7.An electric field was applied along the long axis, it was as-sumed to be constant. For the other two directions, periodicboundary conditions were introduced. Coulomb interactionof the charge carriers as well as geminate and nongeminaterecombination were accounted for. We extended the modelin order to take intrachain transport along conjugated seg-ments of the polymer chains into account. Therefore, we in-troduced an effective conjugation length CL , consisting of 4or 10 monomer units, along which the charge transport—dueto delocalization—is assumed to be instantaneous. The hop-ping process between the conjugated segments was calculatedusing the Miller-Abrahams jump rate. The results were av-eraged over at least 200 runs, with ten polaron pairs per run.Details of this approach are described elsewhere .Assuming a perfect exciton dissociation, we just consideredthe charge transfer state: polaron pairs. They were generatedon adjacent sites, the hole on a donor site and the electron onan acceptor site. During the Monte Carlo steps of hopping,they can either separate—assisted by the energetic disorderand the electric field—or recombine. The latter process hap- V o c [ V ] j sc [ m A / c m ] F ill F a c t o r [ % ] x6 pristine annealed FIG. 5: Open circuit voltage V oc (top), short circuit current density j sc (middle) and fill factor (bottom) of a pristine (dashed line) andannealed (solid line) P3HT:PCBM solar cell in dependence on tem-perature. The pristine samples levels off at low temperatures due todouble diode behaviour, the annealed device is limited by the built-in potential. The corresponding current–voltage characteristics areshown in Fig. 4 pens with an effective recombination rate k eff = τ − eff , corre-sponding to the inverse effective lifetime of the polaron pair.A polaron pair was considered separated once one of its con-stituents reached an electrode.The dissociation yield, describing the successful separationof a polaron pair, is shown in dependence on the conjuga-tion length in Fig. 7. We considered two electric fields, 0and V/m. The latter corresponds to the short circuit casein a 100nm thick device with a built-in voltage of 1V. Thus,the two fields approximately span the fourth quadrant of thecurrent–voltage characteristics of a bulk heterojunction solarcell under illumination. For both effective lifetimes consid-ered, 10ns and 10 µ s, the field dependence of the dissociationprocess is not negligible, but weak. A dissociation yield be-ing comparable to the external quantum efficiency—havingits maximum around 80%—can thus only be achieved whenconsidering the effective conjugation length of the polymerchains. The fast intrachain process leads to an efficient chargepair separation process. This significant outcome implies thatin a state-of-the-art polymer solar cell under working condi-tions, the field dependence of the polaron pair dissociationwill reduce the fill factor, but only slightly.In accordance with our Monte Carlo simulations, we point C o ll e c t i on D i s t an c e [ n m ] FIG. 6: Collection distance of pristine (dashed line) and annealed(solid line) P3HT:PCBM solar cell in dependence of temperature.The internal field under short circuit and open circuit conditions wasused in Eqn. (3). The dotted line indicates the thickness of the bulkheterojunction solar cell of 105nm. D i ss o c i a t i on Y i e l d V/m τ eff =10ns τ eff =10 µ s FIG. 7: Monte Carlo simulation of the dissociation yield of a polaronpair in dependence of the conjugation length CL at T = 300 K. Twodifferent fields are shown, V/m and V/m, corresponding to theflat band case and the short circuit condition, respectively. out that we do expect the free polaron generation to be electricfield dependent, in contrast to the proposition by Ooi et al. ,who make the charge collection solely responsible for the pho-tocurrent losses. Another publication could be misunder-stood to imply that the dominant loss mechanism in polymer solar cells is only due to bimolecular polaron recombination.The authors found that the same bimolecular recombinationcurrent dominates the dark current and the illuminated solarcell under open circuit. We note that their methods only con-sider polaron recombination currents, not polaron pair recom-bination.From our investigations, we find the photocurrent in or-ganic solar cells to be influenced by polaron pair dissociation,polaron recombination and also charge extraction. However,we see the need to distinguish between pristine and annealedP3HT:PCBM solar cells in discussing the limiting factors. Inannealed samples, the performance is not limited by polaronrecombination. We expect, however, a slightly field dependentpolaron pair dissociation, which also influences the fill factorand thus the photocurrent. In contrast, pristine devices show amore severly limited photocurrent and fill factor as comparedto their annealed couterparts. From our experiments, we seethat the drift length particularly at low fields is not sufficientfor a high yield of charge extraction. Thus, the photocurrentof pristine P3HT:PCBM solar cells is limited by both, polaronpair dissociation and polaron recombination, but in annealeddevices mostly the influence of polaron pair dissociation isseen. The process of charge extraction needs to be accountedfor in both, pristine and annealed devices.In conclusion, we investigated the polaron pair dissociationand polaron recombination in pristine and annealed bulk het-erojunction solar cells based on P3HT:PCBM blends by us-ing photo-induced charge extraction experiments as well asMonte Carlo simulations. From our experiments, we find thatthe collection distance is larger than the device thickness un-der most conditions, except for the pristine cell at open cir-cuit. Therefore, the photocurrent of state-of-the art polymersolar cells is not limited by the recombination of free po-larons. Concerning polaron pair dissociation, we found veryhigh separation yields due to the delocalization of charge car-riers along conjugated segments of the donor polymer chains.This is accompanied by only a weak field dependence of theyield in the range relevant for solar cells under working condi-tions, with a significant amount of dissociation already at zerofield. The latter is driven by the energetic and spatial disorder,but only made possible by delocalization along the extendedpolymer chains. Finally, the photocurrent of polymer solarcells can only be described accurately when polaron pair dis-sociation, polaron recombination as well as charge extractionare taken into account. This can only be done with macro-scopic simulations applying the appropriate physical models. Acknowledgments
The author thanks the Chair of Experimental Physics VIfor its continuing support, in particular the people involved inthe experiments, simulations and discussions around this pa-per: Vladimir Dyakonov, Andreas Baumann, Alexander Wa-genpfahl and Thomas Strobel. S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon,D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, Nat. Photon. ,297 (2009). C. Brabec, U. Scherf, and V. Dyakonov, Organic Photovoltaics(Wiley VCH, Weinheim, Germany, 2008). J. Schafferhans, A. Baumann, C. Deibel, and V. Dyakonov, Appl.Phys. Lett. , 093303 (2008). A. Pivrikas, G. Juˇska, A. J. Mozer, M. Scharber, K. Arlauskas,N. S. Sariciftci, H. Stubb, and R. ¨Osterbacka, Phys. Rev. Lett. ,176806 (2005). C. Deibel, A. Baumann, and V. Dyakonov, Appl. Phys. Lett. ,163303 (2008). J. C. Scott and G. G. Malliaras, Chem. Phys. Lett. , 115 (1999). Z. E. Ooi, R. Jin, J. Huang, Y. F. Loo, A. Sellinger, and J. C.de Mello, J. Mater. Chem. , 1605 (2008). V. D. Mihailetchi, L. J. A. Koster, J. C. Hummelen, and P. W. M.Blom, Phys. Rev. Lett. , 216601 (2004). C. L. Braun, J. Chem. Phys. (9), 4157 (1984). L. Onsager, Phys. Rev. , 554 (1938). R. Sokel and R. C. Hughes, J. Appl. Phys. , 7414 (1982). G. Juˇska, K. Arlauskas, M. Vili¯unas, and J. Koˇcka, Phys. Rev.Lett. , 4946 (2000). A. J. Mozer, G. Dennler, N. S. Sariciftci, M. Westerling,A. Pivrikas, R. ¨Osterbacka, and G. Juˇska, Phys. Rev. B , 035217(2005). G. Juska, K. Arlauskas, J. Stuchlik, and R. Osterbacka, J. Non-Cryst. Sol. , 1167 (2006). G. Juˇska, K. Geneviˇcius, N. Nekraˇsas, G. Sliauˇzys, andR. ¨Osterbacka, Appl. Phys. Lett. , 013303 (2009). M. Pope and C. E. Swenberg, Electronic Processes in OrganicCrystals and Polymers, 2nd edition (Oxford University Press,USA, 1999). C. G. Shuttle, B. O’Regan, A. M. Ballantyne, J. Nelson, D. D. C.Bradley, J. de Mello, and J. R. Durrant, Appl. Phys. Lett. ,093311 (2008). G. Juˇska, K. Geneviˇcius, N. Nekraˇsas, G. Sliauˇzys, andG. Dennler, Appl. Phys. Lett. , 143303 (2008). A. Foertig, A. Baumann, D. Rauh, V. Dyakonov, and C. Deibel,Charge carrier concentration and temperature dependent recom-bination in polymer–fullerene solar cells, arXiv:0907.1401 [cond-mat.mtrl-sci], 2009. A. Baumann, J. Lorrmann, C. Deibel, and V. Dyakonov, Appl.Phys. Lett. , 252104 (2008). S. Bange, M. schubert, and D. Neher, Charge mobility deter-mination by current extraction under linear increasing voltages:the case of non-equilibrium charges andeld-dependent mobilities,arXiv:0907.1513 [cond-mat.mtrl-sci], 2009. G. Juˇsska, K. Arlauskas, M. Vili¯unas, K. Geneviˇcius,R. ¨Osterbacka, and H. Stubb, Phys. Rev. B , R16235 (2000). J. Bisquert and V. S. Vikhrekno, J. Phys. Chem. B , 2313(2004). C. Deibel, A. Wagenpfahl, and V. Dyakonov, Phys. Stat. Sol.Rapid Research Letters , 175 (2008). C. Deibel, T. Strobel, and V. Dyakonov, Phys. Rev. Lett. (2009). C. G. Shuttle, A. Maurano, R. Hamilton, B. O’Regan, J. C.de Mello, and J. R. Durrant, Appl. Phys. Lett.93