Effect of Charge Trapping on Geminate Recombination and Polymer

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Effect of Charge Trapping on Geminate Recombination and Polymer Solar Cell Performance Chris Groves,*,† James C. Blakesley,‡ and Neil C. Greenham Cavendish Laboratory, Cambridge University, J.J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom ABSTRACT In this letter, we examine the effect of charge trapping on geminate recombination and organic photovoltaic performance using a Monte Carlo model. We alter the degree of charge trapping by considering energetic disorder to be spatially uncorrelated or correlated. On correlating energetic disorder, and so reducing the degree of trapping, it is found that power conversion efficiency of blend and bilayer devices improves by factors of 3.1 and 2.6, respectively. These results are related to the experimental data and quantum chemical calculations for poly[9,9-dioctylfluorene-co-bis-N,N′-(4-butylphenyl)-bis-N,N′-phenyl-1,4-phenylenediamine] (PFB)/ poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) as well as poly(3-hexylthiophene) (P3HT)/(6,6)-phenyl-C61-butyric acid methyl ester (PCBM) solar cell systems. The minimization of traps at the heterojunction between electron- and hole-accepting materials, perhaps by molecular design, appears to be a promising strategy to achieve large gains in PV performance. It is also shown that macroscopically measurable quantities such as mobility and energetic disorder are not necessarily good predictors of nanoscale geminate recombination process. KEYWORDS Photovoltaic diode, semiconducting polymer, trapping, charge transport, Monte Carlo

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rganic photovoltaics (OPVs) offer a promising route to low-cost renewable energy since they can be made from solutions of active materials using scalable printing techniques. In a typical OPV, charges are generated by dissociating photogenerated excitons at a donor/acceptor interface. However, due to the low dielectric constant (ε ∼ 3-4) of the materials commonly used, the geminate charge pair formed upon exciton dissociation experiences a strong Coulombic attraction and may recombine. Geminate charge pair recombination (GR) has been identified as a key loss mechanism in polymer/polymer1-3 OPV devices. The situation in polymer/fullerene devices is less clear with some reports showing GR limits OPV performance4-6 and others showing that bimolecular recombination7-9 dominates. In either case, improving our understanding of GR and finding ways to minimize it seems a promising route to improve the performance of OPVs to the point where they can be successfully commercialized. At the most basic level, the degree of GR in OPVs is determined by the competition between the recombination routes an interfacial geminate charge pair can take to the ground state,10 and the transport processes that lead to free charges. While this underlying principle is straightforward,

GR in OPVs is a complex process to understand and control since both recombination11-14 and transport15-17 depend sensitively upon the local configuration of the polymers or donor/acceptor domains. In this article, we examine in more detail the effect of charge transport on GR. Charge transport in the conjugated polymers, oligomers, and small molecules used in OPVs is polaronic in nature, and so transport proceeds by hops between the various polymer segments or molecules.17-19 The landscape through which the charges move is energetically disordered due to the nanoscale structural and conformational disorder typical in polymer and OPV films. This energetic disorder gives rise to the characteristic field and charge-density dependent mobility of conjugated polymers,19,20 while also playing a key role in determining the field- and temperature-dependence of GR in OPVs.21 Since the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) are energetically disordered, we should consider at what energies the geminate charges are created. As a first approximation, we might assume that geminate charges occupy random energies within the density of states.19,22,23 However, recent investigations11,12 on the poly[9,9-dioctylfluorene-co-bis-N,N′-(4butylphenyl)-bis-N,N′-phenyl-1,4-phenylenediamine] (PFB)/ poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) system suggest that this may not always be appropriate. In ref 11, quantum chemical calculations are performed to determine the nature of the lowest excited state for a variety of PFB/ F8BT chain orientations, and it is found that only some orientations have a geminate pair as the lowest excited state. Reference 11 also gives information about the energetic environment that is associated with these geminate pair

* To whom correspondence should be addressed. E-mail: Chris.Groves@ Durham.ac.uk. † Present address: School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom. ‡

Present address: The Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam-Golm, Germany. Received for review: 01/11/2010 Published on Web: 02/09/2010 © 2010 American Chemical Society

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producing regions of the heterojunction. Placing an excited F8BT and PFB chain alongside one another causes the charge distribution of the molecules to change, which in turn gives rise to a Coulombic attraction that modifies the local HOMO and LUMO level. This variation in HOMO and LUMO level at the PFB/F8BT heterojunction is additional to the energetic disorder that would be expected in pure F8BT or pure PFB. Thus the energetic distribution of the HOMO and LUMO levels at the PFB/F8BT interface is broader than in the bulk materials.12 It was found that the chain orientations that have a geminate charge pair as their lowest excited state have an attractive, that is, low energy character, and in ref 12 it is shown that this attractive interaction in PFB/F8BT heterojunctions can be as large as 80 meV. Thus the local HOMO and LUMO levels at the PFB/F8BT interface where the geminate charges are created may be depressed by up to 80 meV, and this is in addition to the Coulombic attraction between geminate charges of several hundred millielectronvolts. Thus it appears that the molecular structure of PFB/ F8BT heterojunctions favors the creation of energetically trapped geminate charges, a speculation supported by the observation that geminate charge carriers in PFB/F8BT blends hardly move prior to recombination.10 However, even if we were to disregard the molecular interactions of PFB/F8BT, we would expect a general bias for the creation of geminate charges at low energy sections of donor/ acceptor heterojunctions due to the energy dependence24 of Fo¨rster energy transfer by which excitons migrate around the device. Trapping of geminate charges at the interface will therefore, to some extent, be a general concern in OPVs. However, there are ways in which the degree of trapping can be mitigated. For example, spatial correlations in energetic disorder,25,26 which reduce the probability of charge trapping,26 have been observed in some materials.27-30 Furthermore, trapping can also be affected via the standard deviation of energetic disorder, σ, which in turn has been shown to depend on the degree of device annealing30 as well as the molecular weight31 and regioregularity32 of the polymer. So, given that the degree of trapping experienced by carriers varies between OPV systems and can be influenced by molecular design and deposition conditions, in this letter we investigate what role charge trapping has on OPV performance and what benefits can be obtained by controlling the degree of trapping. It is found that trapping can substantially affect GR, with experimentally accessible changes in the spatial distribution of energetic disorder resulting in improvements of the power conversion efficiencies of bilayer and blend OPVs by factors of 2.5 and 3.1, respectively. This suggests that strategies to minimize charge trapping, for example, molecular design of materials to minimize Coulomb interaction energy upon excitation, is a promising route to improve the performance of OPVs. The Monte Carlo model used here is similar to that reported previously.22,23,33 The polymer is represented by a cubic lattice of hopping sites spaced 1 nm apart. Blend © 2010 American Chemical Society

morphologies of average domain size 8 nm are generated by a simulated annealing method,34 while bilayer morphologies are simply defined. The device structures in all cases are 70 nm thick, and 70 nm in extent in the orthogonal directions. When choosing the arrangement of energetic disorder for use in the simulation, we consider two situations designed to give differing degrees of energetic trapping. The first is to assume that energetic disorder is spatially random, while the second is to assume energetic disorder is spatially correlated with the latter giving rise to fewer trap states.26 There are a variety of ways one can implement spatially correlated energetic disorder,25,26,30 however, since we are primarily interested in the reduction in trapping which correlated disorder provides rather than correlated disorder itself, we use the simple approach of Gartstein and Conwell.26 In ref 26, a value of energetic disorder, Ui, is first picked at random from a Gaussian distribution of width, σ for each hopping site in the simulation. Then, correlated energetic disorder values, Uj, are calculated in the following manner

Uj )

∑ K(rij)Ui

(1)

{

(2)

where

K(rij) )

N rij e rc 0 rij > rc

N is a normalization factor to determine the standard deviation of the distribution of Uj, rij is the separation between the site j and i, and rc is the correlation length. The resulting distribution of Uj is Gaussian in shape. If rc ) 0 then the value of disorder, Uj, reduces to the randomly distributed Ui, and so disorder is uncorrelated. When rc > 0, then the value of energetic disorder, Uj, is dependent upon all of the values of Ui within a radius rc, and so disorder is correlated. Here we assume rc ) 1 nm, which is within the bounds of what might occur in reality since rc ) 0 corresponds to uncorrelated disorder and in some materials rc has been determined to be as large as 3-5 molecules.28,29 In Figure 1, we show the effect of these assumptions upon the probability distribution, p, of the change in energetic disorder, ∆U between adjacent hopping sites. Here p is calculated by logging the change in energy between each pair of adjacent sites in the simulation volume. Large values of ∆U correspond to traps within the material. Despite the short-range nature of the correlation used here, the proportion of deep isolated traps is shown to be substantially reduced. Note that traps sites are picked from the same energetic distribution as all other hopping sites unless otherwise specified, in contrast to other investigations in which additional trap populations are appropriate.35 In this context of this paper, a trap is a hopping 1064

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FIGURE 1. The probability distribution p of the change in energetic disorder neighboring sites ∆U when energetic disorder was uncorrelated (squares) and correlated (circles).

site in the tail of the Gaussian density of states that is additionally surrounded by hopping sites of a higher energy. Hence our results are appropriate to any energetically disordered material. Transport proceeds via nearest neighbor hops onto the appropriate polymer type at a rate characterized by a Marcus expression

(

Rifj ) υhop exp -

(Ej - Ei + ER)2 4ERkT

)

(3)

FIGURE 2. Simulated J-V curve for PV devices in a (a) bilayer and (b) blend with 8 nm sized domains topology, when energetic disorder was uncorrelated (squares) and correlated (circles).

values give a low-field mobility of 10-4 cm2/(V s) when energetic disorder is uncorrelated. When disorder is correlated, the value of normalization factor, N, is chosen to keep σ ) 75 meV, while all other parameters are kept constant. For simplicity, electrons and holes are chosen to have the same transport parameters. First we examine the effect of correlated disorder on OPV performance. Figure 2a,b shows J-V curves for a bilayer and a blend respectively for spatially correlated and spatially random energetic disorder. For both devices, the fill factor (FF), short-circuit current and open circuit voltage (Voc) are all substantially improved in the case of spatially correlated disorder. Consequently, the power conversion efficiency of the spatially correlated bilayer and blend devices is better than that in the corresponding spatially random devices by factors of 2.5 and 3.1, respectively. Similar differences in power conversion efficiency were seen in spatially correlated and spatially random blend devices with domain sizes of 4 and 12 nm. Note that the standard deviation of energetic disorder (σ), polaron energy (2ER), hopping prefactor (υhop), and morphology are the same in both cases, and so the difference in performance arises solely because of how energetic disorder is spatially distributed. To examine more deeply the reasons for the differences observed, Figure 3 shows the bulk carrier mobility in pristine material and the

Here Ei and Ej are the potential energies of the sites i and j respectively, ER is half the polaron energy, and υhop is a prefactor which scales the mobility. Site energies include energetic disorder, the electric field, F, and all electrostatic interactions between charges and image charges. Recombination occurs between adjacent carriers at a constant rate of 107s-1. While the choice of recombination rate is somewhat arbitrary, the 100 ns lifetime of geminate charges is similar to the ∼40 ns lifetime measured PFB/F8BT blends10 as well as recent Monte Carlo simulations.16 The behavior of each carrier is then determined at random in proportion to the rates of the allowed recombination or hopping processes. Photoinjection of carriers occurs at random heterojunctions within the device at a rate G ) 1.16 × 1022 cm-3 s-1 (which corresponds to approximately 1 sun intensity for the blend device, and significantly more for the bilayer due to the reduced heterojunction area), and dark injection occurs via hopping over a 0.4 eV barrier at each contact. PV device simulations are run for a sufficient length of time, and over a sufficient number of configurations of energetic disorder, to ensure accurate sampling of average behavior. We assume that ε ) 4, half the polaron energy ER ) 0.25 eV, standard deviation of energetic disorder σ ) 75 meV, T ) 298 K, the diagonal bandgap between the donor and acceptor is 2 eV, and hopping prefactor υhop ) 1011s-1. These © 2010 American Chemical Society

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FIGURE 4. Geminate pair separation efficiency, ηGS measured for a bilayer at a field of F ) 104 V/cm (circles) and 105 V/cm (squares) as a function of the trap energy, Ut for when only the electron is trapped (open) or when both electron and hole are trapped (closed). F ) 105 V/cm and 104 V/cm correspond approximately to the field in an OPV device at short circuit and close to open circuit respectively.

FIGURE 3. Mobility, µ (solid), and geminate pair separation efficiency, ηGS (open), measured for a bilayer as a function of F. Uncorrelated disorder is represented by squares, correlated disorder is represented by circles, and triangles represent uncorrelated disorder with the mobility adjusted to match that of correlated disorder at the same field.

of 50 meV, whereas ηGS is halved when the trap energy is increased to 125 meV and is almost zero for trap energies of 150 meV. In the situation when both carriers are trapped, we observe similarities between the modeled data and spectroscopic data for PFB/F8BT,10 as a proportion of the trapped geminate charges recombine at the positions in which they were injected. Note that this is in contrast to our previous simulations,23 in which carriers were generated at random energies within the HOMO and LUMO. There it was observed that geminate charges moved significant distances along the plane of the interface, and so it seems that immobile geminate charges are a result of strong Coulombic attraction and interfacial charge trapping. Now if we consider the effects of only one carrier being trapped, as may occur in a blend system with differing values of σ, for example poly(2-methyloxy-5-(3′,7′-dimethyloctyloxy)-p-phenylene vinylene (OC1C10PPV)/(6,6)-phenyl-C61-butyric acid methyl ester (PCBM),37 the value of ηGS drops only marginally with increasing trap energy. This suggests that trapping of one carrier does not necessarily lead to GR. Of course, while GR may be avoided with the escape of one carrier, the remaining carrier may act as a bimolecular recombination center.38 However, we note that the trapped charge is more likely to move after the removal of the separated carrier due to the lessening of the Coulomb interaction, and so may not necessarily lead to a loss in OPV performance. As an aside, we also examined the effect both carriers having excess energy, that is, with Ut being negative. We could discern no difference in ηGS when Ut ) 0 and when electrons and holes are injected with an excess energy of 150 meV (i.e., Ut ) -150 meV for electrons and Ut ) 150 meV for holes), showing that the “hot” carriers thermalized rapidly in this simulation and gained no subsequent advantage to their dissociation behavior. We examine the effect that trapping both charge carriers has upon the field dependence of ηGS for a bilayer in Figure 5a. As expected, increasing trap energy requires that the

geminate separation efficiency, ηGS measured on a bilayer when disorder is spatially correlated and spatially random. Geminate separation efficiency is predicted by performing many trials in which a single charge pair is injected at a random heterojunction position in a bilayer device, and the eventual fate of the carriers is noted. For the purposes of this simulation, successful separation is defined as when carriers are separated by more than the thermal capture radius (here 16 nm). While spatially correlated disorder shows a slightly larger mobility than spatially random disorder (as expected26), there is a profound difference in ηGS, especially at low fields, which in turn leads to the large increases in FF seen in Figure 2. To test whether difference in mobility is the sole cause of the difference in ηGS,23 the spatially random simulation was repeated with υhop scaled to give the same mobility as for the spatially correlated simulation at the same field. It is found that the difference in mobility accounts for only a small portion of the difference in separation efficiency. Therefore, it is the arrangement of the energetic disorder, and not the mobility, that is the primary cause of the difference in spatially random and spatially correlated OPV performance. The observation that bulk mobility does not always well describe OPV performance has been made by a number of other authors.13,16,36 We now examine the effect of trapping more explicitly by determining ηGS as a function of the energy with which geminate charges are injected in an otherwise spatially random energetic environment. Figure 4 shows ηGS when only the electron is trapped, with energy +Ut, and when the electron and hole are both trapped, with energy +Ut and -Ut respectively, at values of electric field that approximate short-circuit and close to open-circuit conditions in an OPV. First we shall consider the data corresponding to both carriers being trapped, which may correspond to the situation in PFB/F8BT OPVs.11 At fields approximating to short circuit, the effect of trapping is negligible below trap energies © 2010 American Chemical Society

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we are not attempting to fit experimental data here, it is interesting to speculate as to why ηGS is only ∼50% for a bilayer when Ut ) 0 and F ) 105 V/cm, while poly(3hexylthiophene) (P3HT)/PCBM blend solar cells have ηGS ∼60% under the same conditions,39 noting that bilayers provide better conditions for geminate pair separation than blends.23 Spano28 has shown that the low-temperature emission from thin films of P3HT can be explained very well if one considers energetic disorder to be correlated over 3-4 molecules. Hence, correlated disorder of the P3HT in P3HT/ PCBM blended solar cells may play a role in improving the dissociation probability above that which would be expected for uncorrelated disorder, as in Figure 2. Note however, that a complete description of why P3HT/PCBM solar cells operate efficiently will probably be due to many factors including, for example, the high on-chain mobility of P3HT16 and the ability to tune the morphology to an optimum configuration by annealing.36 Recently it has been shown that poly[N-900hepta-decanyl-2,7-carbazole-alt-5,5-(40,70-di-2-thienyl20,10,30-benzothiadiazole) (PCDTBT), when blended with fullerene has ηGS approaching 100%,40 a surprising value when again noting that the bulk heterojunction is not optimal for geminate pair separation.23 It would be interesting to examine PCDTBT to see whether energetic disorder is spatially ordered in a fashion that reduces the probability of trapping. We also include fits to data in Figure 5a by the effective medium Onsager-Braun41 model. A full description of the equations and fitting procedure for this and subsequent models is given in the Supporting Information. The OnsagerBraun model is a simple technique that has often been used empirically to describe the field dependence of photocurrents. Best fits were obtained when the dimensionless ratio of the zero-field dissociation rate and recombination rate was 0.174, 0.151, 0.0673, and 1.64 × 10-2 for a trap energies of 0, 50, 100, and 150 meV, respectively. It can be seen that generally the quality of the fits are rather poor since they do not capture the gradual nature of the improvement in dissociation efficiency with increasing field. This is to be expected, as the model assumes a single value for the initial charge-pair separation, r, and corresponding binding energy, ∆E, and hence does not represent an ensemble of disordered systems in which some charge pairs are more easily dissociated than others. Additionally, the Onsager-Braun model does not fully capture the physics relevant to charge separation.42 In the present Monte Carlo model, we do not consider positional disorder that would give rise to a distribution in r, but there is still a variation in escape probability due to the difference between the energy of the injection site (Ut) and the random energy of the disordered surroundings. To improve the fit to the modeled data, we must therefore consider a model which, in some manner, allows carriers to have a distribution in escape probability. We repeated the fitting using the method of Goliber and Perlstein,43 in which an ensemble value for ηGS is derived

FIGURE 5. Geminate pair separation efficiency, ηGS measured for a bilayer as a function of field for electron and hole trap energies Ut ) 0, 50, 100, and 150 meV. Symbols are Monte Carlo predictions, while solid lines denote (a) Onsager-Braun fits, (b) standard GoliberPerlstein fits with a Gaussian distribution of initial starting radii, and (c) fitting with Onsager-Braun while using a Gaussian distribution of initial binding energies. In panels b and c, the parameters used for the fits were a mobility of 10-4 cm2/(V s) and a recombination rate of 107 s-1 as used in the Monte Carlo simulations. In panel c, the binding energy is assumed to be Gaussian distributed with a width of 150 meV, in essence assuming that each carrier contributes 75 meV independently to the overall energy distribution.

field be increased to maintain a particular value of ηGS. However, it is interesting to note the nonlinear reduction in ηGS with increasing trap energy. This shows that even modest improvements in trapping, for example by reducing σ, could yield sizable improvements in device efficiency. Although © 2010 American Chemical Society

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by assuming a Gaussian distribution of initial charge-pair separation distances. When using the same values of mobility and recombination rate as for the Monte Carlo simulation, we found that reasonable fits were obtained using average initial separation radii, a, of 2.4, 2.3, 1.7, and 0.87 for values of Ut ) 0, 50, 100, 150, respectively (see Figure 5b). Interface trapping can therefore be represented by a reduction in the initial separation radius in the Goliber and Perlstein model. A further improvement in fitting was observed (Figure 5c) when we modified the distribution of initial charge-pair separation distances such that the initial charge-pair binding energy, ∆E, formed a Gaussian distribution with a width of 150 meV (assuming that each carrier independently samples an environment with 75 meV disorder). Considering that there is only one free parameter, the mean binding energy, remarkably good descriptions of the Monte Carlo results are obtained with mean ∆E of 130, 140, 210, and 400 meV, for increasing trap energies, respectively. While this model empirically describes the Monte Carlo simulations very well, it is clear that there is not a simple direct relationship between Ut in the Monte Carlo simulation and ∆E in Onsager-Braun type models. Here we have presented simulation results which have shown the importance of trapping upon the GR process and ultimately OPV performance. Devices which display spatially random, or uncorrelated, disorder are compared with those that have spatially correlated disorder. It is found that devices with spatially correlated disorder, which exhibit a smaller degree of trapping than in the devices with spatially random disorder, have substantially improved power conversion efficiencies of blend and bilayer devices by factors of 3.1 and 2.5, respectively. These improvements are shown to have little to do with the variations in bulk mobility between the two cases examined and are instead primarily due to the spatial arrangement of energetic disorder. This suggests that considering GR in terms of bulk parameters is not always appropriate and that considering the local properties of materials and blends would provide better understanding.44 Closer examination of the effect of trap energy has uncovered detailed behavior depending upon whether one or both carriers are trapped. Both carriers being trapped, as may occur in PFB/F8BT solar cells, is shown to significantly affect geminate separation yield. By contrast, strong trapping of only one charge carrier is shown to only slightly affect separation efficiency. These findings have suggested that reducing the degree of trapping, either by molecular design or by altering the processing conditions, could be a very productive route to improving the performance of OPVs.

Additional simulations were performed on the Hamilton Computing Cluster at the University of Durham. The authors thank David Beljonne of the University of Mons-Hainaut, and Jan Anton Koster of the University of Eindoven for many useful discussions. Supporting Information Available. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1)

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Acknowledgment. This work was supported by the European Commission FP-6 program MODECOM (NMP-CT2006-016434), and was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England. © 2010 American Chemical Society

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DOI: 10.1021/nl100080r | Nano Lett. 2010, 10, 1063-–1069