Interplay Between Triplet-, Singlet-Charge Transfer States and Free

Article pubs.acs.org/JPCC

Interplay Between Triplet‑, Singlet-Charge Transfer States and Free Charge Carriers Defining Bimolecular Recombination Rate Constant of Organic Solar Cells Ardalan Armin,*,† James R. Durrant,‡,§ and Safa Shoaee*,∥ †

Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia Campus, Brisbane 4072, Australia ‡ SPECIFIC IKC, Swansea University, Baglan Bay Innovation Centre, Port Talbot, Swansea SA12 7AX, United Kingdom § Centre for Plastic Electronics, Department of Chemistry, Imperial College London, London SW7 2AZ, U.K. ∥ Optoelectronics of Organic Semiconductors, Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany S Supporting Information *

ABSTRACT: Despite the myriad of organic donor:acceptor materials, only few systems have emerged in the life of organic solar cells to exhibit considerable reduced bimolecular recombination, with respect to the random encounter rate given by the Langevin equation. Monte Carlo simulations have revealed that the rate constant of the formation of electron−hole bound states depends on the random encounter of opposite charges and is nearly given by the Langevin equation for the domain sizes relevant to efficient bulk heterojunction systems. Recently, three studies suggested that charge transfer states dissociating much faster than their decay rate to the ground state, can result in reduced bimolecular recombination by lowering the recombination rate to the ground state as a loss pathway. A separate study identified another loss pathway and suggested that forbidden back electron transfer from triplet charge transfer states to triplet excitons is a key to achieving reduced recombination. Herein we further explain the reduced bimolecular recombination by investigating the limitations of these two proposals. By solving kinetic rate equations for a BHJ system with realistic rates, we show that both of these previously presented conditions must only be held at the same time for a system to exhibit non-Langevin behavior. We demonstrate that suppression of both of the parallel loss channels of singlet and triplet states can be achieved through increasing the dissociation rate of the charge transfer states; a crucial requirement to achieve a high charge carrier extraction efficiency.

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exhibited certain degrees of order in molecular packing,7 charge transport still remains a hopping process in these systems with very short-range delocalization of the charge carrier wavefunctions between the sites. As such (bulk) charge carrier mobility in diodes has rarely exceeded 0.1 cm2 V−1 s−1,8 although larger values have been reported in transistors,9 operating in different carrier concentration, electric field, and morphological regimes to diodes. Another obstacle to improving charge extraction is the electron mobility of the acceptors; fullerenes are the most dominantly used acceptors, with electron mobility on the order of 10−3 cm2 V−1 s−1. Several studies have shown that slower carriers limit the charge collection efficiency,2,10 and thus further increasing the hole mobility of the donors blended with fullerenes has no beneficial impact on the efficiency as long as the electron mobility is limited by the acceptor. 11,12 Yet there has been no donor:acceptor system reported with slower carrier mobility exceeding 10−3 cm2 V−1 s−1. As such and failing to further

INTRODUCTION In organic solar cell, charge collection efficiency is the result of the competition between bimolecular recombination of the charge carriers and their extraction rate at the electrodes;1−3 dictating the thickness of the active layer. In particular, in junctions with active layer thickness on the order of several hundreds of nanometer−favorable for scaling up and large scale fabrication−the built-in electric field is smaller than that of thin (100) has been reported only in very few systems in the life history of organic solar cells.22 Based on a previous work of Koster et al.23 and new experimental evidence, Burke et al.24 and Armin et al.22 have suggested that a highly reduced recombination may originate from a fast dissociation of the charge transfer states with respect to their decay rate to the ground state. This results not only in an efficient charge generation but also lowers the bimolecular recombination through slowing the decay rate of the CT states to the ground state, as the main loss channel.25,26 We note that the relation between intrinsic recombination of bound species and bulk recombination has been theoretically investigated by Hilczer and Tachiya.27 In another study, Rao et al. have suggested that triplet CT states (formed through encountering free charges) have a different loss channel from the singlet states.28 The authors proposed that if the back electron transfer from triplet CT states to triplet excitons is turned off, this can

Figure 1. State diagram of the BHJ solar cells considering the role of spin. The two main loss pathways of the CT states to the ground states are the decay of singlet CT states at the rate kf to the ground state and the loss of the triplet CT states through back electron transfer to triplet excitons at rate kBET.

a scheme singlet excitons are generated upon photoexcitation at rate Gopt, creating singlet CT states (1CT) at rate kd,ex. 1CT can then decay to the ground state (geminate loss) at rate kf or dissociate to free carriers at rate kd. Bimolecular recombination of spin uncorrelated carriers at rate kr will then result in regeneration of almost 25% singlet and 75% triplet CT states, according both to the spin statistics and because 1CT and 1CT are degenerate in energy.30 While kf is a loss rate for singlets, the decay of triplet CT states to the ground state is quantum mechanically forbidden. If the energy of triplet excitons, either of the donor or acceptor, is less than the 3CT, back electron transfer can occur at a rate kBET.29 The resulted triplet excitons are dead-ends and eventually annihilate through triplet-free carrier annihilation at the rate constant kTA. In the absence of 13970

DOI: 10.1021/acs.jpcc.7b04825 J. Phys. Chem. C 2017, 121, 13969−13976

Article

The Journal of Physical Chemistry C

Figure 2. Calculated kinetics and rates of Charge transfer state, free charges, and total charges for excitation densities of 1016 cm−3 (a) and 1019 cm−3 (b) for kf = 5 × 108Hz, kd = 2 × 109 Hz, kISC = 109 Hz, and kBET = 106 Hz. (a) The initial decay of total charges is a single exponential decay due to the decay of the CT states to the ground state. A plateau, from which charge generation is quantified, can be reached in a dynamic equilibrium if the excitation density is low (≤1016 cm−3) (c). At this equilibrium condition the dissociation rate of the CT state and bimolecular encounter rate of free charges are almost equal (c), and therefore, the composition of the system stays constant during the plateau as in panel (a). At high excitation densities [(b) and (d)] equilibrium and subsequently the plateau do not exist.

triplet fission, the exact value of kTA does not affect the kinetic of the system due to energetic arguments. Therefore, back electron transfer from 3CT to T1 acts as a loss pathway for the triplet CT states through triplet excitons at a rate kBET. Within the framework of Onsager−Braun model, the rate equations describing photoexcitation are ⎛ t⎞ n ph dnS1 exp⎜⎜ − ⎟⎟ = −kd,exnS1 − k f,exnS1 + dt tp ⎝ tp ⎠

(1)

dn T1 = −k TAn T1nCS + kBETn3CT dt

(2)

within their realistic range. Exciton dissociation rate to CT states is a fast process on the order of 1013 Hz or greater.31,32 Typical exciton lifetimes for organic semiconductors are on the order of 100s of picoseconds33 (see Supporting Information for our systems) corresponding to kf,ex = 1010 Hz and kTA is on the order of 1010 cm3 s−1.28 The intersystem crossing rate, kISC, has been reported to be within a broad range of 106 Hz34 to 109 Hz.29 According to Heiber et al.21 in the blends with nanometer-size domains the carrier encounter rate constant is given by Langevin rate, or at least very close to it. For a given system this can be evaluated from Langevin expression for recombination rate dominated by faster carrier mobility ≈ 10−3cm2 V−1 s−1). Next, we show that kf is a (μfullerene e donor:accetor system property, while kd is also dependent on the composition ratio of the blend. Determination of kf, kd, and Charge Generation Yield. Fitting the experimental transient absorption spectroscopy (TAS) data with the solution of rate equations, will determine the kinetic rates of the CT state and free charge densities for a given system. The interpretation of TAS data, which is often used to probe the CT and CS states, is, however, not as straightforward as predicted by these simple rate equations. To be able to use eq 1 in relation with TAS data in order to evaluate kd, kf, and charge generation yield, the following conditions must be met: (i) the spectral feature of photoinduced absorption of the charges must be unambiguously decoupled from singlet and triplet excitons in either of spectrum or time domains; (ii) the excitation density must be kept low (see Figure 2) such that bimolecular recombination does not start at early times. This simplifies the rate equations, rules out kr and kBET, and limits the number of fitting parameters to kd, kf when exciton-related rates are separately measured and known; and (iii) exciton diffusion, which is a

dn1CT = 0.25k rnCS2 − kdn1CT − k f n1CT + kd,exnEX dt + kISC(n3CT − n1CT)

(3)

dn3CT = 0.75k rnCS2 − kdn3CT − kBETn3CT dt + kISC(n1CT − n3CT)

dnCS = −k rnCS2 + kd(n1CT + n3CT) − kcollnCS dt

(4)

(5)

where nS1, nT1, n1CT, n3CT, and nCS are the volume densities of singlet and triplet excitons, singlet and triplet CT states, and free charges, respectively. kcoll is the collection rate of charges (the photocurrent, if the experiment is performed not at open circuit condition), kTA is the annihilation rate of triplet excitons with free carriers and nph the number of absorbed pump photons per volume. The solution to these coupled rate equations will be meaningful only if the rate constants are 13971


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The Journal of Physical Chemistry C pathway for “delayed charge generation,” must be negligible. If the latter is the case, which can be checked by considering the decay and lifetime of singlet excitons, an additional “pump” term for CT states must be included in eq 1 to account for delayed CT state generation through excitons diffusion. What is often observed in photoinduced absorption spectra is the absorption of photogenerated charges, either of the acceptor anions or more commonly the donor cations, in both forms of CT states and free charges. However, they are not primarily distinguishable due to the broadness of their respective spectral features arising from energetic disorder. As such, a signal that is proportional to the sum of bound and free carrier densities, n(t) = n1CT(t) + n3CT(t) + nCS(t), rather than individual terms is often measured. Furthermore, there is no evidence in the literature whether bound and free charges should exhibit different absorption cross sections; therefore, one can imagine that the photoinduced absorption signal is evenly influenced by each of these species. Before addressing the experimental data, we first present some preliminary results to illustrate the effect of dissociation and recombination rates for different excitation. In Figure 2 the modeled kinetics of a system is shown with kd,ex = 10 THz, kf,ex = 10 GHz, kf = 0.5 GHz, kd = 2 GHz, kr = 1.3 × 10−10 cm−3 s−1, and excitation pulse length of 50 fs. Panels (a) and (b) show the density of free and bound charges for two different excitation fluences of 1016 and 10−19 photon cm−3, respectively. Panels (c) and (d) show the respective recombination and dissociation rates. An initial decay in the population of total charges is due to the decay of CT states to the ground state, allowing for quantifying kf. For the low excitation density of 1016 photon cm−3 a plateau is reached at 1 ns at which an equilibrium is reached between free and bound charges as seen from panel (b). When the excitation density is chosen to be 1019 photon cm−3, such plateau and equilibrium can never be achieved. When normalizing the total carrier density, the plateau quantifies the charge generation yield, which can be written as25

CG =

kd kd + k f

(6)

in the absence of both intersystem crossing of triplet singlet CT states and back electron transfer to the triplet excitons. Therefore, in a time-resolved photoinduced absorption experiment, only at low excitation densities a plateau is observed, consistent with temporal separation of CT state decay and observation of the onset of bimolecular recombination of free charges. From the experimental data CG and kf can be quantified from which kd will be inferred. Figure 3 shows the experimental data for the kinetic of charges in three model systems of: PCDTBT:PC70BM (a); PTB7:PC70BM (b); and TAPC:PC70BM (c) at different blend ratios, which we used to extract rates for kf and kd. The fitted kf, kd, and CG are shown in each panel. It is apparent that kf is predominantly dependent on the material system, i.e., on the donor:acceptor molecules and less sensitive to their blend ratio. This is because the decay of the CT states is a single-step process with a rate constant, which can be defined within the framework of Marcus theory by the electronic coupling between the LUMO− of the acceptor and HOMO+ of the donor molecules, reorganization energy of the CT state, and the Coulomb interaction of the charge pair. However, kd is strongly dependent on the blend ratio as expected and increases when the blend is more optimized. We

Figure 3. Experimental data on the kinetic of polaron peak in PCDTBT:PC70BM (a), PTB7:PC70BM (b), and TAPC:PC70BM (c) at different composition ratios. The solid lines corresponds to fits by eq 1, which reduces to a single exponential at low excitation density in the absence of back electron transfer. For all experiments small laser fluence of 76 nJ/cm2 (for PCDTBT blends) and 15 nJ cm−2 (for TAPC and PTB-7 blends) were used in order to delay the onset of bimolecular recombination as seen from the clear formation of a plateau. The samples were pumped at 560 nm (PCDTBT blends), 650 nm (PTB-7 blends), and 350 nm (TAPC blends) and probed at 1000 nm (for PCDTBT and PTB-7 blends) and 750 nm (for TAPC blends).

should note that kd depends on the blend ratio and film morphology as it is a multiple step process that involves the movement of the electron and/or the hole through multiple hopping. Therefore, kd is dependent on the electron and hole 13972


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The Journal of Physical Chemistry C mobilities10 and the number of accessible states as the separation distance between electron and the hole increase.35 The fittings on Figure 3 are consistent with calculated values of exciton dissociation and CT state generation36 and thus determines a reasonable range for the kf and kd to be used further throughout this article.

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RESULTS AND DISCUSSION Now we turn to the solution of eq 1 in order to investigate the influence of kf, kd, and back electron transfer rate kBET on the reduction of bimolecular recombination rate constant. We define the reduction of bimolecular recombination rate with respect to the encounter rate of electrons and holes (kr) at which CT states are formed. As such we define the “reduced bimolecular recombination” as a case in which the effective recombination rate constant of the free carriers to the ground state, β (via bound states) is smaller than the bimolecular encounter rate constant kr. It is worth to mention that according to the Monte Carlo simulations of Heiber et al.,21 in the domain sizes relevant to efficient BHJ systems, Langevin rate βL =

μin + μp ϵϵ0

is still a good approximation for kr.

According to eq 1 and the state diagram shown in Figure 1, the bimolecular recombination of free charges to the ground state is mediated by recombination of bound states (triplet and singlet CT states). As such, a well-defined bimolecular recombination rate cannot be attributed to free carriers per se. We define the effective bimolecular recombination rate constant of the free charges to the ground state β as a rate that satisfies βnCS2 = k f n1CT + kBETn3CT

(7)

β is a bimolecular recombination rate constant that can be measured through different experimental methods, such as photoCELIV, transient absorption, double injection, and timeresolved microwave conductivity; these methods do not quantify kr. The two terms on the right-hand side of the equation are the loss channels for the photoexcitations: singlet CT states decaying to the ground state; and triplet CT states undergoing back electron transfer to the triplet excitons, which will eventually annihilate. We now examine the limitations of the proposals for the mechanism of reduced recombination: large kd/kf ratio proposed by Burke et al.24 and Armin et al.;22 and blocked back electron transfer of triplet CT states to triplet excitons by Rao et al.28 We do so by evaluating the kinetic of free and bound charges and the effective bimolecular recombination reduction factor γCT γCT =

k rnCS2 kr = β k f n1CT + kBETn3CT

Figure 4. Kinetics of photogenerated carrier density (free and bound charges) at different back electron transfer rates, kBET, when the decay rate of the singlet CT states is fixed at 1 GHz and kISC = 1GHz. (a) Results for a case in which kd = 1 GHz. (b) Same kinetics for kd = 100 GHz. In both cases it is evident that as the ratio of kBET/kd vanishes the onset of bimolecular recombination shifts to the longer times, indicative of reduced recombination induced by suppression of triplet loss channel. (c) Calculated reduction factor based on eq 4 versus kBET. The solid lines show the expected reduction factor without considering the role of triplet CT states. In absence of back electron transfer (kBET ≪ kd) taking triplet CT states into account results in four times larger reduction factor compared to cases in which triplets are ignored. When kBET ≫ kd, even when kd ≫ kf the bimolecular recombination is diffusion-controlled with the reduction factor γ ≈ 1.

(8)

which can also be imagined as the ratio between the encounter rate (the rate of the formation of the CT states) and the recombination rate to the ground state. Results of numerical solution for eqs 1 and 4 are presented in Figure 4. We consider two systems with the same singlet CT state decay rate of kf = 1 GHz (which is chosen based on the typical experimental values presented in Figure 3), kISC = 1GHz and diffusion controlled encounter rate of kr = 1.3 × 10−10 cm−3 s−1 (corresponding to mobility sum of the order of 10−3 cm2 V−1 s−1). Figure 4a shows the kinetics of the total number of carriers including CT and free charges (as one would observe from time-resolved photoinduced absorption experiment)

normalized to the excitation density for kd = 1 GHz, and Figure 4b shows the kinetics for kd = 100 GHz. As kBET decreases with respect to kd, the onset of bimolecular recombination shifts to longer time scales due to the reduction in the recombination to the ground state. Figure 4c shows the 13973


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kd needs to be larger than both kf and kBET in order for bimolecular recombination to be reduced. When kBET ≪ kd the reduction factor γ is four times larger than what has previously been thought.24,22 Furthermore, when kBET ≈ kd bimolecular recombination cannot be reduced. This has been the case in many BHJ systems so far, in which high efficiencies can only be achieved in thin active layers due to the considerable bimolecular recombination of free charges. These are crucial understandings that bridge the properties of donor:acceptor systems at the molecular levels to macroscopic device properties such as bimolecular recombination rate constant and ultimately fill factor of solar cell devices. It is still an ongoing question as to how kd can be increased further in donor:acceptor system by material design. Increasing kd relative to the decay and back electron transfer rates suppresses both triplet and singlet loss channels yielding reduced bimolecular recombination and maximizes charge generation yield simultaneously. This is a key for the future of BHJ solar cells.

calculated reduction factor of bimolecular recombination with respect to the diffusion-limited rate, kr. The conclusions from this figure are (i) when kBET ≪ kd the reduction factor is 4 times larger than when the role of triplet CT states is not taken into account as per previous work of Armin et al. and Burke et al.22,24 In cases where kd< kf, suppression of triplets can only result in a reduction of ∼8 times; (ii) when kBET ≫ kd regardless of the ratio kd/kf, bimolecular recombination is diffusion controlled and no reduction factor can be achieved. Suppression of back electron transfer between triplet CT states to triplet exciton is a necessity to achieve reduced bimolecular recombination; (iii) simultaneous reduction of kBET and increasing kd/kf are critical to achieving large reduction factors; (iv) Rao et al. have suggested that in order for the triplet loss channel to be blocked, back electron transfer between triplet excitons and triplet CT state must be energetically mismatched. This is true only when kBET is small relative to kd. As such, increasing dissociation rate kd in a BHJ system can simultaneously block both triplet and singlet loss channels; and (v) when kd and kISC are of the same order, increasing back electron transfer rate from triplet CT states to triplet excitons, kBET will result in significant loss on charge generation as shown in Figure 4a. This is not the case when kd is significantly larger than kISC such that the singlet CT states dissociate to free carriers rapidly before they undergo intersystem crossing to triplet CT states (Figure 4b). If loss pathways to the triplet excitons at rate kBET is blocked, kd/kISC plays no role in charge generation yield. These remarks indicate that the previously suggested reduction factor with respect to Langevin rate22 γ = γCTγGEO =

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CONCLUSIONS In summary we investigated the two previously presented explanations for reduced bimolecular recombination in BHJ solar cells. While there is as yet no complete theory of suppressed recombination, different parts of the problem have been addressed and progress has been made in building a theoretical model and in rationalizing experimental results. First we explained the limitations and conditions for acquiring dissociation rate and decay rate constant of charge transfer states and charge generation quantum yield from time-resolved photoinduced absorption spectroscopy measurements. Using realistic rate constants we modeled a BHJ system taking into account the role of triplet CT states and their back electron transfer to the triplet excitons. Our results indicate that in order to reduce bimolecular recombination significantly with respect to the diffusion limited encounter rate of the charge carriers, one needs to suppress both triplet and singlet CT state loss channels simultaneously. This can be achieved through lowering the decay or back electron transfer rate of singlet and triplet states, respectively, or increasing their dissociation rate. We showed that suppressing either of the channels has no strong impact on the reduction of bimolecular recombination. We revised the expression based on the rates of CT states to calculate the bimolecular recombination reduction factor with taking into account the back electron transfer of the triplet states. Finally, our results suggest that increasing the dissociation rate of the CT state is a key approach that can simultaneously result in high generation quantum yield and reduced bimolecular recombination.

kd + k f βL kf

kr

(9)

needs to be revised. γGEO is the reduction factor due to the encounter rate of charges to the geometric confinement of electrons and holes when the mobility is imbalanced (βL/kr). When the back electron transfer to triplet excitons is significant, the reduction factor γ approaches unity and recombination can be described by Langevin theory. However, when back electron transfer is forbidden, γ is four times larger than that described by eq 4. We now derive an analytical expression for the reduction factor with appreciation of the role of triplet CT states. In absence of charge extraction, the encounter rate of carriers krnCS2 equals the regeneration rate of both singlet and triplet CT states. As such eq 4 can be written as γCT =

(n1CT + n3CT) k kf n + BET n kd 1CT kd 3CT

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(10)

In steady state condition and when both kBET and kf are smaller than kd, the density of triplet CT states can be considered to be three times larger than the singlets, and as such, eq 10 can be simplified to γCT =

kd 0.25k f + 0.75kBET

EXPERIMENTAL SECTION

Film Preparation. Polymer (5 mg mL−1) and PC70BM (10 mg mL−1) solutions in chlorobenzene solvent were prepared and stirred to prepare the films with the different polymer loadings. The films were spun on cleaned glass substrates for 1 min at 2500 rpm in air and were then transferred into an inertatmosphere glovebox until the measurements were performed. Samples were prepared by preclearing the glass substrates in acetone and isopropanol for 10 min each and then dried under N2. Ultrafast transient absorption spectroscopy measurements were carried out with a commercial setup that comprises a 1 kHz Solstice (Newport Corporation) Ti:sapphire regenerative

(11)

This reduction factor is sensitive to both ratios kd/kf and kd/ kBET and is consistent with the conclusions on Figure 4. This is consistent with the behavior of BTR:PCBM system, which shows, upon solvent annealing, triplets are suppressed37 and a reduction factor of 150 times is achieved.22 We emphasize that 13974


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amplifier with 800 nm, 90 fs pulses. The output of this laser was split to generate the pump and probe pulses. The tunable pump pulse was generated in a TOPAS-Prime (Light conversion) optical parametric amplifier and used to excite the sample. The probe light was used to generate UV−vis (450−800 nm) and near-IR continuum (900−1450 nm). A HELIOS transient absorption spectrometer (Ultrafast Systems) was used for collecting transient absorption spectra and decays up to 6 ns. The time resolution of this setup was 200 fs. The samples were kept at all times under a nitrogen atmosphere.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b04825. Transient absorption spectroscopy and kinetics of the studied systems (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

James R. Durrant: 0000-0001-8353-7345 Safa Shoaee: 0000-0001-8386-2893 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors like to thank Pabitra Tuladhar Shakya for preparation of the samples used for transient absorption measurements. S.S. is a Sofja Kovalevskaja awardee of Alexander von Humboldt Foundation. Thanks to the Alexander von Humboldt Foundation and the Welsh Assembly Government Ser Cymru programme for funding.

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REFERENCES

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Interplay Between Triplet-, Singlet-Charge Transfer States and Free

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