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Trap-Limited Exciton Diffusion in Organic Semiconductors Oleksandr V. Mikhnenko, Martijn Kuik, Jason Lin, Niels van der Kaap, Thuc-Quyen Nguyen, and Paul W. M. Blom* Excited states in organic semiconductors, imposed either by electro- or by photoexcitation, are referred to as excitons, and are known to migrate throughout the organic material.[1] In an organic semiconductor singlet excitons migrate between conjugated segments via Förster energy transfer.[2] Due to the disordered nature of the polymers such hopping can be regarded as diffusion. The exciton diffusion length, the average distance an excitation can migrate in a material during its lifetime, is generally used as a quantitative characterization of this process. The exciton diffusion length has been determined using a variety of measurement techniques such as fluorescence quenching in thin films of organic semiconductors, in which one or both interfaces act as an exciton quenching wall,[3–13] exciton density modulation due to light absorption,[14–16] exciton-exciton annihilation,[17–19] photocurrent modeling in solar cells,[20–24] and fluorescence quenching in thin films with randomly distributed quenchers.[25–31] For a large number of (disordered) organic semiconductors, exciton diffusion lengths of typically 5–10 nm have been reported. The dynamics of exciton migration in organic semiconductors is governed by the exciton diffusion coefficient. Knowledge of the exciton diffusion coefficient is therefore required in order to describe the spatial- and temporal evolution of the exciton population in organic semiconductors. Experimentally, it can be determined by modeling the photoluminescence (PL) decay curves.[5,25,30,32,33] In an experiment on a series of poly(p-phenylene vinylene) derivatives (PPVs) with different amounts of disorder, reflected in a three order of magnitude difference in the charge carrier mobility, the exciton diffusion coefficient also varied by one order of magnitude.[34] Remarkably, the exciton diffusion length in this series of PPV derivatives all amounts to about 6

Dr. O. V. Mikhnenko, Dr. M. Kuik, N. van der Kaap Zernike Institute for Advanced Materials University of Groningen Nijenborgh 4, 9747 AG Groningen, The Netherlands Dr. O. V. Mikhnenko, Dr. M. Kuik, J. Lin, Prof. T.-Q. Nguyen Center for Polymers and Organic Solids Department of Chemistry and Biochemistry University of California at Santa Barbara Santa Barbara, CA, 93106, USA Dr. O. V. Mikhnenko Dutch Polymer Institute P. O. Box 902, 5600 AX, Eindhoven, The Netherlands Prof. P. W. M. Blom Max Planck Institute for Polymer Research Ackermannweg 10, 55128, Mainz, Germany E-mail: [email protected]

DOI: 10.1002/adma.201304162

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nm, since the increase of the diffusion coefficient was compensated by a decrease of the PL decay time. A possible explanation could be that the PL decay time in these pristine polymer films is governed by the time excitons need to diffuse to non-radiative recombination centers. This will lead to shorter PL decay times in materials with faster diffusion and consequently to a constant exciton diffusion length under the condition that the different polymers would have an equal amount of non-radiative recombination centers. For application in organic solar cells, long exciton diffusion lengths are highly desired since that would strongly loosen the demands on the nanometer-sized morphology in donor:acceptor blends. The fundamental question here is whether the exciton diffusion in semiconductors presently used in organic solar cells is limited by extrinsic quenching defects. For this purpose we investigate the amount of exciton quenching defects in a range of organic semiconductors, 6 conjugated polymers and 5 small molecules, all solution processed. The structural formulas of the materials used in this study are shown in Figure 1. To explain how the concentration of exciton quenchers is measured in these materials we will use the wellknown low bandgap polymer poly[2,6-(4,4-bis-(2-ethylhexyl)4H-cyclopenta[2,1-b;3,4-b′] dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) as an example. This polymer is chosen as a model system since it exhibits a single exponential luminescence decay in thin films, which strongly simplifies the interpretation of the PL dynamics. We find from time-resolved luminescence, by adding a low concentration of randomly distributed fullerene quenchers, that the background concentration of the exciton quenching defects in PCPDTBT amounts to 6 × 1017 cm−3. The same methodology has been applied to a series of organic semiconductors investigated in this work. For all cases a concentration of exciton quenchers in the range of 1017–1018 cm−3 is found. Figure 2 depicts the measured PL decays of PCPDTBT in three different states; a dilute solution, a pristine solid film, and a solid blend with 0.1 wt% [6,6]-phenyl C61-butyric acid methyl ester (PCBM) added. It can be observed that the PL decay time in the pristine film is shorter than in solution but longer than in the blend. In the solid blend with PCBM the PL decay time is shorter than in the pristine film because excitons are quenched at randomly distributed PCBM molecules, which are known to be efficient quenchers due to the ultra-fast electron transfer.[35] The amount of quenched excitons – and the shortening of the PL decay time – is controlled by the process of exciton diffusion. Significant quenching is only expected when the exciton diffusion length is similar or longer than the average distance between the quenching sites. As in many other organic semiconductors, the PL decay time of PCPDTBT is shorter in a solid film than in a dilute

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COMMUNICATION Figure 1. Chemical structures of poly(3-hexylthiophene) (P3HT); poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b; 3,4-b′]dithiophene)-alt-4,7-(2,1,3benzothiadi-azole)] (PCPDTBT); poly[(4,4′-bis(2-ethylhexyl)dithieno[3,2-b:2′,3′-d]silole)-2,6-diyl-alt-(2,1,3-benzothiadiazole)-4,7-diyl] (Si-PCPDTBT); poly(9,9-dioctylfluorene-alt-benzothiadiazole) (F8BT); random copolymer of poly(2-methoxy-5-(3′,7′-dimethyloctyloxy)-p-phen- ylene vinylene) and poly[4′-(3,7-dimethyloctyloxy)-1,1′-biphen- ylene-2,5-vinylene] (NRS-PPV); poly[2-methoxy-5-(2’-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV); 2,5-dihexyl-3,6-bis[4-(5-hexyl-2,2′:5′,2″-terthiophene-5″-yl)phenyl]pyrrolo[3,4-c]-pyrrole-1,4-dione (SM1); 2,5-dihexyl-3,6-bis[4-(5-hexylthiophene-2-yl) phenyl]-pyrrolo[3,4-c]-pyrrole-1,4-dione (SM2); 2,5-dihexyl-3,6-bis[4-(5-hexyl-2,2′-bithiophene-5-yl)-phenyl]pyrrolo[3,4-c]-pyrrole-1,4-dione (SM3); 7,7′-(4,4-bis(2-ethylhexyl)-4H-silolo[3,2-b:4,5-b′]dithiophene-2,6-diyl)bis(6-fluoro-4-(5′-hexyl-[2,2′-bithiophen]-5-yl)benzo[c][1,2,5]thiadiazole) (SM4); and 7,7′-(4,4-bis(2-ethylhexyl)-4H-silolo[3,2-b:4,5-b′]dithiophene-2,6-diyl)bis(5-fluoro-4-(5′-hexyl-[2,2′-bithiophen]-5-yl)benzo[c][1,2,5]thiadiazole) (SM5).

solution. In a solution polymeric chains are well isolated by solvent molecules, while in thin films they are closely packed. It has been shown that interchain exciton hopping in thin

Figure 2. Normalized PL decays of PCPDTBT solution, pristine film and blend with 0.1 wt% PCBM. All the decays are nearly monoexponential.

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films is one order of magnitude more efficient than intrachain hopping in solution of a prototypical conjugated polymer.[36,37] These experimental findings are supported by quantum-chemical calculations showing that the electronic coupling between localized segments of an isolated polymer chain is much weaker than the coupling between closely packed chains.[37,38] Consequently, for a polymer in solution, excitons are too slow to diffuse toward the defects in the polymeric chain, where they can be quenched. On the contrary, in a thin film the efficient interchain hopping increases the probability for excitons to encounter defects. Thus the reduction of the PL decay time in a thin film, when compared to solution, can be explained by diffusion limited quenching at impurities and defects.[39] For that reason we assume that in materials that are studied here the effect of diffusion limited quenching at impurities has a stronger influence on the PL decay time than the possible formation of aggregates and delocalized excited states. This assumption will be justified further in the text. In the following we will estimate the concentration of such quenching sites in PCPDTBT. Figure 3 shows the dependence of the reciprocal PL decay time versus PCBM concentration in the PCPDTBT:PCBM blends (symbols). In recent studies[30,40,41] we have demonstrated that PCBM molecules form an intimate mixture in blends with PCPDTBT in the concentration range of

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c0 =

Figure 3. Stern-Volmer plot of PCPDTBT:PCBM blends. The experimental data points (symbols) are fitted (thick line) with Equation (1). Exciton quenching defects in pristine films of concentration c0 can be accounted for by shifting the Stern-Volmer plot along the abscissa (thin line). The cross-points with the ordinate correspond to the measured PL decay time and intrinsic exciton lifetime J0−1 in the pristine film. The inset is a J −1 f schematic representation of the electron transfer process from polymer to the defect state for the case of electron trapping and exciton quenching.

0.01–10 wt% (Figure 3). As a consequence, these experimental data can therefore be described by the Stern-Volmer formula:[42] 1 1 = + 4B r Dc J Jf

(1)

where τ is the PL decay time of a PCPDTBT:PCBM blend with PCBM concentration c; τf is the PL decay time in the pristine polymer film; r = re + rq is the sum of the exciton and PCBM radii; and D is the exciton diffusion coefficient. It is reasonable to set r to 1 nm.[30,43] Thus the only unknown variable is the exciton diffusion coefficient. By fitting the experimental data with Equation (1), as shown in Figure 3 (thick solid line), an exciton diffusion coefficient of 3 × 10−3 cm2s−1 is obtained from the slope. It is important to note that the Stern-Volmer relation (1) can only be used to extract the exciton diffusion coefficients in organic semiconductors that exhibit monoexponential PL decays in thin films as well as in blends, such as PCPDTBT (Figure 2). With the derived exciton diffusion coefficient we can use Equation (1) to estimate the concentration of exciton quenching defects – c0 – in pristine PCPDTBT, thus in the absence of PCBM. Assuming that the exciton quenching efficiency is equal for PCBM and the defects, the total concentration of exciton quenchers q in the polymer:PCBM blend film is: q = c + c0

(2)

Substitution of (2) into (1) yields: 1 1 = − 4B r Dc 0 + 4B r Dq J Jf

(3)

If no exciton quenching defects in the pristine film were present, then the PL decay time in such a film would correspond to the “intrinsic” exciton lifetime, τ0. By setting q = 0 in (3) we get:

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1 4B r D



1 1 − Jf J0



(4)

The obtained expression can be used to estimate the concentration of exciton quenching defects, c0. The only unknown variable in this relationship is the intrinsic exciton lifetime, τ0, which can be approximated by the PL decay time in a dilute solution. The PL decays in Figure 2 were deconvoluted with the instrument response function yielding τf = 146 ps and τ0 = 212 ps. Insertion of these numbers into Equation (4) results in the value of c0 = 6 × 1017 cm−3 for the exciton quenching defect concentration in PCPDTBT. From Equation (3) it follows that the exciton quenching defects can be geometrically represented by shifting the SternVolmer plot along the abscissa of the value c0 (thin line in Figure 3). The intersection of this shifted line with the ordinate will correspond to the intrinsic exciton lifetime J0−1. It should be noted that the slope of this Stern-Volmer plot does not depend on the quenching defect concentration, c0. Consequently, the extracted exciton diffusion coefficient of 3 × 10−3 cm2 s−1 is a true intrinsic material parameter that does not depend on the presence of the exciton quenching defects. The same measurements and analysis have been carried out on a series of organic semiconductors, 5 other conjugated polymers and 5 small molecules, as listed in Figure 1, all processed from solution (See Supporting Information). It is worth noting that some organic semiconductors such as P3HT, MEH-PPV, and NRS-PPV show bi-exponential PL decay in thin films. For this reason the Stern-Volmer analysis cannot be directly applied to these materials. Instead we modeled the exciton dynamics in these systems using a Monte Carlo simulation (see Supporting Information Figures S2 and S3). Bi-exponential decay can be described by two regimes of exciton diffusion in the presence of exciton quenching defects: (i) downhill migration toward lower energy sites and (ii) temperature activated hopping.[5] Pronounced bi-exponential decay dynamics are usually observed in polymers that have a relatively large degree of energetic variation such as NRS-PPV or P3HT (see Supporting Information). On the other hand, materials such as PCPDTBT or small molecules that have less energetic disorder usually show monoexponential PL decay dynamics. These observations can be rationalized by diffusion limited quenching at defects. In materials with small disorder parameter the process of downhill migration can be neglected. Consequently, at room temperature the exciton diffusion can be described by a single diffusion coefficient according to temperature activated hopping and the Stern-Volmer analysis can be applied. In materials with larger distribution of excitonic states the downhill migration becomes important and thus exciton diffusion must be described with a variable diffusion coefficient (Figure S3 in Supporting Information). At room temperature the downhill migration is faster than the temperature activated hopping.[5] Therefore the diffusion limited quenching at defects is governed by the downhill migration leading to multi-exponential PL decays. We modeled this processes using Monte Carlo simulation and achieved excellent fits (Figures S3, S5, and S7). We estimated the intrinsic exciton lifetime, τ0, to be the PL decay time of isolated molecules in solution. Our estimation

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does not take into account the formation aggregates and related delocalization effects when going from solution to solid state. We assumed that diffusion limited quenching has a stronger influence on the PL decay time in thin film, τf, than the other effects. To evaluate our assumption we consider P3HT – a typical organic semiconductor that is known to form aggregates in thin films. Gregg et al. presented an elegant method of determining the concentration of the defects in P3HT by compensation using cobaltocene.[44] The addition of electron donating cobaltocene led to filling up the electron traps. As a consequence, the PL decay rate of P3HT:cobaltocene blend increased up to 954 ps as compared to 437 ps of neat P3HT. Moreover, the PL decay becomes monoexponential upon addition of cobaltocene. In agreement with our argumentation, this observation suggests that the multi-exponential character of PL decay is due to exciton quenching at the defects. Interestingly the PL decay of the compensated film is very close to our estimation of τ0 of 600–900 ps for P3HT. Finally, the number of traps 1.2 × 1018 cm−3 found by Gregg et al. is almost identical to the value, which we found using our method 1.7–3.3 × 1018 cm−3. The agreement between our work and Gregg et al., giving independently the same exciton lifetime and amount of quenchers, strongly supports our original assumption that in P3HT the dynamics of PL decay in condensed state is predominantly governed by the exciton quenching effects on defects. Figure 4a summarizes the concentration of exciton quenchers in pristine thin films for the materials studied here. We observe that this concentration is typically in the range of 1.7 × 1017–2.2 × 1018 cm−3 (mean value ± standard deviation on log10 scale). The amount of exciton quenchers is surprisingly similar to a universal electron trap density that was recently reported for a large range of conjugated polymers.[45] The number of electron traps typically amounts to 3–5 × 1017 traps/ cm3, centered at an energy ∼ 3.6 eV below the vacuum level with a typical width of its Gaussian energy distribution of ∼ 0.1 eV (Ref. [45]. As a further example of this universal behavior we performed hole- and electron transport measurements on our model polymer PCPDTBT. The electron current is observed to be one order of magnitude lower than the hole current, which indicates that the electron current is slightly trap-limited (see Supporting Information Figure S1). For this polymer the measured electron currents can be reproduced for Gaussian traps located 0.3 eV below the LUMO level and a density of trapping sites of 5 × 1017 cm−3. This trap concentration is again nearly equal to the concentration of exciton quenchers of 6 × 1017 cm−3 found from time-resolved PL measurements (Figure 3). This result strongly suggests that the exciton quenching defects and the electron traps are the same species, most likely a hydrated oxygen defect.[45] The electron transfer to the trap level is a probable mechanism of exciton quenching, similarly to the exciton quenching at polymer-fullerene interfaces. The inset of Figure 3 schematically illustrates that the exciton quenching and the electron trapping are essentially the same processes of electron transfer to the trap level. Recombination of trapped electrons with free holes in polymer light-emitting diodes is shown to be non-radiative.[46] Figure 4b shows a plot of experimentally determined exciton diffusion length versus measured trap concentration. The trap limited exciton diffusion length must be about a half of the

Figure 4. (a) Concentration of exciton quenchers in a series of organic semiconductors consisting of 6 conjugated polymers and 5 small molecules (Figure 1). The shaded area represents the concentration range 1.7 × 1017–2.2 × 1018 cm−3. (b) One dimensional exciton diffusion length √ −1 versus trap density. The solid curve is a plot of L d = 2 3 c 0 .

characteristic distance between the traps that is one over cubic root of the trap density. Indeed, the experimental data closely √ −1 follows the curve L d = 2 3 c 0 in accordance with the trap limited diffusion. Materials such as P3HT and SM1 show high density of excitonic traps and short exciton diffusion length, while F8BT and SM2 are characterized by lower trap density and longer diffusion length. Furthermore, in better ordered organic semiconductors with a higher diffusion coefficient, excitons are able to find the quenching defects faster, leading to shorter PL decay times and a constant Dτf value. It is important to note that longer exciton diffusion lengths were found in single crystals of organic compounds.[15,16] Such systems are characterized by a high level of purity and do not suffer from the exciton quenching defects, as opposed to solution-processed conjugated polymers and small molecules. In conclusion, we showed that the concentrations of electron traps and exciton quenching defects in a series of organic semiconductors are nearly identical. Since the energy of the electron trap is located below the LUMO of a polymer, excitons can be quenched at these traps via electron transfer. Our findings strongly suggest that the electron traps and exciton quenching defects in pristine films share the same origin. The fact that the quenching defects have a concentration typically in the

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1017–1018 cm−3 regime in a large variety of organic semiconductors explains why their exciton diffusion length is so similar, in spite of large variations in their exciton diffusion coefficient.

Experimental Section PCPDTBT, Si-PCPTDBT were supplied by Konarka. NRS-PPV, MEH-PPV, and small molecules were synthesized in house. P3HT was purchased from Sigma-Aldrich. F8BT was acquired from Cambridge Display Technology. PCBM was purchased from Solene BV. Thin films of semiconductor:PCBM blends for spectroscopy measurements were spin-coated from chlorobenzene or chlroroform solution in a nitrogenfilled glove box. The thickness of each film was about 100 nm. The samples were encapsulated with a clean glass substrate using epoxy glue to avoid contact with air. For time-resolved PL measurements samples were excited by Ti-Sapphire laser at 780 nm or at 390 nm. The PL decays were recorded by a streak camera or time-correlated single photon counter. The instrument response function was varied between 3 ps and 50 ps depending on the time range of specific experiment. The software for Monte Carlo simulation is described in the Supporting Information.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgments The work of O. V. Mikhnenko forms part of the research program of the Dutch Polymer Institute (project #518). Part of this work (modeling of exciton diffusion in PPVs and small molecules) was supported by the NSF-SOLAR (Award #1035480). T.Q.N. thanks the Camille Dreyfus Teacher Scholar Award and the Alfred Sloan Research Fellowship program. We thank Hamed Azimi, Markus Scharber and Mauro Morana of Konarka Technologies for the supply of PCPDTBT, Thomas S. van der Poll and Guillermo C. Bazan for providing SM4 and SM5 materials; Chunki Kim and Jianhua Liu for providing the DPP materials. We acknowledge Maria Antonietta Loi and Alexander Mikhailovsky for the assistance with the time-resolved PL measurements and for helpful discussions. Received: August 19, 2013 Revised: October 31, 2013 Published online: December 19, 2013

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Trap-limited exciton diffusion in organic semiconductors.

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