Article pubs.acs.org/JPCC
Relating Nongeminate Recombination to Charge-Transfer States in Bulk Heterojunction Organic Photovoltaic Devices Liang Xu, Jian Wang, Yun-Ju Lee, and Julia W. P. Hsu* Department of Materials Science and Engineering, University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080, United States S Supporting Information *
ABSTRACT: The importance of nongeminate recombination of free photogenerated carriers through charge-transfer (CT) states compared with at the electrode interfaces in bulk heterojunction (BHJ) organic photovoltaic (OPV) devices was investigated using impedance spectroscopy (IS) and low-energy external quantum efficiency (EQE) measurement. Thin (∼60 nm) poly(di(2-ethylhexyloxy)benzo[1,2-b:4,5-b′]dithiophene-co-octylthieno[3,4-c] pyrrole-4,6-dione):[6,6]-phenyl-C70-butyric acid methyl ester (PBDT-TPD:PC71BM) OPVs processed with varying concentrations of solvent additive 1-chloronaphthalene (CN) provide a well-controlled system in which only the donor−acceptor interfacial area, hence CT concentration, is changed. We found that additive inclusion resulted in increased CT state concentration, measured by low-energy EQE spectroscopy, and higher nongeminate recombination, determined from IS. In contrast, the energetic disorder in the BHJ, as determined from the dependence of carrier density on open-circuit voltage, did not show a dependence on CN concentration, suggesting that it is not related to changes in donor−acceptor morphology. The correlated relationship between nongeminate recombination strength and CT state concentrations presents unambiguous evidence of CT states as the major channels in nongeminate recombination loss in these BHJ OPV devices.
1. INTRODUCTION Charge-transfer (CT) states at the donor−acceptor (D−A) interfaces have been shown to govern charge generation in bulk heterojunction (BHJ) organic photovoltaic (OPV) devices by providing the intermediate step in the process of dissociating excitons into free carriers.1−5 In particular, geminate recombination at CT states, the reverse process of exciton dissociation that causes excitons to decay back to ground state, has been extensively studied for the purpose of better understanding charge generation in OPVs;2−8 however, after the split of bound electron−hole pairs into free carriers, the role of CT states on nongeminate recombination of these free carriers, which is considered the major charge loss mechanism in highperformance BHJ OPVs,8−10 has been examined only in studies based on electroluminescence (EL) technique, which probes only a minor population of injected carriers undergoing radiative recombination in OPVs.11,12 Therefore, direct measurements on nongeminate recombination of photogenerated carriers in OPVs under operating conditions, which is believed to be mostly nonradiative,12−14 together with measurement of CT states are critical to elucidate the role of CT states in nongeminate recombination loss. In addition, surface recombination of minority carriers at the “wrong” electrode (holes at cathode or electrons at anode) is nonnegligible in high-performance BHJ OPVs with active layer thicknesses typically 2 V), we observe saturation of Jph for all devices, which implies efficient collection of all photogenerated free carriers. By comparing the saturated Jph values, we conclude that free carrier generation is significantly enhanced by the B
DOI: 10.1021/acs.jpcc.5b05227 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
EQE spectra, which reflect the relative CT state concentrations21 in different CN-concentration devices. The result clearly establishes that higher concentration CN devices contain larger CT state concentrations. 3.3. Impedance Spectroscopy Analysis and Recombination Dynamic. To study nongeminate recombination dynamics of the photogenerated free carriers in operating OPV devices, frequency-domain IS measurements25−27 were performed under open-circuit condition, at which recombination is the only pathway for these photogenerated free carriers. The IS data were modeled with an equivalent circuit26,28 (Figure 3a, inset) to extract a series resistance Rs from contact
addition of CN up to 5 vol %. From EQE measurements under equivalent 1 Sun illumination (Figure 1b), a wavelengthindependent increase in EQE spectral response from 400 to 730 nm, that is, above the absorption band of PBDT-TPD and PC71BM, is observed with increased CN concentration that again saturates above 5 vol % CN. This indicates that free carrier generation from both polymer and fullerene is enhanced with CN inclusion. By integrating the EQE spectra with respect to the AM1.5G spectrum,20 we obtain Jsc for different CN concentration devices, which shows good agreement to Jsc measured from J−V characterization (Figure 1b, inset). The enhancement in free carrier generation with CN additive has been attributed to suppressed formation of large polymer aggregates, resulting in a finely mixed active layer blend morphology with smaller D−A domains and larger interfacial areas. Atomic force microscopy (AFM) was performed on films processed with 0 and 5 vol % CN, from which we observed decease in surfaces roughness (represented by root-meansquare roughness) with CN additive (Figure S2). This result confirms morphological optimization due to CN inclusion consistently with previous studies.16,17 3.2. CT State Concentration versus CN Concentration. To quantify the change in interfacial area with CN addition, low-energy EQE spectroscopy was performed with incident photon energy below the absorption edge of both PBDT-TPD and PC71BM to measure CT state concentrations.21−23 Figure 2 shows the EQE spectra of devices processed with 0, 0.1, and 5
Figure 3. Impedance spectroscopy data for conventional PBDTTPD:PC71BM BHJ solar cells. (a) Ceq versus Voc, (b) n versus Voc, and (c) τ versus intensity for devices processed with different amount of CN. All color and symbol schemes used here are the same as in Figure 1a. The equivalent circuit used in IS analysis is shown in the inset of panel a. Solid lines in panel b indicate that all devices have similar slope of log(n) versus Voc, that is, Ech.
Figure 2. EQE versus incident photon energy of conventional PBDTTPD:PC71BM BHJ solar cells: 0 vol % CN (black solid line), 0.1 vol % (red solid line), and 5 vol % (blue solid line). The dashed lines show the Gaussian fits representing CT contribution. Relative CT state concentrations, as measured by the integrated areas under the Gaussian fits, are shown in inset.
layers, electrodes, and active layer, a recombination resistance Rrec corresponding to the derivative of recombination current, and a equivalent capacitance Ceq of the constant phase element corresponding to both carrier accumulation within active layer (chemical capacitance Cμ) and at the electrodes due to parallel plate capacitance (geometric capacitance Cg).25,27,29 Here only one set of parallel RC circuit (Rrec∥Ceq) is needed because under open-circuit condition all of the photogenerated charges held by Ceq recombine through Rrec. For different CN devices, a plot of Ceq (Ceq = Cμ + Cg) versus open-circuit voltage (Voc) measured under different illumination intensities (Figure 3a) is used to calculate the average photogenerated carrier density n26,27,30
vol % CN versus incident photon energy ranging from 1.35 to 2.1 eV. Absorption well below optical gap of both PBDT-TPD (∼1.94 eV) and PC71BM (∼1.7 eV)17 is observed and attributed to electronic transition from the ground-state directly into the interfacial CT state.21−23 These CT absorption bands can be fitted with Gaussian curves, from which the interfacial CT state energy (ECT) is determined.22 For all three different CN concentration devices, the spectral shape of fitted CT band (dashed curves in Figure 2) is found to be invariant. The same ECT of 1.55 ± 0.01 eV, which is in good agreement with value in literature (1.53 eV),3 was obtained, suggesting unchanged intermolecular interactions in the D−A system by additive inclusion. Another approach of extracting ECT by fitting the exponential absorption tail of the sub-bandgap CT absorption was also applied (Figure S3),23,24 from which an invariant ECT of ∼1.5 eV was obtained for all devices independent of the CN concentrations. In contrast, an increase in the CT band amplitude is observed with higher CN concentration. Figure 2 (inset) shows the integrated areas under the Gaussian fits in the
n=
1 qL
∫0
Voc
(Ceq − Cg) dV
(1)
where q is the elementary charge and Cg is the Ceq measured in dark assuming a fully depleted active layer (as indicated by arrow in Figure 3a). Dielectric constant of 3.5 ± 0.1 is obtained for PBDT-TPD:PC71BM BHJ films independent of CN concentration. The exponentially increasing behavior of Ceq C
DOI: 10.1021/acs.jpcc.5b05227 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C with respect to Voc indicates that Ceq is dominated by Cμ at light intensity ≥1 mW/cm2, for which the charge accumulation in the bulk of active layer is accurately probed by impedance measurement. Figure 3b shows n obtained using eq 1 as a function of Voc for different CN devices, which are all parallel, that is, the same functional dependence. Lower n is observed for the CN devices, indicating less carrier accumulation at open-circuit condition with additive inclusion. Moreover, the dependence of n with respect to Voc gives information on density of states: In disordered materials the bandtail states have an exponential energy dependence with a bandtail slope (Ech) that can be obtained from n α exp(Voc/2Ech); 2 arises from assuming the polymer and fullerene have an identical tail.31 From our IS results, all devices regardless of CN concentrations exhibit identical Ech of 68 ± 4 meV. This result shows that the energetic disorder is unaffected by inclusion of additive, suggesting that its origin is unrelated to D−A morphology. Furthermore, the small perturbation carrier lifetime (τ) is calculated as the product of Rrec and Cμ.26,27 τ with respect to illumination intensity for devices with different CN concentrations is shown in Figure 3c, which exhibits a monotonic decrease in τ at a given intensity with the increase in CN concentration up to 5 vol %. Such decrease in τ with increase in CN concentration indicates enhanced recombination in device with higher CN concentration, which is consistent which the lower charge accumulations in higher CN concentration devices, as demonstrated in Figure 3b. 3.4. Bimolecular Recombination versus CT State Concentration. To further quantify the nongeminate recombination in different CN devices, we model the charge recombination dynamics based on bimolecular recombination32,33 R = k rec(n) ·n2
Figure 4. (a) krec versus CN concentration under different white-light LED illumination intensities: 1 mW/cm2 (red circle), 10 mW/cm2 (blue diamond), and 50 mW/cm2 (black triangle). (b) Jsc (red) under 1 Sun illumination and krec (black) under 50 mW/cm2 of white-light LED illumination versus CN concentration.
nongeminate recombination strongly indicates that CT states at D−A interfaces, rather than blend−electrode interfaces, are the preferential pathway of nongeminate recombination in these BHJ OPVs. Moreover, on the basis of published values of electron mobility (μe ≈ 1 × 10−3 cm2 V−1 s−1) and hole mobility (μh ≈ 2.9 × 10−5 cm2 V−1 s−1) in PBDT-TPD:PC70BM BHJ blend,10 we calculated the Langevin recombination coefficient following both the original model using sum of μe and μh (kL,S = e/εε0(μe + μh))36 as well as the later model proposing to use minimum of μe and μh (kL,M = e/eε0min (μe,μh)).37 The choice of which model to use is beyond the scope of this study.38 The largest krec experimentally obtained from the 5 vol % CN device at 50 mW/cm2 illumination (4.2 ± 0.2 × 10−11 cm3 s−1) is in between kL,M (1.4 × 10−11 cm3 s−1) and kL,S (4.8 × 10−10 cm3 s−1), which is quite reasonable. In addition, the free carrier recombination and free carrier generation show close correlation in devices processed with additive, as shown in Figure 4b that Jsc under 1 Sun illumination and krec under 50 mW/cm2 of white-light LED illumination vary with CN concentration in a similar manner. From lowenergy EQE spectroscopy, we have shown that the use of CN additive increases interfacial CT state concentration. As a result, both charge generation and recombination are enhanced due to the increase in CT state concentration. Such similar behaviors of charge generation and recombination with respect to CN concentration provide compelling evidence that interfacial CT states are the intermediate states for both processes in these high-performance OPVs.
(2)
where R is the bimolecular recombination rate and krec is carrier-density-dependent bimolecular recombination rate coefficient; identical carrier density for electrons and holes is assumed. Using the n and τ values extracted from IS data, krec can be obtained following the equation33 k rec =
1 (1 + λ) ·n·τ(n)
(3)
where λ is determined from the power law dependence between τ and n (τ = τ0n−λ). Detailed plot of τ versus n for different CN devices is shown in Figure S5, and values of λ are listed in Table S1. In Figure 4a, we plot krec for different CN concentration devices under three representative illumination intensities. At each CN concentration, krec increases with the increasing intensity, showing the highly carrier-density-dependent recombination strength (λ > 1) that has been previously reported in multiple studies.33−35 More importantly, at a given intensity, krec increases with increasing CN concentration up to 5 vol % before saturating, indicating stronger bimolecular recombination in device with higher CN concentration. Given that active layer thickness, device geometry, and electrode materials are kept the same independent of additive concentration, the surface recombination at active layer blend−electrode interfaces, a non-negligible nongeminate recombination pathway in thin OPV devices,15 is invariant in the different CN devices. Therefore, our result of a clear correlation between increased CT states concentration and
4. CONCLUSIONS In conclusion, we utilized a combination of J−V, abovebandgap and sub-bandgap EQE measurements, and impedance spectroscopy to probe the relationship between charge generation and recombination in thin PBDT-TPD:PC71BM BHJ OPVs processed with different concentrations of CN additive. Inclusion of CN was found not to affect BHJ energetic disorder but to introduce more interfacial CT states, leading to enhanced free-carrier photogeneration. At the same time, we established that nongeminate recombination is correspondingly increased in samples with higher CT state concentrations. D
DOI: 10.1021/acs.jpcc.5b05227 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
(8) Etzold, F.; Howard, I. A.; Mauer, R.; Meister, M.; Kim, T.-D.; Lee, K.-S.; Baek, N. S.; Laquai, F. Ultrafast Exciton Dissociation Followed b y Nong eminate Ch arge R e combinatio n in PCDTBT:PCBM Photovoltaic Blends. J. Am. Chem. Soc. 2011, 133, 9469−9479. (9) Park, S. H.; Roy, A.; Beaupré, S.; Cho, S.; Coates, N.; Moon, J. S.; Moses, D.; Leclerc, M.; Lee, K.; Heeger, A. J. Bulk Heterojunction Solar Cells with Internal Quantum Efficiency Approaching 100%. Nat. Photonics 2009, 3, 297−302. (10) Bartelt, J. A.; Beiley, Z. M.; Hoke, E. T.; Mateker, W. R.; Douglas, J. D.; Collins, B. A.; Tumbleston, J. R.; Graham, K. R.; Amassian, A.; Ade, H.; et al. The Importance of Fullerene Percolation in the Mixed Regions of Polymer-Fullerene Bulk Heterojunction Solar Cells. Adv. Energy Mater. 2013, 3, 364−374. (11) Wetzelaer, G.-J. A. H.; Kuik, M.; Blom, P. W. M. Identifying the Nature of Charge Recombination in Organic Solar Cells From ChargeTransfer State Electroluminescence. Adv. Energy Mater. 2012, 2, 1232−1237. (12) Tvingstedt, K.; Vandewal, K.; Gadisa, A.; Zhang, F.; Manca, J.; Inganäs, O. Electroluminescence From Charge Transfer States in Polymer Solar Cells. J. Am. Chem. Soc. 2009, 131, 11819−11824. (13) Vandewal, K.; Tvingstedt, K.; Gadisa, A.; Inganäs, O.; Manca, J. V. On the Origin of the Open-Circuit Voltage of Polymer−Fullerene Solar Cells. Nat. Mater. 2009, 8, 904−909. (14) Ohkita, H.; Cook, S.; Astuti, Y.; Duffy, W.; Tierney, S.; Zhang, W.; Heeney, M.; McCulloch, I.; Nelson, J.; Bradley, D. D. C.; et al. Charge Carrier Formation in Polythiophene/Fullerene Blend Films Studied by Transient Absorption Spectroscopy. J. Am. Chem. Soc. 2008, 130, 3030−3042. (15) Reinhardt, J.; Grein, M.; Bühler, C. Identifying the Impact of Surface Recombination at Electrodes in Organic Solar Cells by Means of Electroluminescence and Modeling. Adv. Energy Mater. 2014, 4, 1400081. (16) Aïch, B. R.; Lu, J.; Beaupré, S.; Leclerc, M.; Tao, Y. Organic Electronics. Org. Electron. 2012, 13, 1736−1741. (17) Bartelt, J. A.; Douglas, J. D.; Mateker, W. R.; Labban, A. E.; Tassone, C. J.; Toney, M. F.; Fréchet, J. M.; Beaujuge, P. M.; McGehee, M. D. Controlling Solution-Phase Polymer Aggregation with Molecular Weight and Solvent Additives to Optimize PolymerFullerene Bulk Heterojunction Solar Cells. Adv. Energy Mater. 2014, 4, 1301733. (18) Liao, H.-C.; Ho, C.-C.; Chang, C.-Y.; Jao, M.-H.; Darling, S. B.; Su, W.-F. Additives for Morphology Control in High-Efficiency Organic Solar Cells. Mater. Today 2013, 16, 326−336. (19) Mihailetchi, V.; Koster, L.; Hummelen, J.; Blom, P. Photocurrent Generation in Polymer-Fullerene Bulk Heterojunctions. Phys. Rev. Lett. 2004, 93, 216601. (20) Cowan, S. R.; Wang, J.; Yi, J.; Lee, Y.-J.; Olson, D. C.; Hsu, J. W. P. Intensity and Wavelength Dependence of Bimolecular Recombination in P3HT:PCBM Solar Cells: a White-Light Biased External Quantum Efficiency Study. J. Appl. Phys. 2013, 113, 154504. (21) Vandewal, K.; Widmer, J.; Heumueller, T.; Brabec, C. J.; McGehee, M. D.; Leo, K.; Riede, M.; Salleo, A. Increased OpenCircuit Voltage of Organic Solar Cells by Reduced Donor-Acceptor Interface Area. Adv. Mater. 2014, 26, 3839−3843. (22) Vandewal, K.; Tvingstedt, K.; Gadisa, A.; Inganäs, O.; Manca, J. V. Relating the Open-Circuit Voltage to Interface Molecular Properties of Donor:Acceptor Bulk Heterojunction Solar Cells. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 125204. (23) Street, R. A.; Hawks, S. A.; Khlyabich, P. P.; Li, G.; Schwartz, B. J.; Thompson, B. C.; Yang, Y. Electronic Structure and Transition Energies in Polymer−Fullerene Bulk Heterojunctions. J. Phys. Chem. C 2014, 118, 21873−21883. (24) Hawks, S. A.; Li, G.; Yang, Y.; Street, R. A. Band Tail Recombination in Polymer:Fullerene Organic Solar Cells. J. Appl. Phys. 2014, 116, 074503. (25) Xu, L.; Lee, Y.-J.; Hsu, J. W. P. Charge Collection in Bulk Heterojunction Organic Photovoltaic Devices: an Impedance Spectroscopy Study. Appl. Phys. Lett. 2014, 105, 123904.
Given the invariant surface recombination at active layer blend−electrode interfaces among different devices, our finding of stronger nongeminate recombination in photovoltaic devices with more CT states provides irrefutable support that nongeminate recombination predominantly occurs through CT states in these BHJ OPV devices. Thus, interfacial CT states are the intermediate states for both free carrier generation and recombination processes in these high-performance BHJ OPVs.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b05227. J−V curves under AM1.5 100 mW/cm2 illumination of devices processed with different amount of additive CN as well as device characteristics are given. AFM images of devices processed with 0 and 5 vol % CN are included. A different approach in sub-bandgap EQE analysis is shown. It also includes IS data under open-circuit conditions under different illumination intensities in Nyquist plots together with their equivalent circuit fitting results. Moreover, τ versus n from IS for devices processed with different amount of CN is provided with slope fittings. (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This project is sponsored by National Science Foundation (NSF) DMR-1305893 and University of Texas at Dallas. J.W.P.H. acknowledges the support from Texas Instruments Distinguished Chair in Nanoelectronics.
■
REFERENCES
(1) Benson-Smith, J. J.; Goris, L.; Vandewal, K.; Haenen, K.; Manca, J. V.; Vanderzande, D.; Bradley, D. D. C.; Nelson, J. Formation of a Ground-State Charge-Transfer Complex in Polyfluorene//[6,6]Phenyl-C61 Butyric Acid Methyl Ester (PCBM) Blend Films and Its Role in the Function of Polymer/PCBM Solar Cells. Adv. Funct. Mater. 2007, 17, 451−457. (2) Deibel, C.; Strobel, T.; Dyakonov, V. Role of the Charge Transfer State in Organic Donor-Acceptor Solar Cells. Adv. Mater. 2010, 22, 4097−4111. (3) Vandewal, K.; Albrecht, S.; Hoke, E. T.; Graham, K. R.; Widmer, J.; Douglas, J. D.; Schubert, M.; Mateker, W. R.; Bloking, J. T.; Burkhard, G. F.; et al. Efficient Charge Generation by Relaxed ChargeTransfer States at Organic Interfaces. Nat. Mater. 2014, 13, 63−68. (4) Nayak, P. K.; Narasimhan, K. L.; Cahen, D. Separating Charges at Organic Interfaces: Effects of Disorder, Hot States, and Electric Field. J. Phys. Chem. Lett. 2013, 4, 1707−1717. (5) Clarke, T. M.; Durrant, J. R. Charge Photogeneration in Organic Solar Cells. Chem. Rev. 2010, 110, 6736−6767. (6) Braun, C. L. Electric Field Assisted Dissociation of Charge Transfer States as a Mechanism of Photocarrier Production. J. Chem. Phys. 1984, 80, 4157−4161. (7) Proctor, C. M.; Kuik, M.; Nguyen, T. Q. Charge Carrier Recombination in Organic Solar Cells. Prog. Polym. Sci. 2013, 38, 1941−1960. E
DOI: 10.1021/acs.jpcc.5b05227 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C (26) Garcia-Belmonte, G.; Boix, P. P.; Bisquert, J.; Sessolo, M.; Bolink, H. J. Simultaneous Determination of Carrier Lifetime and Electron Density-of-States in P3HT:PCBM Organic Solar Cells Under Illumination by Impedance Spectroscopy. Sol. Energy Mater. Sol. Cells 2010, 94, 366−375. (27) Elliott, L. C. C.; Basham, J. I.; Pernstich, K. P.; Shrestha, P. R.; Richter, L. J.; DeLongchamp, D. M.; Gundlach, D. J. Probing Charge Recombination Dynamics in Organic Photovoltaic Devices Under Open-Circuit Conditions. Adv. Energy Mater. 2014, 4, 1400356. (28) Garcia-Belmonte, G.; Guerrero, A.; Bisquert, J. Elucidating Operating Modes of Bulk-Heterojunction Solar Cells From Impedance Spectroscopy Analysis. J. Phys. Chem. Lett. 2013, 4, 877−886. (29) Bisquert, J. Chemical Capacitance of Nanostructured Semiconductors: Its Origin and Significance for Nanocomposite Solar Cells. Phys. Chem. Chem. Phys. 2003, 5, 5360−5364. (30) Proctor, C. M.; Kim, C.; Neher, D.; Nguyen, T.-Q. Nongeminate Recombination and Charge Transport Limitations in Diketopyrrolopyrrole-Based Solution-Processed Small Molecule Solar Cells. Adv. Funct. Mater. 2013, 23, 3584−3594. (31) Kirchartz, T.; Nelson, J. Meaning of Reaction Orders in Polymer:Fullerene Solar Cells. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 165201. (32) Shuttle, C.; O’Regan, B.; Ballantyne, A.; Nelson, J.; Bradley, D.; Durrant, J. Bimolecular Recombination Losses in Polythiophene: Fullerene Solar Cells. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 113201. (33) Maurano, A.; Hamilton, R.; Shuttle, C. G.; Ballantyne, A. M.; Nelson, J.; O’Regan, B.; Zhang, W.; McCulloch, I.; Azimi, H.; Morana, M.; et al. Recombination Dynamics as a Key Determinant of Open Circuit Voltage in Organic Bulk Heterojunction Solar Cells: a Comparison of Four Different Donor Polymers. Adv. Mater. 2010, 22, 4987−4992. (34) Shuttle, C. G.; O’Regan, B.; Ballantyne, A. M.; Nelson, J.; Bradley, D. D. C.; de Mello, J.; Durrant, J. R. Experimental Determination of the Rate Law for Charge Carrier Decay in a Polythiophene: Fullerene Solar Cell. Appl. Phys. Lett. 2008, 92, 093311. (35) Clarke, T. M.; Lungenschmied, C.; Peet, J.; Drolet, N.; Mozer, A. J. A Comparison of Five Experimental Techniques to Measure Charge Carrier Lifetime in Polymer/Fullerene Solar Cells. Adv. Energy Mater. 2015, 5, 1401345. (36) Langevin, P. Recombinaison Et Mobilites Des Ions Dans Les Gaz. J. Phys. Theor. Appl. 1903, 28, 433. (37) Koster, L. J. A.; Mihailetchi, V. D.; Blom, P. W. M. Bimolecular Recombination in Polymer/Fullerene Bulk Heterojunction Solar Cells. Appl. Phys. Lett. 2006, 88, 052104. (38) Heiber, M. C.; Baumbach, C.; Dyakonov, V.; Deibel, C. Encounter-Limited Charge-Carrier Recombination in Phase-Separated Organic Semiconductor Blends. Phys. Rev. Lett. 2015, 114, 136602.
F
DOI: 10.1021/acs.jpcc.5b05227 J. Phys. Chem. C XXXX, XXX, XXX−XXX
