Understanding the Apparent Charge Density Dependence of Mobility

Apr 4, 2014 - ABSTRACT: Energetic disorder in organic semiconductors leads to strong dependence of recombination kinetics and mobility on charge ...
0 downloads 0 Views 850KB Size
Download PDF
Article pubs.acs.org/JPCC

Understanding the Apparent Charge Density Dependence of Mobility and Lifetime in Organic Bulk Heterojunction Solar Cells Florent Deledalle,† Pabitra Shakya Tuladhar,† Jenny Nelson,‡ James R. Durrant,† and Thomas Kirchartz*,‡,§,∥ †

Department of Chemistry and Centre for Plastic Electronics and ‡Department of Physics and Centre for Plastic Electronics, Imperial College London, South Kensington campus, London, SW7 2AZ, United Kingdom § IEK5-Photovoltaics, Forschungszentrum Jülich, 52425 Jülich, Germany ∥ Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Strasse 199, 47057 Duisburg, Germany S Supporting Information *

ABSTRACT: Energetic disorder in organic semiconductors leads to strong dependence of recombination kinetics and mobility on charge density. However, observed mobilities and reaction orders are normally interpreted assuming uniform charge carrier distributions. In this paper, we explore the effect of the spatial distribution of charge on the determination of mobility and recombination rate as a function of average charge density. Since the spatial gradient changes when the thickness of a device is varied, we study thickness series of two different polymer:fullerene systems and measure the charge density dependence of mobility and lifetime. Using simulations, we can show that the high apparent reaction orders frequently observed in the literature result from the spatial gradient of charge density at open circuit. However, the mobilities, measured at short circuit, are less affected by the gradients and therefore may show substantially different apparent charge density dependence than the recombination constants, especially for small device thicknesses.

I. INTRODUCTION The synthesis of low band gap polymers with energy levels that allow efficient exciton splitting with low energetic offsets at the heterojunction to a fullerene acceptor has driven the efficiencies of state of the art polymer:fullerene solar cells up to 9.2%.1 However, the electronic properties of these blends with low band gap polymers still hardly ever allow fabrication of efficient devices with absorber thicknesses much larger than 100 nm due to low mobilities and/or insufficiently long charge carrier lifetimes.2−5 The resulting nongeminate recombination of the carriers and its nonlinear dependence upon charge carrier density has indeed been shown to control the shape of current−voltage curves of many efficient polymer:fullerene solar cells.6−8 Understanding how mobility and recombination rate respond to charge carrier concentration in an operating cell is therefore important, as it could provide insight into the fundamental mechanism of recombination. However, all experimental techniques accessing spatially averaged carrier densities will face issues when spatial charge carrier gradients within the active layer become too strong. Within the framework of the multiple-trapping model, the recombination rate and mobility should increase with carrier concentration.9−14 The recombination rate R typically follows a power law with average charge carrier density n,̅ with the exponent in R ∝ n̅δ, called the reaction order. Recently, investigations using different characterization techniques observed large variations in these reaction orders.15−21 Understanding the origins of these variations is therefore a key consideration for the analysis © 2014 American Chemical Society

of nongeminate recombination in organic solar cells. Recent device simulation studies have shown that limited device thickness can result in inflated apparent reaction orders as a result of strong spatial variations in charge density at open circuit.22 In this paper, we build upon this study by showing experimentally that the observed differences in reaction orders between several experimental polymer:fullerene systems can be explained by taking into account their different thicknesses without having to invoke any different recombination mechanisms. By combining charge extraction, transient photovoltage and drift-diffusion modeling studies, we determine the consequences of spatial variations in charge carrier density in thin organic solar cells. We show that this spatial variation strongly affects the charge-density dependence of the observed recombination rate, while it has little effect on the chargedensity dependence of the mobility. This carrier profile across the active layer thickness depends mostly on the net applied voltage (V − Vbi) and the thickness of the active layer and appears to be relatively insensitive to the microstructure of the blend. Received: March 25, 2014 Revised: April 4, 2014 Published: April 4, 2014 8837

dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842

The Journal of Physical Chemistry C

Article

II. CHARGE DENSITY DEPENDENCE OF RECOMBINATION AND MOBILITY Charge density dependence of carrier mobility and recombination rate constant has been associated with disorder in electron and hole polaron energy levels,9−14 an important feature of organic semiconductors. The inhomogeneity of structures (local orientations of the polymer chains, conformations) and compositions (donor, acceptor, charged or neutral impurities) at the nanoscale of materials with low relative permittivity affect the energy landscape in which the polarons spatially evolve and can lead to low-lying states that act as charge traps.11,23,24 The presence of this density of states within the forbidden band gap has a critical influence on the charge transport as well as the recombination of initially separated holes and electrons in our systems.25 If we assume for the moment that recombination of one free carrier with free or trapped charges of opposite polarity dominates recombination in the blend and follows a Langevin type relation,25,26 we would obtain locally for the recombination rate (of, for example, a free electron and a hole) under forward bias (V ≫ kT) n * ntotp R ∝ n freeptot = free ntotptot ∝ k rec tot ntot (1)

forward bias, the photogenerated population (under operating conditions) is usually in large excess to the one at thermodynamic equilibrium (if the material is not doped) which implicitly means that the excess carrier population is not much different from the total population. Since we do not observe k*rec(Δntot) ∝ μ*(Δntot) in some experiments, one of our assumptions must be violated. One interpretation is that eq 1 describes a local model valid at a point x in the device, while the experiment only measures spatially integrated values of Δntot and Δptot. While the spatial averages of Δntot and Δptot (Δn̅ and Δp)̅ are identical, they are not identical at any given point in the volume of the absorber,32 but instead are strong functions of the position in the device. A simulation study has already verified that arbitrarily high reaction orders can result from spatial variations in charge density in thin devices at open circuit.22 Indeed, in the experiments mentioned just above, the P3HT devices used in previous publications investigating the reaction order are optimized and the active layer is consequently thicker than 200 nm.29,33 On the other hand, many more devices in the literature today, like the ones based on PTB7, have optimized thicknesses in the range 80−110 nm usually due to inferior properties of carrier transport compared with P3HT.1 Moreover, the measurements related to effective mobility are normally done under short-circuit condition, while the measurements of decay dynamics are conducted at open circuit.

The detailed calculation leading to eq 1 from the general form assuming V ≫ kT can be found in Supporting Information section 0 using the Shockley-Read-Hall distribution function according to ref 27. Here, nfree is the free electron concentration, ntot and ptot are the total electron and hole concentrations, and krec * is the effective recombination constant.28 The effective mobility μ* of an electron in the same model would be n μ* = free μn0 ntot (2)

III. SIMULATIONS OF THE SPATIAL CHARGE DISTRIBUTION In order to verify that the spatial gradient of charge carriers is responsible for the observed high reaction orders and the discrepancy between k*rec (Δntot) and μ*(Δntot) observed, we conducted further 1D device simulations. These simulations are based on a drift diffusion model where recombination via tail states has been considered alongside direct band-to-band recombination to maintain the generality of the results to different recombination types. The device simulation based on Advanced Semiconductor Analysis (ASA) has been previously used in refs 22, 25, and 34. More details about the modeling including the tables of parameters can be found in Supporting Information, section 3a and 3b. Figure 1 presents the simulated spatial distribution of excess carriers (compared with short circuit in the dark) at open circuit and at short circuit for two different thicknesses of the active layer 50 and 150 nm. First we can compare the excess electron and hole concentrations at open circuit for the two thicknesses. The built-in voltage Vbi is the change of the electrostatic potential over the absorber layer, which is governed by the difference in work functions of the two electrodes together with any band bending in the vicinity of the electrodes due to pinning. Nevertheless, the open-circuit voltage Voc represents the splitting between the quasi-Fermi levels measured at opposite contacts and is therefore light dependent, i.e., the difference of electrochemical potential over the absorber layer. Thus, for a wide range of light intensities Vbi is larger than Voc and the bands are never completely flat. In this case, the excess carriers relative to equilibrium are created by a combination of photogeneration and injection at the contacts. The lower the illumination level, the more the injected carriers will dominate the population of excess carriers within the active layer. Figure 1a shows that for the rather low thickness of 50 nm, the excess carrier profiles at open circuit are very steep and the increase in concentration vs illumination is strongly position dependent.

where μn0 is the mobility of free electrons above the mobility edge, which means that the effective mobility of electrons is reduced relative to the mobility of free electrons by the fraction of those electrons that are trapped. Note that the term nfree/ntot appears in both eqs 1 and 2. Thus, the effective recombination constant k*rec is proportional to the effective mobility μ* in this model and therefore also has the same dependence on total electron concentration ntot. Shuttle et al.29 show that experimental measurements of carrier transport dynamics and nongeminate recombination in poly(3-hexylthiophene):[6,6]phenyl C61-butyric acid methyl ester P3HT:PC61BM devices indicated the same dependence on carrier concentration for both recombination rate and drift mobility, as one would expect from a multiple trapping model.30,31 However, more recently Rauh et al. proposed a similar study with thieno[3,4b]thiophene/benzodithiophene (PTB7):[6,6]-phenyl C71-butyric acid methyl ester (PC71BM) in which these two key variables were found to show a different dependence on carrier density at room temperature,31 with a reaction order substantially higher than two (3.5). These experimental observations investigating the reaction order are apparently inconsistent with the multiple trapping model discussed above and might suggest that the fundamental recombination mechanism is different for different devices made from the same polymer:fullerene blend or from one material to another. By extracting the charges under short-circuit conditions, charge extraction technique can access the excess carriers compared with the reference point (dark; 0 V). Furthermore, in 8838

dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842

The Journal of Physical Chemistry C

Article

zero-dimensional model should therefore result in better agreement with the one-dimensional simulation than at open circuit. This implies that the slope of mobility vs carrier concentration should be much more closely related to the density of states than the reaction order. The calculated profiles of optical absorption across the active layer thickness for the 50 and 150 nm thick devices can be found in Supporting Information section 4 based on the ellipsometry data published in ref 35. Finally, we note that the measurements of mobility are done at short circuit while the carrier lifetimes are usually measured at open circuit. This will result in a different apparent dependence of the observed mobility on carrier concentration than of the apparent recombination rate. Moreover, a difference in the dependence on carrier concentration between mobility and recombination rate would not necessarily hint at a change in the recombination mechanism.

IV. EXPERIMENTAL DETERMINATION OF REACTION ORDERS FOR TWO THICKNESS SERIES To further investigate the effect of thickness on the apparent density dependence of krec * and μ* and to confirm the trends observed in the simulations, devices of several thicknesses based on PTB7:PC71BM and P3HT:PC61BM have been studied experimentally. The device fabrication is described in the Experimental Details. The PTB7:PC71BM devices were made from the same solution and with the same cathode evaporation run. This allows us to neglect any potential change in intrinsic defect density or in semiconductor-electrode energetics which could happen between different evaporation runs. The experimental methodology to measure the nongeminate recombination rate from measurements at open circuit and the effective drift mobility at short circuit as described by Shuttle et al.16,29 was strictly applied in this study. (The linearity of the short-circuit current Jsc with light intensity for the PTB7 based devices as shown in Supporting Information section 1 supports the validity of the methodology for our study.) Previous work shows that geminate losses were negligible for optimized devices of both systems. The assumption that the recombination of separated holes and electrons is the main loss process in the photovoltaic operating regime is supported by successful prediction of the open-circuit voltages for a wide range of light intensities based on the measurements of recombination dynamics according to the methodology we proposed in the past15,16,36 (see Supporting Information section 5). Figure 2a shows the carrier dependency of the nongeminate recombination rate calculated from the measurements of excess carrier densities using charge extraction (after correction for geometric capacitance and incurred charge losses occurring during sweep out)36 and transient lifetime measured by transient photovoltage, following the empirical relations:22

Figure 1. Simulations of the spatial distribution of excess electrons and holes across the active layer at open circuit for 50 nm thin (a) and 150 nm thick (c) devices and at short circuit for 50 nm thin (b) and 150 nm thick (d) devices. The solid lines are related to the excess density of electrons, the dashed lines to the excess density of holes.

The excess hole concentration, for instance, increases strongly with voltage at the cathode, i.e., where the hole concentration is lowest, and will be weakly voltage dependent close to the anode. However, the integral hole concentration will not change much with voltage at least for low light intensities and open-circuit voltages as the large increase close to the cathode will hardly contribute to the integral. At higher light intensities, the open-circuit voltage will approach the built-in voltage, the excess carrier concentrations will be more homogeneous, and the average excess carrier concentrations will increase with voltage more strongly. In essence, the large spatial gradient leads to a situation where the measured average excess carrier density Δn̅ ≈ 1/d∫ d0Δntot(x) dx, over the thickness of the active layer d, increases with open-circuit voltage only very slowly while Voc < Vbi. Since the recombination rate is usually expressed as R = k*rec(np − n0p0) in forward bias, the effective recombination constant k*rec needs to increase quite steeply with Δn̅ to obtain the observed exponential voltage dependence of the recombination rate. It is assumed here that the total photogenerated population of carriers (mostly trapped) is largely superior to the one at equilibrium (which is usually similar to implying that the active layer is not doped). Therefore, the steep gradients in Δn̅ directly cause large apparent reaction orders.22 Figure 1b shows the excess electron and hole concentrations for a device with an active layer of 150 nm thickness. Here, the spatial gradients of electron and hole concentrations are substantially less steep relative to the 50-nmthick device. Thus, the situation at 150 nm thickness will resemble the zero-dimensional model discussed in the context of eqs 1 and 2 much more, and the reaction orders will be more consistent with the charge density dependence of mobility. Figures 1c and d show the dependence of excess electron and hole density at short circuit for the same two thicknesses (50 and 150 nm). In this case, the spatial distribution of charges is controlled by absorption rather than injection from the contacts. Since the optical generation rates are not strong enough functions of position in these thin films (compared to the charge carrier gradients simulated for open circuit), the thickness will not have a strong influence on the result. The

⎛ qV ⎞ Δn ̅ = Δ n0 exp⎜ oc ⎟ and ⎝ mkT ⎠ ⎛ qVoc ⎞ ⎟ where τTPV = τ0 exp⎜ − ⎝ ϑkT ⎠ m δ= +1 ϑ * = k rec 8839

1 1 Δn ̅ δ − 2 = = Δn ̅ τΔn̅ Δn ̅ δτTPV δτ0Δ n0 δ − 1 dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842

The Journal of Physical Chemistry C

Article

crystallinity PCDTBT: PC71BM43 (see Supporting Information section 6).

V. REAL REACTION ORDER It becomes clear from the experimental and modeling observations on the thickness series of PTB7:PC71M that the apparent reaction order increases to values substantially higher than 2 for the thin devices. However, it is extremely unlikely that the predominant loss process involves more than 2 carriers. Furthermore, while the reaction order decreases with thickness, we observe a light ideality factor (see Supporting Information section 7) of the three devices within the same range, constantly larger than 1 and which does not change noticeably when increasing the thickness. According to ref 44 this supports the idea that within the range 60−130 nm of thickness of the active layer, the main mechanism of nongeminate recombination probably has not changed in nature, contrary to what the apparent reaction order would have suggested. Ideally measurements of thick devices would be recommended to experimentally access the ‘bulk‘ reaction rate. Previous simulations predict a saturation of the reaction order at around 150 nm.22 However, due to low mobility-lifetime products, charge extraction might be inefficient for thicker devices leading to an underestimation of the total excess carrier densities. Furthermore, unintentional doping might lead to small space charge region widths even for thicker devices which would then also lead to high apparent reaction orders that have nothing to do with the recombination mechanism. Alternatively, the simulations show that higher overlaps of the spatial distributions of carriers are achievable even for relatively thin devices if measurements are done under higher illuminations. The challenge here would be to make sure these high illumination levels would still be representative of operating conditions. Overall, when the thickness or the doping concentration is a barrier to obtaining meaningful insight into the exact recombination mechanism, the study of the ideality factor derived from illumination dependent open-circuit voltage measurements would be a related alternative indicator of the recombination mechanism.44

Figure 2. Nongeminate recombination rate k*rec (solid symbols) and effective mobility μ* (empty symbols) function of charge density for (a−b) experimental and simulated PTB7 based devices at 60 nm (circles), 90 nm (triangles) and 130 nm (squares). (c) Experimental data for P3HT devices at 85 nm (circles) and the previous published data at 230 nm (triangles) as a reference and (d) simulations based on parameters representative of the thin device as well as what would be obtained if the thickness was increased to 230 nm (everything else kept constant).

(dashed lines from the monoexponential fits of the measurements of electron density Δn̅(Voc) and carrier lifetimes τTPV(Voc) at high illuminations and dots from the direct calculation via 1/(Δn̅ × τn)) and the effective drift mobility (open symbols) of PTB7:PC71BM systems at three different thicknesses, namely, 60, 90, and 130 nm. Similar to the results presented by Rauh et al.31 for PTB7:PC71BM and Hawks et al.37 for PBDTTT-C:PC71BM, the carrier dependence of the drift mobility μ* and recombination rate k*rec show a clear discrepancy for thicknesses around 100 nm. However, the thicker the active layer is, the less steep krec * becomes, consistent with the above argument and with simulations as shown in Figure 2b.22 We then made an intentionally suboptimal thin P3HT:PC61BM device whose active layer thickness was measured to be around 85 nm. Figure 2c shows both the data published previously using a 230-nm-thick device for comparison (in triangles)29 and the results obtained experimentally for this 85-nm-thick device (in circles) (the simulations here for P3HT in Figure 2d used parameters based on the thin device and reproduces the expected behavior when the thickness of the active layer is increased, with everything else kept constant, although the list of parameters is not expected to be exactly valid for the thick P3HT:PCBM device due to, in particular, known vertical segregation in P3HT:PCBM blends).38,39 Nevertheless, it becomes clear that although the thick P3HT device presents a similar dependency for both krec * and μ*, krec * is still strongly thickness dependent just like in the case with the PTB7:PC71BM devices. This thickness threshold, beyond which the mobility and apparent recombination rate do not share the same dependency in carrier density, highlights indirectly when the distribution of carriers becomes more heterogeneous in the bulk. We point out that these observations have been obtained for two different systems with different blend morphology,33,40−42 and have been observed as well for another system with intermediate

VI. CONCLUSION To conclude, the hypothesis that, at any point in the bulk heterojunction blend, the spatial gradients in holes and electrons can be neglected has often been implicitly assumed in the study of recombination dynamics. We have demonstrated using modeling and experimental studies on blends of different levels of crystallinity that the active layer thickness is a key determinant of the spatial distribution of carriers within the active layer. This spatial distribution of carriers becomes more heterogeneous for thin devices where the assumption neglecting the spatial gradients in carriers breaks down, in particular, at open-circuit condition. This in turn will have a fundamental impact on the way recombination rate and carrier mobility will correlate with carrier concentration and is therefore paramount to consider while identifying the fundamental mechanism behind nongeminate recombination by studying the reaction orders. Since these shifts in spatial distribution of carriers are governed by the active layer thickness, it is valid for all bulk heterojunction solar cells. This consequently cannot be ignored when trying to establish some general design rules for improving charge transport in organic solar cells. 8840

dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842

The Journal of Physical Chemistry C

■

VII. EXPERIMENTAL DETAILS Materials. The protocol for device preparation is as follows. PTB7 based solar cells were designed in conventional architecture ITO/PEDOT:PSS/PTB7:PC71BM/Ca/Al. The ITO on glass substrates were all precleaned and plasma-treated during 7 min at 25 mbar. The solution was prepared in 1:1.25 blend ratio in chlorobenzene (CB) with 3 vol % of 1,8diiodooctane (DIO) leading to a final concentration of 25 mg/ mL. The solution was kept under stirring at 80 °C overnight. The films were made by spin-casting the solution on preheated substrate at 80 °C. Likewise, P3HT based solar cells were prepared in conventional architecture ITO/PEDOT:PSS/ P3HT:PC61BM/Ca/Al. The solution was prepared in 1:1 blend ratio in CB at the concentration of 30 mg/mL. The solution was kept under stirrer overnight at 60 °C. The P3HT films were made by blade coating. In both systems, the cathodes were deposited by evaporation to obtain Ca and Al whose thicknesses were assessed to be 25 and 150 nm, respectively. Each pixel area was 4.5 mm2. For the series based on PTB7 blends, the devices originate from the same solution and the same run of cathode evaporation to be in a position where any effect on the interface active layer/electrodes can be neglected. The overall performance of the devices used in this study is presented in Supporting Information sections 1 and 2. Charge Extraction and Transient Photovoltage. Charge extraction at open circuit enables measurement of the photogenerated Δn̅ = nlight − ndark charges developing in the active layer while at open circuit under different illumination levels, i.e., different photovoltages. The sweep out was performed by switching to short circuit. The time length of each illumination is a compromise between reaching a steady state and not warming up the device under study. The latter was under N2 atmosphere during the experiment. Transient photovoltage is a small perturbation technique measuring the decay of the perturbation of the photovoltage resulting from the injection of a small amount of charges from a N2 dye laser while the device is held at open-circuit conditions and under constant background illumination. These two techniques lead to the calculation of the recombination rate. The details of the experimental setup and the method used have been described elsewhere.8,15,16,36,45,46 Charge extraction at short circuit has been presented previously in ref 29. Thickness Measurements. The thickness of the devices was measured using a Dektak profilometer precalibrated using a 100 nm gold film deposited on quartz calibration module. The total uncertainty of the active layer thickness is no more than 10 nm for the range of devices presented herein.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS F.D. and J.R.D. are thankful for the support from the EPSRC APEX grant EP/H040218/2 and SPECIFIC grant EP/I019278. T.K. acknowledges funding by an Imperial College Junior Research Fellowship. J.N. acknowledges the support of the Royal Society via a Wolfson Merit Award and of EPSRC via projects EP/J5200021 and EP/G031088.

■

REFERENCES

(1) He, Z.; Zhong, C.; Su, S.; Xu, M.; Wu, H.; Cao, Y. Enhanced Power-Conversion Efficiency in Polymer Solar Cells Using an Inverted Device Structure. Nat. Photonics 2012, 6, 591−595. (2) Faist, M. A.; Shoaee, S.; Tuladhar, S.; Dibb, G. F. A.; Foster, S.; Gong, W.; Kirchartz, T.; Bradley, D. D. C.; Durrant, J. R.; Nelson, J. Understanding the Reduced Efficiencies of Organic Solar Cells Employing Fullerene Multiadducts as Acceptors. Adv. Energy Mater. 2013, 3, 744−752. (3) Kirchartz, T.; Agostinelli, T.; Campoy-Quiles, M.; Gong, W.; Nelson, J. Understanding the Thickness-Dependent Performance of Organic Bulk Heterojunction Solar Cells: The Influence of Mobility, Lifetime, and Space Charge. J. Phys. Chem. Lett. 2012, 3, 3470−3475. (4) Li, W.; Hendriks, K. H.; Roelofs, W. S. C.; Kim, Y.; Wienk, M. M.; Janssen, R. A. J. Efficient Small Bandgap Polymer Solar Cells with High Fill Factors for 300 Nm Thick Films. Adv. Mater. 2013, 25, 3182−3186. (5) Peet, J.; Wen, L.; Byrne, P.; Rodman, S.; Forberich, K.; Shao, Y.; Drolet, N.; Gaudiana, R.; Dennler, G.; Waller, D. Bulk Heterojunction Solar Cells with Thick Active Layers and High Fill Factors Enabled by a Bithiophene-Co-Thiazolothiazole Push-Pull Copolymer. Appl. Phys. Lett. 2011, 98, 043301. (6) Street, R. A.; Cowan, S.; Heeger, A. J. Experimental Test for Geminate Recombination Applied to Organic Solar Cells. Phys. Rev. B 2010, 82, 121301. (7) Shuttle, C. G.; Hamilton, R.; O’Regan, B. C.; Nelson, J.; Durrant, J. R. Charge-Density-Based Analysis of the Current-Voltage Response of Polythiophene/Fullerene Photovoltaic Devices. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 16448−16452. (8) Maurano, A.; 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. (9) Tanase, C.; Meijer, E. J.; Blom, P. W. M.; de Leeuw, D. M. Unification of the Hole Transport in Polymeric Field-Effect Transistors and Light-Emitting Diodes. Phys. Rev. Lett. 2003, 91, 216601. (10) Tanase, C.; Blom, P. W. M.; de Leeuw, D. M.; Meijer, E. J. Charge Carrier Density Dependence of the Hole Mobility in Poly(PPhenylene Vinylene). Phys. Status Solidi A 2004, 201, 1236−1245. (11) Street, R. A.; Song, K. W.; Northrup, J. E.; Cowan, S. Photoconductivity Measurements of the Electronic Structure of Organic Solar Cells. Phys. Rev. B 2011, 83, 165207. (12) Nelson, J. Diffusion-Limited Recombination in PolymerFullerene Blends and Its Influence on Photocurrent Collection. Phys. Rev. B 2003, 67, 155209. (13) Gill, W. D. Drift Mobilities in Amorphous Charge-Transfer Complexes of Trinitrofluorenone and Poly-N-Vinylcarbazole. J. Appl. Phys. 1972, 43, 5033. (14) Borsenberger, P. M.; Pautmeier, L. T.; Bässler, H. Nondispersive-to-Dispersive Charge-Transport Transition in Disordered Molecular Solids. Phys. Rev. B 1992, 46, 12145−12153.

ASSOCIATED CONTENT

S Supporting Information *

Detailed calculations of the expression of the recombination rate R. Device performance and J−V curves for thin P3HT and thickness series of PTB7 based devices. List of parameters used in the ASA drift-diffusion simulations. Generation profiles within the active layer calculated by Matrix Modeling Technique for PTB7 and P3HT devices. Prediction of the open-circuit voltage for a wide range of light intensities for all the devices presented herein. Light ideality factors for the PTB7 devices. This material is available free of charge via the Internet at http://pubs.acs.org. 8841

dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842

The Journal of Physical Chemistry C

Article

(15) Shuttle, C. G.; O’Regan, B.; Ballantyne, A. M.; Nelson, J.; Bradley, D. D. C.; Durrant, J. R. Bimolecular Recombination Losses in Polythiophene: Fullerene Solar Cells. Phys. Rev. B 2008, 78, 113201. (16) 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. (17) Mozer, A. J.; Dennler, G.; Sariciftci, N. S.; Westerling, M.; Pivrikas, A.; Ö sterbacka, R.; Juška, G. Time-Dependent Mobility and Recombination of the Photoinduced Charge Carriers in Conjugated Polymer/Fullerene Bulk Heterojunction Solar Cells. Phys. Rev. B 2005, 72, 035217. (18) Leong, W. L.; Cowan, S. R.; Heeger, A. J. Differential Resistance Analysis of Charge Carrier Losses in Organic Bulk Heterojunction Solar Cells: Observing the Transition from Bimolecular to TrapAssisted Recombination and Quantifying the Order of Recombination. Adv. Energy Mater. 2011, 1, 517−522. (19) 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. (20) Foertig, A.; Baumann, A.; Rauh, D.; Dyakonov, V.; Deibel, C. Charge Carrier Concentration and Temperature Dependent Recombination in Polymer-Fullerene Solar Cells. Appl. Phys. Lett. 2009, 95, 052104. (21) Chen, S.; Choudhury, K. R.; Subbiah, J.; Amb, C. M.; Reynolds, J. R.; So, F. Photo-Carrier Recombination in Polymer Solar Cells Based on P3ht and Silole-Based Copolymer. Adv. Energy Mater. 2011, 1, 963−969. (22) Kirchartz, T.; Nelson, J. Meaning of Reaction Orders in Polymer:Fullerene Solar Cells. Phys. Rev. B 2012, 86, 165201. (23) Rivnay, J.; Noriega, R.; Northrup, J. E.; Kline, R. J.; Toney, M. F.; Salleo, A. Structural Origin of Gap States in Semicrystalline Polymers and the Implications for Charge Transport. Phys. Rev. B 2011, 83, 121306. (24) Garcia-Belmonte, G.; Bisquert, J. Open-Circuit Voltage Limit Caused by Recombination through Tail States in Bulk Heterojunction Polymer-Fullerene Solar Cells. Appl. Phys. Lett. 2010, 96, 113301. (25) Kirchartz, T.; Pieters, B. E.; Kirkpatrick, J.; Rau, U.; Nelson, J. Recombination Via Tail States in Polythiophene:Fullerene Solar Cells. Phys. Rev. B 2011, 83, 115209. (26) Kuik, M.; Koster, L. J. A.; Wetzelaer, G. A. H.; Blom, P. W. M. Trap-Assisted Recombination in Disordered Organic Semiconductors. Phys. Rev. Lett. 2011, 107, 256805. (27) Kirchartz, T.; Nelson, J. Device Modelling of Organic Bulk Heterojunction Solar Cells. In Topics in Current Chemistry; Springer: Berlin, 2013; pp 1−46. (28) Monroe, D. Hopping in Exponential Band Tails. Phys. Rev. Lett. 1985, 54, 146−149. (29) Shuttle, C. G.; Hamilton, R.; Nelson, J.; O’Regan, B. C.; Durrant, J. R. Measurement of Charge-Density Dependence of Carrier Mobility in an Organic Semiconductor Blend. Adv. Funct. Mater. 2010, 20, 698−702. (30) MacKenzie, R. C. I.; Kirchartz, T.; Dibb, G. F. A.; Nelson, J. Modeling Nongeminate Recombination in P3ht:Pcbm Solar Cells. J. Phys. Chem. C 2011, 115, 9806−9813. (31) Rauh, D.; Deibel, C.; Dyakonov, V. Charge Density Dependent Nongeminate Recombination in Organic Bulk Heterojunction Solar Cells. Adv. Funct. Mater. 2012, 22, 3371−3377. (32) Deibel, C.; Wagenpfahl, A.; Dyakonov, V. Origin of Reduced Polaron Recombination in Organic Semiconductor Devices. Phys. Rev. B 2009, 80, 075203. (33) Li, G.; Shrotriya, V.; Yao, Y.; Huang, J.; Yang, Y. Manipulating Regioregular Poly(3-Hexylthiophene): [6,6]-Phenyl-C61-Butyric Acid Methyl Ester Blends-Route Towards High Efficiency Polymer Solar Cells. J. Mater. Chem. 2007, 17, 3126−3140.

(34) Schäfer, S.; et al. Influence of the Indium Tin Oxide/Organic Interface on Open-Circuit Voltage, Recombination, and Cell Degradation in Organic Small-Molecule Solar Cells. Phys. Rev. B 2011, 83, 165311. (35) You, J.; Li, X.; Xie, F.-x.; Sha, W. E. I.; Kwong, J. H. W.; Li, G.; Choy, W. C. H.; Yang, Y. Surface Plasmon and Scattering-Enhanced Low-Bandgap Polymer Solar Cell by a Metal Grating Back Electrode. Adv. Energy Mater. 2012, 2, 1203−1207. (36) Shuttle, C. G.; Maurano, A.; Hamilton, R.; O’Regan, B.; de Mello, J. C.; Durrant, J. R. Charge Extraction Analysis of Charge Carrier Densities in a Polythiophene/Fullerene Solar Cell: Analysis of the Origin of the Device Dark Current. Appl. Phys. Lett. 2008, 93, 183501−183501. (37) Hawks, S. A.; Deledalle, F.; Yao, J.; Rebois, D. G.; Li, G.; Nelson, J.; Yang, Y.; Kirchartz, T.; Durrant, J. R. Relating Recombination, Density of States, and Device Performance in an Efficient Polymer:Fullerene Organic Solar Cell Blend. Adv. Energy Mater. 2013, 1201−1209. (38) Kim, Y.; Choulis, S. A.; Nelson, J.; Bradley, D. D. C.; Cook, S.; Durrant, J. R. Device Annealing Effect in Organic Solar Cells with Blends of Regioregular Poly(3-Hexylthiophene) and Soluble Fullerene. Appl. Phys. Lett. 2005, 86, 063502. (39) Xu, Z.; Chen, L.-M.; Yang, G.; Huang, C.-H.; Hou, J.; Wu, Y.; Li, G.; Hsu, C.-S.; Yang, Y. Vertical Phase Separation in Poly(3Hexylthiophene): Fullerene Derivative Blends and Its Advantage for Inverted Structure Solar Cells. Adv. Funct. Mater. 2009, 19, 1227− 1234. (40) Li, G.; Shrotriya, V.; Huang, J.; Yao, Y.; Moriarty, T.; Emery, K.; Yang, Y. High-Efficiency Solution Processable Polymer Photovoltaic Cells by Self-Organization of Polymer Blends. Nat. Mater. 2005, 4, 864−868. (41) Hammond, M. R.; et al. Molecular Order in High-Efficiency Polymer/Fullerene Bulk Heterojunction Solar Cells. ACS Nano 2011, 5, 8248−8257. (42) Erb, T.; Zhokhavets, U.; Gobsch, G.; Raleva, S.; Stühn, B.; Schilinsky, P.; Waldauf, C.; Brabec, C. J. Correlation between Structural and Optical Properties of Composite Polymer/Fullerene Films for Organic Solar Cells. Adv. Funct. Mater. 2005, 15, 1193−1196. (43) Blouin, N.; Michaud, A.; Gendron, D.; Wakim, S.; Blair, E.; Neagu-Plesu, R.; Belletête, M.; Durocher, G.; Tao, Y.; Leclerc, M. Toward a Rational Design of Poly(2,7-Carbazole) Derivatives for Solar Cells. J. Am. Chem. Soc. 2007, 130, 732−742. (44) Kirchartz, T.; Deledalle, F.; Tuladhar, P. S.; Durrant, J. R.; Nelson, J. On the Differences between Dark and Light Ideality Factor in Polymer:Fullerene Solar Cells. J. Phys. Chem. Lett. 2013, 2371− 2376. (45) Credgington, D.; Durrant, J. R. Insights from Transient Optoelectronic Analyses on the Open-Circuit Voltage of Organic Solar Cells. J. Phys. Chem. Lett. 2012, 3, 1465−1478. (46) Credgington, D.; Jamieson, F. C.; Walker, B.; Nguyen, T. Q.; Durrant, J. R. Quantification of Geminate and Non-Geminate Recombination Losses within a Solution-Processed Small-Molecule Bulk Heterojunction Solar Cell. Adv. Mater. 2012, 24, 2135−2141.

8842

dx.doi.org/10.1021/jp502948y | J. Phys. Chem. C 2014, 118, 8837−8842