2.1. J-V Characteristics
Herein we study devices made from three different PBDTTT-C:PC71BM compositions; namely, 50 wt% PC71BM, 60 wt% PC71BM, and 67 wt% PC71BM. In order to understand the differences in performance from a general standpoint, we optimized each blend individually for active-layer thickness (Figure 2). For plots with error bars we refer the reader to the supplementary information. In agreement with previous reports,31 we find that the optimal blend weight ratio has 60 wt% PC71BM. In Figure 2 the active-layer spin speed was used as a relative unit for thickness because a measurement of the absolute thickness of all active layers was not necessary for the following J-V comparisons. From the trends in Figure 2 we see that both the 60 wt% PC71BM and 67 wt% PC71BM devices are able to maintain high fill factors at thicknesses where the JSC is locally maximized. The 50 wt% PC71BM blend, on the other hand, begins to suffer losses in fill factor while the JSC is still increasing with increasing thickness. Based on typical absorbed photon flux vs. active-layer thickness plots for BHJ OPVs,51, 54 we hypothesize that, in this case, the charge-collection efficiency is greater in films with higher fullerene content, allowing the active layers to be optimized at the first absorption maximum.51–54 Thus, it appears that the favorable overall absorption of higher PBDTTT-C content active layers (50 wt% PC71BM) cannot be exploited due to excessive nongeminate losses with modest increases in active-layer thickness. This assessment of the J-V characteristics and device performance is supported by our transient optoelectronic measurements discussed below.
Figure 2. (a) Fill Factor, (b) JSC, (c) VOC, and (d) PCE dependence on spin speed for the compositions examined in this study. All data points are averaged over 6 devices, and the solid lines are added as guides to the eye.
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We also observed a robust trend in VOC with fullerene loading for the compositions examined herein; namely, that the open-circuit voltage is always higher for lower fullerene content (Figure 2c). Though the differences in VOC between blends is only on the order of ∼10 mV, this trend was consistently reproduced from different polymer and PC71BM batches, as well as from many devices fabricated at different laboratories (ICL and UCLA). The observation that VOC decreases with higher PCBM content over a wide composition range has also been found in other polymer systems.32, 33, 35, 55–, 58 Sparing contact effects, the VOC is a function of energy levels and the steady-state carrier concentration determined by the balance between generation and recombination.9, 18, 22, 59, 60 Earlier investigations into the reason for the composition dependence of VOC found that the change in VOC with fullerene content can be explained with changes in the CT-state energy and that kinetic arguments were not necessary to explain the trends.32, 35 To verify whether this is the case in our devices as well, and to better understand how the PBDTTT-C:PC71BM composition affects energy levels, recombination, and the overall device performance, we performed transient optoelectronic measurements and electroluminescence studies.
2.2. Transient Optoelectronic Analysis
Table 1. J-V Characteristics and device parameters of different blend compositions processed under identical conditions. The device characteristics were averaged over 4 devices (± standard deviation). Thickness measurements were averaged over ≥ 4 locations and taken with an AFM. The built-in voltage was derived from the intersection of light and dark curves.
|Composition||VOC [mV]||JSC [mA/cm2]||FF [%]||PCE [%]||Active Layer Thickness [nm]||Relative Dielectric Constant (ϵr)||Built-in Voltage [V]|
|50 wt% PC71BM||715 ± 3||11.4 ± 0.1||61.3 ± 0.5||4.98 ± 0.1||67 ± 4||3.7||0.79|
|60 wt% PC71BM||708 ± 1||13.6 ± 0.2||64.5 ± 0.5||6.22 ± 0.1||82 ± 2||3.8||0.805|
|67 wt% PC71BM||698 ± 3||14.6 ± 0.3||60.8 ± 1.2||6.18 ± 0.1||105 ± 5||3.9||0.78|
Figure 3a shows n(VOC) as measured by CE, and (c) gives the total carrier lifetime as a function of average carrier concentration. We first see from Figure 3a that for a given average carrier density, the VOC(n) is consistently different across blend ratios, where VOC(50 wt% PC71BM) > VOC(60 wt% PC71BM) > VOC(67 wt% PC71BM) for a given n = constant. Thus, for identical average charge densities n, the quasi-Fermi level splitting is larger for lower fullerene content, which indicates a significant composition-induced shift in the density of states. For lower fullerene loadings, the band tails of the polymer HOMO and PC71BM LUMO are either further separated from each other in energy, lower in magnitude, or a combination of both when compared to the higher PC71BM loading cases. We have schematically indicated this apparent shift in the density of states in Figure 3b. While the magnitude or energetic separation of the density of states around the band edges changes with composition, the slope of n vs. VOC, and therefore the shape of the DoS, is not significantly affected.64
Figure 3. (a) The average carrier concentration as a function of VOC and (c) the total carrier lifetime as a function of average carrier concentration for all PBDTTT-C:PC71BM weight ratios studied herein. (b) is a schematic showing how the density of states shifts with composition. Note that an increase in the absolute density of states at given energy or a shift of the DoS in energy are indistinguishable from a charge extraction measurement. We cannot discern whether the change is primarily in the HOMO or LUMO or whether both change equally.
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In order to analyze the recombination kinetics, we examine the total carrier lifetime as a function of average carrier density (Figure 3c). Much like Figure 3a, Figure 3c shows that τ(n) is also shifted across compositions. However, despite the larger VOC values, τ(n = constant) goes as τ(50 wt% PC71BM) < τ(60 wt% PC71BM) < τ(67 wt% PC71BM). Thus, nongeminate recombination is actually fastest in the 50 wt% PC71BM blend, followed by the slower 60 wt% PC71BM and 67 wt% PC71BM blends, respectively. This indicates that the small differences in VOC are due to two effects that partly compensate each other, namely a change in DoS and a shift in recombination dynamics. The higher magnitude and/or energetic shift in DoS induced by higher fullerene content is partly compensated by a concomitant reduction of the recombination rate, which, taken together, leads to only a slightly lower open-circuit voltage when compared to a lower fullerene content case.
The dominating recombination mechanism responsible for the trends in τ(n) of Figure 3c is of fundamental interest to understanding what limits the efficiency of a given active layer. A common approach for describing nongeminate recombination is via a Langevin-type mechanism, where the recombination coefficient krec is directly proportional to the carrier mobility (μ).65 To examine the validity of a Langevin-type model, we used the technique described in Reference 66 to evaluate carrier drift mobilities as a function of average carrier concentration (Figure 4a). From Figure 4a we see that the mobility is weakly carrier-density dependent, offsetting between compositions, and actually largest for the 67 wt% PC71BM blend, following μ(67 wt% PC71BM) > μ(60 wt% PC71BM) > μ(50 wt% PC71BM). For comparison, we plot the nongeminate recombination coefficient also in Figure 4a as calculated from Equation (4). The data in Figure 4a and Figure 3c have exactly the opposite trend one would expect if Langevin-type recombination were dominant. In this particular case, larger PC71BM content increases the mobility and simultaneously decreases the recombination rate. Moreover, it is clear that the nongeminate recombination coefficient and the mobility have significantly different dependencies on average carrier density, which has been previously noted by Rauh et al.30 In the following electroluminescence section, we provide further evidence that, in this case, phase-segregation effects are likely the dominating factor in determining the nongeminate recombination properties.
Figure 4. (a) Average carrier mobilities of the different blend ratios under study measured by the method in Reference 66 and the effective nongeminate recombination coefficient as a function of average carrier concentration. (b) The resulting mobility-lifetime product (lifetime from Figure 3c) as a function of average carrier concentration. Note the different scales for the charge density n.
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To combine these dynamical constants into one effective assay of the electrical properties of the blend, we plot the mobility-lifetime product in Figure 4b using the data from Figure 3c and Figure 4a that overlap in carrier density. Clearly, higher PC71BM concentrations result in vastly superior electrical properties in this composition range. The differences in μτ(n) between the 50 wt.% PC71BM and 67 wt.% PC71BM blends approaches an order of magnitude over the measured carrier concentration range, which explains why the 50 wt% PC71BM blend has suboptimal photovoltaic properties.67 In this case, the relative improvements of μτ appear to afford acceptable fill factors at active-layer thicknesses corresponding roughly to the first absorption maximum for the 60 wt% PC71BM and 67 wt% PC71BM blends, but not the 50 wt% PC71BM blend (Figure 2).
Finally, in order to further understand the nature of these differences in recombination characteristics, we attempt to reconstruct the J-V curves and predict open-circuit voltages assuming that the generation rate is independent of voltage and that nongeminate recombination is the dominating loss process throughout the photovoltaic operating regime. Figure 5a–c shows the J-V reconstructions and Figure 5d the attendant VOC predictions of all blend ratios using the methods detailed in previous works (dark J-V reconstructions are provided on a logarithmic scale in Figure S1).14, 15, 18 The excellent agreement between measured and predicted values for all blend ratios in Figure 5 suggests that non-geminate recombination alone is sufficient to understand the shape of the J-V curves and the magnitudes of the open-circuit voltages for all compositions. In the final section below, we examine the electroluminescence spectra of the different blends to further specify the nature of this nongeminate, non-Langevin, type of recombination and, moreover, better understand why it is so sensitive to blend composition.
Figure 5. (a–c) J-V reconstructions comparing experimentally measured (solid lines) and reconstructed values (open points) based on the method detailed in References 14 and 16. (d) The light intensity dependence of VOC for each blend and the corresponding predicted VOC using the methods detailed in Reference 18.
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Figure 6a shows the electroluminescence spectra for each of the PBDTTT-C:PC71BM weight ratios and the pure PBDTTT-C polymer. The normalized 50 wt% PC71BM blend EL resembles that of the pure polymer, but with the high-energy cutoff ∼0.1 eV redshifted and a stronger low-energy emission tail. When progressing through the composition range, the EL spectra continue to redshift and appear to be in a transitionary phase at the optimal 60 wt% PC71BM blend ratio. Further examination shows that the photon energy corresponding to the maximum emission intensity (Emax) for the 60 wt% PC71BM blend was strongly voltage-dependent, where under injection conditions of ≤40 mA/cm2 the spectrum resembles that of the 67 wt% PC71BM device, but with increased current it shifts rapidly to resemble the 50 wt% PC71BM (Figure 6b). This luminescence transition, consistent with our charge extraction data, is an indicator of the important DoS evolution that takes place over a relatively narrow composition range. While the optimal 60 wt% PC71BM device EL was sensitive to injection conditions, the relative spectral intensities of the 50 wt% PC71BM and 67 wt% PC71BM blends were insensitive to injection, which is similar to what has been found for other polymer:PCBM systems.68
Figure 6. (a) Electroluminescence spectra of the different blend films and pure PBDTTT-C (all at J = 160 mA/cm2). (b) Shift in the EL emission maximum with injection conditions. (c) The linear relationship between CT emission band peak position (at J = 80 mA/cm2) and VOC at equal carrier concentrations.
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Looking closer at the blend EL spectra in Figure 6a, they appear to be composed of primarily two emission bands: one with peak intensity around ∼1.0–1.15 eV and the other at ∼1.4 eV. In order to quantitatively assess this observation, we reduced and deconvoluted each spectrum into two Gaussian emission profiles,34 attributing the higher-energy Gaussian at ∼1.4 eV to pure polymer emission and the low-energy Gaussian centered around ∼1.1 eV to CT-state emission (Figure S2). The presence of PBDTTT-C singlet activation in the electroluminescence spectra is consistent with the findings of Faist et al.69 for the case where the donor has an optical band gap of <1.7 eV (Eg,PBDTTT-C = 1.6 eV) and the donor/acceptor CT-energy is near the singlet energy of one of the pure materials. Based upon this finding, we hypothesize that, in this case, the CT energy is quite close to the polymer's singlet energy and the DoS modulation from fullerene loading significantly affects the singlet activation process. Faist et al.69 qualitatively found that singlet activation of one component correlated with reduced photovoltaic performance, which is in agreement with the case here, where the poorly performing 50 wt% PC71BM blend shows by far the most singlet activation, followed consecutively by the electrically superior 60 wt% PC71BM and 67 wt% PC71BM compositions (Figure S2). A number of photophysical processes can be activated when the blend energy levels are brought in too close proximity;70, 71 however, in this instance, it appears that injected electrons on the PC71BM can more easily transfer onto the PBDTTT-C for cases with less PC71BM loading. This effect would partially nullify the physical separation of charges by material phase segregation, leading to the observed higher nongeminate recombination rates for lower fullerene loadings. It may also seem likely that, in addition to the nongeminate losses detailed above, the 50 wt% PC71BM blend suffers more geminate recombination due to a smaller driving force for interfacial charge separation. However, we note that transient absorption measurements (Figures S3–S5) found strong generation yields for all the compositions studied herein and even a strong polaron yield for neat PBDTTT-C.
For further verification of the connection between our EL and optoelectronic measurements, we take the reduced CT emission band's center of gravity (ECT) and plot it against the VOC at equivalent active-layer charge densities (Figure 6c). We find for the case of VOC(n = 2 × 1016 cm−3) and for EL injection conditions of J = 80 mA/cm2 that the CT emission band's center of mass and VOC scale on precisely a 1-to-1 basis. We note that the CT emission band's center of mass varied weakly with injection conditions (Figure S6) and that the slopes also varied marginally with different VOC(n = constant). Despite these variations, we found that plots of VOC(n = constant) vs. ECT were always linear with slopes near unity. Thus, the offset between open-circuit voltages of different compositions at equivalent carrier densities are reproduced well by our EL analysis, indicating that EL reflects the same DoS that is measured with charge extraction.
Despite significantly different chemical structures, polymer:PCBM stoichiometries, and optimization conditions, similar relationships between PCBM composition, VOC, and ECT have been reported for other conjugated polymer:PCBM blends.34, 35, 72 These prior studies have also found that VOC scales with the CT-state energy in an expected 1-to-1 fashion.35, 73 Primarily two explanations have emerged regarding the observed interrelation between PCBM content, VOC, and ECT,: (i) the VOC and CT-state energy decrease with increasing PCBM content due to an increase in the relative dielectric constant of the film,72 and/or (ii) nanoscale crystallization due to added PCBM stabilizes the LUMO energy76 and thus decreases the VOC and redshifts the CT-state emission.32, 34 Considering the work of Piersimoni et al.32 and Jamieson et al.,74 and because this effect is witnessed over several different polymer/fullerene systems, we believe that morphological differences are the primary cause for such trends. Additionally, Agostinelli et al.75 found that the refractive index of P3HT:PCBM BHJs was only weakly dependent on composition, which further suggests that a change in relative dielectric constant could not fully account for these trends. Composition-induced PC71BM aggregation would be consistent with our n vs. VOC and EL data for the reasons stated above; however, it is difficult to hypothesize about microstructural changes without direct evidence. It is presently unclear whether a change in the density of states with composition as observed for PBDTTT-C:PC71BM blends could be a general feature of polymer:PCBM systems. Given that the energy of the charge transfer state electroluminescence typically shifts with composition in various polymer:PCBM blends but not necessarily with other fullerene-based acceptors,32, 34, 35, 74 our data could be revealing as to why PCBM works so well with an array of different polymers.