Response to Comment on “Charge Carrier Extraction in Organic Solar Cells Governed by Steady‐State Mobilities”

We welcome the comment by Felekidis et al. as it allows us to better highlight a couple of points that might not have been clear in our original publication (OP).1 In the comment, the authors reproduce part of our experiment (only at short-circuit conditions) and then conclude that there is a significant number of carriers that are extracted at short times solely based on a Monte-Carlo simulation. First of all, we would like to note that in the original publication, we specifically considered a solar cell under realistic operating conditions, i.e., close to 1 Sun light intensity, normal device layout, and at a bias voltage close to the maximum power point (MPP). We find that the extraction rate goes through a minimum at a voltage (Vmin) close to the MPP. At this voltage, the extraction rate is determined by the steady-state mobility as measured on, for example, a space-charge-limited diode. We only showed (Figure 3b in OP) the extraction rates at different bias voltages in order to identify Vmin. In contrast, Felekidis et al. only look at short-circuit (SC) conditions in their comment, which is a different experiment. In their comment, the authors chose the short-circuit condition for “reliability” because close to MPP “the field is ill-defined” and that “in the absence of a driving field there should be no visible current transient—any net current transient at apparent “flatband” conditions must, therefore, be due to ill-defined remaining electric fields and unknown contact selectivity.” Whether or not there is a “flatband” condition near the MPP is beside the point. We wish to point out that there is a clear, well-defined driving force for current at Vmin: For example, in the PTB7 case from the OP there is still 50 A m−2 flowing through the device (whereas Jsc = 122 A m−2) so there is still quite some current at the considered point (V = 0.7 V). We did not extract the mobility from SC conditions and we did not claim that the extraction at short-circuit is governed by steady-state mobilities. That conclusion is solely based on the regime near MPP. Of course, the extraction rate at SC is expected to be faster even just considering the larger internal electric field. But it could also very well be that the dispersion has an effect on the extraction at SC for highly disordered systems and thin devices. In any case, at MPP the extraction is slower and charges will have more time to relax. To gauge whether our experimental data are influenced by RC-time issues, the experiment was repeated with different load resistors for measuring the current, a much smaller device area (1 mm2), and a faster time constant of the LED switching (≈50 ns).2 In other words, a faster setup was used. The resulting extraction rates at Vmin are very similar to the rates in the OP: a load resistor of 50 Ω (as used in the OP) or 100 Ω give very similar extraction rates of 1.9 and 1.6 µs−1 respectively giving a mobility 5–5.9 × 10−8 m2 V−1 s−1 (expected ≈3 × 10−8 m2 V−1 s−1 see OP). We even performed an extra experiment at short-circuit for the PTB7:PC[70]BM device (see Figure 1a) at the short-circuit condition, where the RC-time should have the biggest impact as the extraction is faster there. We find that there is very little difference in the extraction rate depending on the load resistance when it is smaller than 200 Ω. We also performed additional drift-diffusion simulations which include the load resistor and different device areas characteristic for typical measurement conditions, see Figure 1b. The parameters were chosen such that they are representative for PTB7:PC[70]BM solar cells (see Table 1 for details). These simulations reveal a negligible effect of the RC time on the extraction rate at Vmin, meaning that measurements at Vmin provide accurate values of the charge carrier mobility. In their comment, the authors also point out that “the conclusion that the equilibrium mobility describes the extraction of all charges clearly cannot be drawn.” It is obvious, however, that any mobility would always correspond to a distribution of extraction times. The point of the steady-state mobility that we discuss in the OP is to describe the mean mobility and not the mobility of all the charges. There are many details that determine whether a Monte-Carlo simulation is accurate or not: the donor–acceptor morphology, dark injection and contacts, Coulomb interactions, recombination, generation of carriers, size of the simulation volume to name but a few.3-6 The statement that “For an infinite device, electrons would relax to the highest (holes to the lowest) of the equilibrium energy (σ2/kT) and the quasi-Fermi energy” is misleading. As shown by Bässler, charge carriers only relax to σ2/kT if carrier–carrier interaction can be excluded, i.e., in an empty device.6 The MC model as shown in ref. 6, Figure 4b uses a perfect sink as the electrodes, which means that the carrier density near the electrodes vanishes, and the device is empty in dark. In a real solar cell, however, the electrodes are not just perfect sinks but also induce charge carriers. The injection of charge carriers by the electrodes is especially important in thin film devices8-10 such as organic solar cells. MC simulations4 and experiments8 on diodes have shown that in the presence of an ohmic contact (as used to optimize the open-circuit voltage) the device is not empty and, therefore, the charge carriers do not relax to σ2/kT highlighting the importance of properly defining the contact. At forward bias, such as close to MPP, these electrodes will inject even more charge, while extraction will be slower. In sum, at finite carrier density, like in an organic solar cell, charge carriers relax much faster and they do not relax to σ2/kT.11 Even in a space-charge-limited diode injected charges very quickly relax and obey a Fermi–Dirac distribution, while still not relaxing to σ2/kT due to state-filling.4 Thus, the mobility measured in a space-charge-limited diode represents a steady-state quantity, but it does not correspond to an empty device. This is one of the reasons why mobilities thus obtained are so valuable in characterizing materials for organic solar cells. It is, therefore, not an equilibrium quantity but a steady-state one and we never suggested that the extraction from an organic solar cell is governed by equilibrium mobilities. Finally, for highly disordered materials or thin devices there might indeed be an influence of dispersion, especially at short-circuit or reverse bias. It is to be expected that some charges are faster than others. However, we trust that we have demonstrated that this effect does not dominate at MPP and that steady-states mobilities indeed give a good description of the transport under those conditions. This can be further demonstrated by the numerous publications that have shown a clear correlation between steady-state mobilities and the performance of organic solar cells.12-21 It would be difficult to reconcile the success of this type of description with early time mobilities that are orders (up to 4) of magnitude higher than the steady-states mobilities. To conclude, we hope that we have convinced the readers that our original analysis is indeed meaningful for an organic solar cell under operating conditions. The authors declare no conflict of interest.