-8 -6 -4 -2 0 2 photocurrent density J Ph  [mA/cm†] -2.0 -1.0 0.0 1.0 applied voltage [V] a) (a)  pristine 10min @ 80° C 10min @ 140° C 10min @ 200° C -2.0 -1.0 0.0 1.0 applied voltage [V] -8 -6 -4 -2 0 2 4 b) (b) 90 nm, Ag 75 nm, Ag  125 nm, Ca/Al 80 nm, Ca/Al 4 offsets for thinner and thicker devices (not shown). As an alternative explanation for this constant offset, we propose the band bending in vicinity of the contacts, which— independently of applied bias—has only one direction and re- sults in an electric field high enough for efficient polaron pair dissociation (see Figure 2). The contact regions would then give a constant contribution to J$_{Ph}$ , which depends on the de- gree of band bending—and therefore the height of the injec- tions barriers—while the bulk region contributes to J$_{Ph}$ as a function of applied voltage and causes the symmetry. The exact nature of this offset and its dependence on the cathode material has to be further investigated. A highly neg- ative offset is crucial for device performance, and should be optimized, e.g. by choice of cathode material. FIG. 4. (Color online) Photocurrent density vs. applied voltage. (a) Influence of thermal treatment for solar cells with Ca/Al cathode. (b) Cells with Ca/Al and Ag cathode, in each case for two different active layer thicknesses. The magnitude of the voltage-independent offset can be influenced by thermal treatment and choice of cathode material. C. Voltage vs. field dependence B. Voltage-independent offset of J$_{Ph}$ E = | V − V$_{POS}$ | / d (2) The active layer thickness d has only little influence on the voltage dependence of the observed photocurrent (Fig- ure 5(a)). Of course the absolute value of J$_{Ph}$ is higher for thicker cells, but the shape of J$_{Ph}$ ( V ) is very similar for cells with thicknesses between 55 and 130 nm. This is surprising, since e.g. polaron pair dissociation and thereby J$_{Ph}$ are sup- posed to be dependent on electric field E . 21 In the simplest ap- proximation, assuming a constant slope in energy bands over the whole extension of the device, the effective field is the fraction of effective voltage and active layer thickness: Characteristic points of the photocurrent, indicated by red dashed lines in Figure 5, lie on top of each other when plot- ted against effective voltage | V − V$_{POS}$ | . When plotted against the calculated field E (Equation (2)), the curves of J$_{Ph}$ disperse (Figure 5(b)). This indicates that the approximation for the in- ternal field in Equation (2) is not realistic. The reason for this is the voltage drop at the contacts (Figure 2), which greatly reduces the electric field in the bulk of the cell. In addition the photocurrent is not only governed by field dependent polaron pair dissociation, but also depends on the extraction of charge carriers. As described below, the active layer thickness does not influence this extraction mechanism. As mentioned above, the photocurrent is composed of two contributions. The first is voltage-dependent and symmetric with respect to POS. The second contribution is a voltage- independent offset, which is crucial for device performance and can be influenced by processing parameters. Figure 4 shows the influence of cathode material and annealing con- ditions on the photocurrent. While the shape of J$_{Ph}$ remains similar, the offset is critically dependent on both cathode ma- terial and thermal treatment. With respect to the pristine sam- ple, the offset decreases after thermal treatment at 80 or 200 $^{◦}$C, but increases upon treatment at 140 $^{◦}$C (Figure 4a). Us- ing Ag as cathode material yields a much smaller offset than Ca/Al, while the shape of the photocurrent curves is very simi- lar (Figure 4b). V$_{POS}$ is also smaller for cells with Ag cathode, with values of about 0.45 V, which is a direct consequence of the higher injection barriers. Active layer thickness d influ- ences the magnitude of the offset as well. The highest negative offset, up to 4.1 mA cm − $^{1}$, was observed for solar cells with Ca/Al cathode, active layer thickness of 120 nm and thermal annealing at 140 $^{◦}$C. These cells had the highest J$_{SC}$ and PCE. As this voltage-independent offset can be influenced by the choice of cathode material without changing the shape of the photocurrent significantly, we assume the contact regions to be responsible for the offset. The voltage dependent part of J$_{Ph}$ then corresponds to the photocurrent generated in the bulk of the solar cell. Ooi et al. explained this offset with self-selective electrodes, 5 resulting in a constant diffusion current J$_{Ph, offset}$ = − ( eDn$_{ph}$ / d ) , where e is the elementary charge, D the diffusivity and n$_{ph}$ the concentration of photogenerated charge carriers at the selective electrode. In contrast to this predicted d − 1 dependence, we observed a maximum (nega- tive) offset for a thickness d of about 120 nm, with smaller To describe the voltage dependence of the photocurrent, we propose a model that takes field-dependent polaron pair (PP) dissociation and voltage dependent polaron extraction by drift and diffusion into account. A well-known model to describe field-dependent PP dissociation was presented by Braun in 1984. 6 Using the field dependence for ion-pair dissociation by Onsager and Langevin recombination for polarons, 7,15 Braun derives the following PP dissociation probability: D. Polaron pair dissociation and charge extraction P$_{Braun}$ ( E ) = k$_{d}$ ( E ) k$_{d}$ ( E )+ k$_{f}$ = $_{k$_{d}$}$( E ) $_{k$_{d}$}$( E )+( µ$_{t}$$_{f}$ ) − 1 , (3)