2 3 4 5 6 7 8 1$^{2}$ 3 4 5 | J Ph  - J Ph (V POS ) |  [mA/cm†] 0.01 0.1 1 10 |V - V$_{POS}$| [V] 3 4 5 6 7 8 9 1 P Braun (E)  exp. data, reverse direction  exp. data, forward direction  P$_{Braun}$(E) • Sokel-Hughes (V)  P$_{Braun}$(E)  Sokel-Hughes (V) 4 5 6 7 8 9 1$^{2}$ 3 4 5 6 7 8 | J Ph  - J Ph (V POS ) |  [mA/cm†] 6 8 0.1 2 4 6 8 1 2 4 6 8 10 |V - V$_{POS}$| [V] a) (a)  130 nm 80 nm 70 nm 55 nm 4 6 10 6 2 4 6 10 7 2 4 6 10 8 |V - V$_{POS}$|/d [V/m] 4 5 6 7 8 $_{9}$1 2 3 4 5 6 7 8 b) (b)  130 nm 80 nm 70 nm 55 nm 5 FIG. 6. (Color online) Comparison of experimental photocurrent (cell with Ca/Al cathode under 1 sun) and a model based on Braun– Onsager theory and extraction. Field dependent part of J$_{Ph}$ in for- ward and reverse direction (left axis) and PP dissociation probabil- ity (right axis) vs. effective voltage. The black lines show the PP dissociation after Braun (dotted), extraction after Sokel & Hughes (dashed) and their combined product (solid). FIG. 5. (Color online) Plot of the photocurrent in reverse direction (with the origin shifted to POS) against effective voltage (a) and calculated field (b) for cells with different active layer thicknesses. While the characteristic points, indicated by the red dashed lines, lie on top of each other in the left graph, they disperse in the right graph. where k$_{d}$ ( E ) = $_{k$_{d}$}$( E ) µ is the PP dissociation rate. It can be calculated by detailed balance from the recombination rate and the Coulomb binding energy, which depends on the PP ra- dius r$_{PP}$ . k$_{f}$ is the decay rate of a PP to the ground state. Since µ and t f = k − 1 f do not influence P$_{Braun}$ ( E ) independently, we use their product µ$_{t}$$_{f}$ as a single parameter. 21 Upon successful separation, the polarons need to travel to the electrodes to be extracted. This part can be described with a term introduced by Sokel and Hughes. 8 They solved the problem of photoconductivity in insulators analytically, ne- glecting dark current, trapping and recombination. The neg- ligence of recombination is a resonable approximation. 22–24 The result depends on temperature T and applied voltage V : Using an effective voltage V$_{eff}$ = | V − V$_{POS}$ | and a calculated field E = | V$_{eff}$ | / d , and adding the constant offset J$_{Ph}$ ( V$_{POS}$ ) , the overall photocurrent can be written as: This combination of Braun-model for polaron pair disso- ciation and the Sokel–Hughes term for charge extraction was first proposed by Mihailetchi et al., 9 but with the assumption that V$_{eff}$ = | V − V$_{0}$ | . This corresponds to the special case of a vanishing offset, where V$_{POS}$ equals V$_{0}$ . Also, they used a Gaussian distribution of polaron pair radii r$_{PP}$ to calculate the dissociation efficiency in the Braun model. While this as- sumption seems reasonable, a fixed value for r$_{PP}$ could de- scribe our data better than a distributed one. describes the experimental photocurrent well in both forward and reverse directions. A set of parameters in a narrow range could be employed to describe the experimental photocurrent of solar cells with different active layer thickness and cathode material over the whole measured range (Figure 7). Using Equation (2) to calculate E , effective values of about 400 nm for d were used in the model, almost independent of measured device thickness and clearly exceeding it. This is a As shown in Figure 6, the product of PP dissociation af- ter Braun and extraction after Sokel–Hughes (Equation (5)) FIG. 7. (Color online) Effective photocurrent J$_{Ph}$ − J$_{Ph}$ ( V$_{POS}$ ) vs. applied voltage for two solar cells with Ca/Al and Ag cathode (sym- bols). For both cells, the experimental data (symbols) agrees well with the model, Equation (5) (solid lines). J$_{Ph}$ = J$_{Ph,max}$$^{[}$ coth$^{(}$ eV$_{eff}$ 2 kT ) − 2 kT eV$_{eff}$$^{]}$ P$_{Braun}$ ( E )+ J$_{Ph}$ ( V$_{POS}$ ) (5) J$_{Ph}$ = J$_{Ph,max}$$^{[}$ exp ( qV / kT + 1 ) exp ( qV / kT − 1 ) − 2 kT qV ] (4) 5 0 -5 J Ph  - J Ph (V POS ) [mA/cm†] -10 -8 -6 -4 -2 0 2 applied voltage [V] Ca/Al cathode, active layer 110 nm  exp. data   fit, Equation (5) Ag cathode, active layer 300 nm  exp. data  fit, Equation (5)