-8 -6 -4 -2 0 photocurrent density [mA/cm†] -1.0 0.0 1.0 applied voltage [V] 3 2 1 0 -1 -2 J [mA/cm†] 102 100 98 time [ms] 0.62 0.60 0.58 0.56 voltage [V] J$_{Ph}$ voltage-independent offset POS 2 sonability of this working mode has been proven by preceding impedance measurements that showed a clear semicircle (with a negligible offset impedance of about 10 $_{W}$, corresponding to the series resistance R$_{s}$ ) in Cole–Cole representation for our cells. Since we have Schottky-like contacts at the metal– semiconductor interfaces of our devices, the value of V$_{CV}$ was determined by the intercept of a linear fit of the Mott–Schottky plot. All presented simulations were done solving the one dimen- sional differential equation system of Poisson‘s equation and the continuity equations for electron and holes in a numerical iterative approach, 11,12 implicitly assuming a band-like trans- port. A 100 nm thick bulk-heterojunction solar cell is calcu- lated at a temperature of T = 300 K containing electrons and holes with equal mobilities of µ$_{n}$ = µ$_{p}$ = 10 − 4 cm$^{2}$/Vs. 13 For the active material, the effective medium approach is used, leading to effective electrical bandgap of E$_{G}$ = 1 . 1 eV be- tween the donor HOMO (highest occupied molecular orbital) and the acceptor LUMO (lowest unoccupied molecular or- bital) level and an effective dielectric constant of e$_{r}$ = 3 . 4. 13 The effective charge carrier densities of LUMO and HOMO— describing the spatial charge carrier densities of electrons n ( x ) and holes p ( x ) by Fermi-Dirac statistics—were set to N$_{c}$ = N$_{v}$ = 10 20 cm − $^{3}$. The interfaces towards the electrodes are assumed to possess injection barriers of 0.1 eV without any surface recombination. 14 Illumination is taken into account by a homogenous charge carrier generation rate G over the whole device. This simpli- fication avoids band bending due to local differences of the charge carrier densities caused by optical interference inside the sample. We use Langevin theory to describe bimolecular charge carrier recombination of free polarons to the ground state. 15 The combination of charge carrier generation and re- combination leads to the following net generation rate: All samples investigated were spin-coated from solution of a 1:1 weight ratio of P3HT and PCBM in chlorobenzene, onto indium tin oxide/glass substrates coated with poly(3,4- ethylenedioxythiophene):poly(styrenesulfonate). After an an- nealing step at 140 $^{◦}$C, metal contacts were applied by ther- mal evaporation; either Ca (3 nm) followed by Al (110 nm) or only Ag (120 nm). All fabrication and characterization took place in a nitrogen atmosphere glovebox. The cells with Ca/Al cathode had fill-factors (FF) of about 60 % and PCE of 2–3 %, as determined with a Xe-lamp, adjusted to simulate standard testing conditions (STC). 10 with the elementary charge q , the dielectric constant$_{e}$$_{0}$, the Boltzmann constant k$_{B}$ and the intrinsic charge carrier density n$_{i}$ = √ N$_{c}$N$_{v}$ exp ( qE$_{G}$ / 2 k$_{B}$T ) . The result of this system are spatially resolved values for the electrical potential and electron and hole densities in form of quasi-Fermi potentials. In order to create a band structure, the potentials have to be transformed into an energy level. Since experimental values of device work functions are not available, the electron conducting contact (here aluminum) is set to a typical value of -4.25 eV, 16 which determines the ab- solute value of all other potentials. In Figure 2 the resulting band structures are presented in the dark and under illumination for two important bias voltages. First, a voltage resulting in flat bands—and therefore zero electric field E , being the spatial derivative of the potential— in the middle of the sample, and second the built-in voltage for comparison. For the capacitance–voltage (CV) measurements we ap- plied a 5 kHz AC voltage with an amplitude of 40 mV to our cells and performed a DC bias sweep. It was carried out under nitrogen atmosphere and without any incident light to the device to prevent distortions due to charge carrier gen- eration. Data acquisition was carried out with an Agilent E4980A LCR-meter in parallel RC circuit mode. The rea- The photocurrent measurements were performed based on the setup proposed by Ooi et al.$^{5}$, using a white 10 W LED for pulsed illumination. The pulse duration was set to 0.5 ms at a duty cycle of 50 %, giving the cell ample time to reach steady-state after switching the light on/off. The illumination level was equivalent to one sun, based on comparison of the short-cuircuit current ( J$_{SC}$ ) reached with the LED to the J$_{SC}$ reached under simulated STC. The active layer thickness was determined with a Veeco Dektak 150 profilometer. II. EXPERIMENTAL U ( x ) = G − q ( µ$_{n}$ + µ$_{p}$ ) e 0 e$_{r}$ $^{(}$np − n 2 i ) (1) FIG. 1. (Color online) Photocurrent density J$_{Ph}$ vs. applied volt- age of a typical P3HT:PCBM solar cells with Ca/Al cathode under 1 sun. The point of optimal symmetry (POS) is indicated by the blue circle. The voltage-dependent, symmetric shape of J$_{Ph}$ is shifted by a constant offset to more negative values. Note that the density of recorded data points is higher between 0 V and 1 V applied voltage. The inset shows the current flowing under pulsed illumination, with an increase in the applied voltage every millisecond.