  Unintentional doping of the active layer is a source for lowered device
performance in organic solar cells. The effect of doping is to induce a
space-charge region within the active layer, generally resulting in increased
recombination losses. In this work, the impact of a doping-induced space-charge
region on the current-voltage characteristics of low-mobility solar cell
devices has been clarified by means of analytical derivations and numerical
device simulations. It is found that, in case of a doped active layer, the
collection efficiency of photo-generated charge carriers is independent of the
light intensity and exhibits a distinct voltage dependence, resulting in an
apparent electric-field dependence of the photocurrent. Furthermore, an
analytical expression describing the behavior of the photocurrent is derived.
The validity of the analytical model is verified by numerical drift-diffusion
simulations and demonstrated experimentally on solution-processed organic solar
cells. Based on the theoretical results, conditions of how to overcome charge
collection losses caused by doping are discussed. Furthermore, the presented
analytical framework provides tools to distinguish between different mechanisms
leading to voltage dependent photocurrents.
