Meaning of reaction orders in polymer:fullerene solar cells

Nongeminate recombination in polymer:fullerene solar cells is frequently characterized using transient optoelectronic measurements that allow the determination of recombination rates, charge carrier lifetimes, and average charge carrier concentrations as a function of voltage. These data are often interpreted in terms of an empirical reaction order defining how recombination depends on measured charge density. In polymer:fullerene solar cells, the empirical reaction orders are often considerably larger than 2, which had previously been explained in terms of the nonlinear relationship between mobile and trapped charge carriers in the presence of an exponential tail of localized states. Here, we show that experimentally determined reaction orders depend not only on the shape of the density of states but also on the spatial distribution of carriers. In particular, in solar cells with small depletion regions due to small active layer thicknesses or due to large unintentional background doping of the polymers, the reaction order can assume values that are much larger than the value expected from the shape of the density of states alone.