Analytical solution for charge carrier transients in a two-layer-structure

The use of photo-conductance decay measurements for determining charge carrier lifetimes in a two-layer structure was up to now limited by the lack of an appropriate analytical solution describing the carrier dynamics. We present an exact solution for arbitrary layer parameters. We prove that in the limit that the lifetime in layer 1 is much higher than in layer 2 the exact solution reduces to the standard approximation with an effective recombination velocity for layer 2. Plots for the deviation of the approximate from the exact solution for wide parameter ranges are presented. Furthermore, we describe a sensitive test for contamination in deposition equipment.