Averaging of laterally inhomogeneous lifetimes for one-dimensional modeling of solar cells

This paper investigates the influence of laterally inhomogeneous cell parameters on solar cell efficiency. A universal procedure is proposed which allows the reduction of a frequency distribution of an arbitrary cell parameter to just one single value for one-dimensional (1D) device modeling. This procedure is in detail investigated for the case of lifetime and diffusion length distributions showing that the frequency distribution of local minority carrier densities (Δn) is the appropriate parameter for solar cell modeling. The actual position of high and low lifetime areas on the cell is found to be of minor influence if Δn is used as an input parameter. Therefore, using the lifetime frequency distribution allows us to include the effect of spatial inhomogeneities in recombination activity in 1D solar cell modeling. Both simulated and experimental examples for the modeling procedure and the quantitative influence of spatial inhomogeneities on solar cell performance are discussed. This article presents a possibility to include laterally resolved measurements of material and process quality data in routine predictive modeling of solar cell performance.