Quantitative theory of the grain boundary impact on the open-circuit voltage of polycrystalline solar cells

Thin film polycrystalline photovoltaics are a mature, commercially-relevant technology. However, basic questions persist about the role of grain boundaries in the performance of these materials, and the extent to which these defects may limit further progress. In this work, we first extend previous analysis of columnar grain boundaries to develop a model of the recombination current of "tilted" grain boundaries. We then consider systems with multiple, intersecting grain boundaries and numerically determine the parameter space for which our analytical model accurately describes the recombination current. We find that for material parameters relevant for thin film photovoltaics, our model can be applied to compute the open-circuit voltage of materials with networks of inhomogeneous grain boundaries. This model bridges the gap between the distribution of grain boundary properties observed with nanoscale characterization and their influence on the macroscale device open-circuit voltage.