  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.
