Impact of non-parabolic electronic band structure on the optical and transport properties of photovoltaic materials

For semiconductors used in photovoltaic devices, the effective mass approximation allows calculation of important material properties from first-principles calculations, including optical properties (e.g. exciton binding energies), defect properties (e.g. donor and acceptor levels) and transport properties (e.g. carrier mobilities). The conduction and valence bands of semiconductors are commonly approximated as parabolic around their extrema, which gives a simple theoretical description, but ignores the complexity of real materials. In this work, we use density functional theory to assess the impact of band non-parabolicity on four common thin-film photovoltaic materials - GaAs, CdTe, Cu$_2$ZnSnS$_4$ and CH$_3$NH$_3$PbI$_3$ - at temperatures and carrier densities relevant for real-world applications. First, we calculate the effective mass at the band edges. We compare finite-difference, unweighted least-squares and thermally weighted least-squares approaches. We find that the thermally weighted least-squares method reduces sensitivity to the choice of sampling density. Second, we employ a Kane quasi-linear dispersion to quantify the extent of non-parabolicity, and compare results from different electronic structure theories to consider the effect of spin-orbit coupling and electron exchange. Finally, we focus on the halide perovskite CH$_3$NH$_3$PbI$_3$ as a model system to assess the impact of non-parabolicity on calculated electron transport and optical properties at high carrier concentrations. We find that at a concentration of 10$^{20}$ cm$^-3$ the optical effective mass increases by a factor of two relative to the low carrier-concentration value, and the polaron mobility decreases by a factor of three. Our work suggests that similar adjustments should be made to the predicted optical and transport properties of other semiconductors with significant band non-parabolicity.