Impact of nonparabolic electronic band structure on the optical and transport properties of photovoltaic materials

The effective mass approximation (EMA) models the response to an external perturbation of an electron in a periodic potential as the response of a free electron with a renormalized mass. For semiconductors used in photovoltaic devices, the EMA 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., polaron radii and 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 nonparabolicity on four common thin-film photovoltaic materials---GaAs, CdTe, ${\mathrm{Cu}}_{2}{\mathrm{ZnSnS}}_{4}$ and ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$---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 quasilinear dispersion to quantify the extent of nonparabolicity 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 ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$ as a model system to assess the impact of nonparabolicity on calculated electron transport and optical properties at high carrier concentrations. We find that at a concentration of ${10}^{20}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ 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 nonparabolicity.