  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.
