  Half-Heuslers, an emerging thermoelectric material group, has complex
bandstructures with multiple bands that can be aligned through band engineering
approaches, giving us an opportunity to improve their power factor. In this
work, going beyond the constant relaxation time approximation, we perform an
investigation of the benefits of band alignment in improving the thermoelectric
power factor under different density of states dependent scattering scenarios.
As a test case we consider the Co-based p-type half-Heuslers TiCoSb, NbCoSn and
ZrCoSb. First, using simplified effective mass models combined with Boltzmann
transport, we investigate the conditions of band alignment that are beneficial
to the thermoelectric power factor under three different carrier scattering
scenarios: i) the usual constant relaxation time approximation, ii) intra-band
scattering restricted to the current valley with the scattering rates
proportional to the density of states as dictated by Fermi's Golden Rule, and
iii) both intra- and inter-band scattering across all available valleys, with
the rates determined by the total density of states at the relevant energies.
We demonstrate that the band-alignment outcome differs significantly depending
on the scattering details. Next, using the density functional theory calculated
bandstructures of the half-Heuslers we study their power factor behavior under
strain induced band alignment. We show that strain can improve the power factor
of half-Heuslers, but the outcome heavily depends on the curvatures of the
bands involved, the specifics of the carrier scattering mechanisms, and the
initial band separation. Importantly, we also demonstrate that band alignment
is not always beneficial to the power factor.
