Band alignment and scattering considerations for enhancing the thermoelectric power factor of complex materials: The case of Co-based half-Heusler alloys

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