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

Abstract

Producing high band and valley degeneracy through aligning of conducting electronic bands is an effective strategy to improve the thermoelectric performance of complex bandstructure materials. 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. Theoretical calculations to identify the outcome of band engineering usually employ detailed density functional theory for bandstructure calculations, but the transport calculations are kept simplistic using the constant relaxation time approximation due to the complications involved with detailed scattering physics. 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. In addition, we show that the bandstructure itself can undergo changes as the bands are aligned in practice, which further affect the band alignment optimization. Our work illustrates the importance of going beyond the constant relaxation time approximation, as well as understanding how the bandstructure of each material behaves when considering band alignment. arXiv:1905.07951v1 [cond-mat.mtrl-sci]

Thermoelectric transport trends in group 4 half-Heusler alloys

“…This would likely influence some of the trends obtained here, but a key remaining challenge would be to realistically assess the relative role of intra-and inter-band scattering in alloys. 72 Also, a high doping concentration would create additional impurity scattering centers that are challenging to describe without adjustable, materials dependent parameters. Thus, partly because of these complexities, we chose to use a constant τ .…”

Nanostructured potential well/barrier engineering for realizing unprecedentedly large thermoelectric power factors

“…On the other hand, this approach has still not been widely applied because the conductivity is also reduced in the presence of potential barriers. Current research efforts in improving the power factor have thus diverted into many other directions, including: i) taking advantage of the density of states in low-dimensional materials through quantum confinement [31], or in bulk materials that include low-dimensional 'like' features [32,33], ii) bandstructure engineering and band-convergence strategies [32,33,34,35,36], iii) modulation doping and gating [37,38,39,40,41,42,43,44,45], iv) introducing resonances in the density of states [46], and even more recently v) concepts that take advantage of the Soret effect in hybrid porous/electrolyte materials [47]. These approaches target improvements either in the Seebeck coefficient or the electrical conductivity, with the hope that the other quantity will not be degraded significantly, and sometimes they report moderate power factor improvements.…”

Impact of the scattering physics on the power factor of complex thermoelectric materials

“…16,17 In the light of numerous studies undertaken recently towards large data materials screening and ranking, not only for TE materials, but for other applications as well, 2,3 it is imperative that some of these details are considered to extract the electronic properties, or at least the consequences of omitting them, understood and quantified. 18 In this work, we relax the constant relaxation time approximation with a code that can consider the full energy, momentum, and band dependence of the scattering rates, considering carrier scattering with phonons and ionized impurities. We study five p-type Co-based half-Heusler alloys, whose complex valence bands 7,19 make them an excellent tool to assess the impact of the scattering physics in the transport properties of complex materials: TiCoSb, ZrCoSb, HfCoSb, ZrCoBi and NbCoSn.…”