Electronic structure and thermoelectric properties of Sb-based semiconducting half-Heusler compounds

Electronic structure and transport properties of four Sb-based semiconducting half-Heusler compounds, $\mathit{MA}$Sb, where $\mathcal{M}=\mathrm{Hf}$ or Zr and $\mathcal{A}=\mathrm{Co}$ or Ir are studied using density-functional theory and Boltzmann transport equation in constant relaxation time ($\ensuremath{\tau}$) approximation. We find that substituting Hf with Zr does not change the band structures of these systems significantly. In contrast, replacing Co with Ir leads to drastic changes in their electronic structures. The valence band maximum occurs at the $L$ point in the Co compounds while it is at the $\ensuremath{\Gamma}$ point in the Ir compounds. The position and hybridization of an $s$-like conduction band vis-\`a-vis the hybridized $d$ bands of Co(Ir) determines the nature of the conduction bands near the band gap region. In addition, there is a direct band gap at the $\ensuremath{\Gamma}$ point in HfIrSb, whereas in the other three compounds, the band gap is indirect, either between $\ensuremath{\Gamma}$ and $X$ or between $L$ and $X$ points. The Co compounds usually give large thermopowers for both $p$ and $n$ dopings. However, ZrIrSb, due to its interesting conduction band structure, gives the best $n$-type thermopower at high temperatures. We discuss in detail how the subtle changes in the electronic structure near the band gap affects $S$, $\ensuremath{\sigma}/\ensuremath{\tau}$, and the power factor.