Physics of the gap formation in half-Heusler compounds and bismuth chalcogenide systems

Using first principles electronic structure calculations based on the density functional theory, we discuss the reasons behind the formation of energy gaps in different classes of narrow-gap semiconductors which are either good or promising thermoelectrics. We find that in half-Heusler compounds such as ZrNiSn and YNiSb, the Ni atoms take active role in the gap formation, both through local symmetry breaking and hybridization. In Bi₂Te₃, the best known room temperature thermoelectric, the subtle gap structure is determined by both spin-orbit interaction and hybridization of Bi p and Te p bands. In other Bi chalcogenides and complex ternary systems containing Bi and Te, it appears that spin-orbit interaction does not play as important a role. We discuss possible reasons for this difference.