Impurity clustering and impurity-induced bands in PbTe-, SnTe-, and GeTe-based bulk thermoelectrics

Complex multicomponent systems based on PbTe, SnTe, and GeTe are of great interest for infrared devices and high-temperature thermoelectric applications. A deeper understanding of the atomic and electronic structure of these materials is crucial for explaining, predicting, and optimizing their properties, and to suggest materials for better performance. In this work, we present our first-principles studies of the energy bands associated with various monovalent (Na, K, and Ag) and trivalent (Sb and Bi) impurities and impurity clusters in PbTe, SnTe, and GeTe using supercell models. We find that monovalent and trivalent impurity atoms tend to come close to one another and form impurity-rich clusters and the electronic structure of the host materials is strongly perturbed by the impurities. There are impurity-induced bands associated with the trivalent impurities that split off from the conduction-band bottom with large shifts towards the valence-band top. This is due to the interaction between the $p$ states of the trivalent impurity cation and the divalent anion which tends to drive the systems towards metallicity. The introduction of monovalent impurities (in the presence of trivalent impurities) significantly reduces (in PbTe and GeTe) or slightly enhances (in SnTe) the effect of the trivalent impurities. One, therefore, can tailor the band gap and band structure near the band gap (hence transport properties) by choosing the type of impurity and its concentration or tuning the monovalent/trivalent ratio. Based on the calculated band structures, we are able to explain qualitatively the measured transport properties of the whole class of PbTe-, SnTe-, and GeTe-based bulk thermoelectrics.