  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 new 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.
