Electronic structure of Ga-, In-, and Tl-doped PbTe: A supercell study of the impurity bands

The physics of deep defect states associated with group-III (Ga, In, Tl) impurities in PbTe has been of great interest over the last several decades. Three different models have been proposed to understand interesting and unusual properties exhibited by these impurities. These are "impurity level" model, "mixed-valence" model, and "autocompensation" model. Recent studies that were carried out using ab initio density-functional theory and supercell models give a detailed microscopic picture of the deep defect states associated with these impurities. The computed single-particle electronic density of states does not support the mixed-valence model where the impurities are supposed to be in 3(+) and 1(+) charge states, rather it is in favor of the impurity level model. In this paper, we present a detailed analysis of the impurity bands, impurity levels in the dilute limit, and the hybridization between the impurity level and the host PbTe bands. We find that the impurity level overlaps the conduction band (In), is in the gap (Ga), and overlaps the valence band (Tl). The possibility of the autocompensation model where impurities in charge states 1(+) and 1(-) coexist (a different type of mixed valency) is briefly discussed.