Cluster calculations of the effects of lattice vacancies in PbTe and SnTe

The $X\alpha$ scattered-wave method, generalized to include the relativistic mass velocity and Darwin terms, has been applied to 27 atom clusters representing bulk PbTe and SnTe in order to study the properties associated with lattice vacancies in these materials. Such properties are deduced via direct comparison of results obtained from "ideal" clusters and corresponding "defect" clusters. The results are compared to the Parada and Pratt calculations of the energy states associated with lattice vacancies in PbTe (obtained via the Koster-Slater method) as well as with previous cluster calculations made on PbS by the present author. A fairly consistent picture is found to emerge from these calculations. In all cases considered, a single cation vacancy is found to yield two holes in the valence band, producing a $p$-type material, while each anion vacancy produces two electrons outside of a filled valence band, leading to $n$-type behavior. The wave functions associated with the holes in the former case are found to be delocalized in nature, whereas those associated with the extra electrons in the case of the anion vacancy seem to be somewhat localized to the vicinity of the vacancy site. The role of the self-consistent relaxation of the electronic states in the presence of the vacancies is discussed, and such effects are shown to be important, especially in the case of an anion vacancy.