The variation of intrinsic defects in XTe (X=Ge, Sn, and Pb) induced by the energy positions of valence band maxima

Revealing the intrinsic defects and further understanding the corresponding origin are of crucial importance in optimizing and designing novel thermoelectric materials. In this work, we applied the first-principles studies on the defects of classical thermoelectric materials XTe (X = Ge, Sn, and Pb). Our results show that the X-vacancy defects in GeTe (in both rhombohedral and cubic phases) and cubic SnTe usually possess low formation energies, leading to the strong tendency of p-type electrical transport. Meanwhile, the formation energies of the defects in PbTe with relatively high stability, such as VTe, TePb, etc., depend sensitively on the chemical potentials of Pb, as well as the accuracy of the band gap, and those defects tend to induce weak n-type transport by default. The intrinsic defect types and the induced carrier concentrations are qualitatively in agreement with the reported data. Detailed analyses reveal that the formation energies of the intrinsic defects depend strongly on the energy positions of valence band maxima (VBM), where compounds with high VBM favor acceptor defects. PbTe shows the lowest VBM among the four materials, due to the low energy of the 6s2 lone-pair electrons, which fundamentally causes the distinctly different intrinsic defects.