Microscopic origin of thep-type conductivity of the topological crystalline insulator SnTe and the effect of Pb alloying

Abstract

The interest in SnTe has recently increased due to its topological crystalline insulator nature, despite the fact that SnTe is always heavily $p$ type. Here, using first-principles calculations, we identify the microscopic origin of the $p$-type conductivity of SnTe. It is found that the negatively charged Sn vacancy (${V}_{\mathrm{Sn}}^{2\ensuremath{-}}$) dominates the electronic properties of SnTe: regardless of the growth conditions, ${V}_{\mathrm{Sn}}^{2\ensuremath{-}}$ always has a negative formation energy within the band gap, which forces the Fermi level below the valence band maximum (VBM), leading to degenerate $p$-type doping. In contrast, the deeper VBM of PbTe increases the formation energy of the Pb vacancy (${V}_{\mathrm{Pb}}^{2\ensuremath{-}}$), allowing for either $n$-type or $p$-type PbTe. So even though standard n doping of SnTe is very difficult, alloying with Pb can achieve $n$ doping by lowering the VBM, thereby inhibiting the formation of cation vacancy and, thus, probably producing a topological crystalline insulator with the Fermi level located near the Dirac point.