First-principles study on structures and energetics of intrinsic vacancies in ${\mathrm{SrTiO}}_3$

We have performed first-principles plane-wave pseudopotential calculations to study the electronic structures, structural optimization, and formation energies of intrinsic vacancies in bulk ${\mathrm{SrTiO}}_3.$ The anion and cation vacancy-induced levels appeared near the valence- and conduction-band edges in the band gap. The formation energies of isolated vacancies with different charge states were obtained, and the defect reaction energies, such as Sr partial Schottky ${(V}_{\mathrm{Sr}}^{2-}{+V}_{\mathrm{O}}^{2+}),$ Ti partial Schottky ${(V}_{\mathrm{Ti}}^{4-}{+2V}_{\mathrm{O}}^{2+}),$ and full Schottky ${(V}_{\mathrm{Sr}}^{2-}{+V}_{\mathrm{Ti}}^{4-}{+3V}_{\mathrm{O}}^{2+})$ were also evaluated. It was found that depending on the atomic chemical potentials, the relative stability of the defect species or reactions is different. The overall trend of the stable defect structures can explain the electrical conductivity of ${\mathrm{SrTiO}}_3$ for different chemical environments experimentally observed.