Understanding the interactions between oxygen vacancies atSrTiO3(001) surfaces

Abstract

We examine the role of neutral divacancies on the electronic and atomic structure at ${\mathrm{SrTiO}}_{3}$ (001) surfaces using a density functional theory + $U$ approach. Our results show that the interactions between divacancies are significantly less repulsive at the SrO-terminated surface (0.05 eV) than at the ${\mathrm{TiO}}_{2}$-terminated one (0.38 eV), mainly due to the increased electrostatic screening at the ionic SrO layer compared to the covalently bonded ${\mathrm{TiO}}_{2}$ layer. The interaction energies are a nonmonotonic function of distance, with the fourth-nearest-neighbor oxygen-oxygen divacancy showing a significantly reduced repulsion at 0 K on the ${\mathrm{TiO}}_{2}$-terminated surface where the defects are in the equatorial oxygen plane. This enhanced reduction in the repulsive interaction is a consequence of the much larger reduction in local symmetry relative to other divacancy arrangements arising from strong coupling with in-plane octahedral distortions. On the SrO-terminated surface, due to increased electrostatic screening, the interaction energy begins to decrease beyond the third-nearest neighbor. On both surfaces, the reduced repulsion (0.05 and 0.38 eV) should permit oxygen vacancy ordering at finite temperatures. Finally, we discuss the emergence of a two-dimensional electron gas due to oxygen divacancies at both the ${\mathrm{TiO}}_{2}$- and SrO-terminated ${\mathrm{SrTiO}}_{3}$ (001) surfaces and contrast them with the case of a single oxygen vacancy. Neutral oxygen vacancies on the SrO termination lead to more electron localization than on the ${\mathrm{TiO}}_{2}$ surface. These results suggest an explanation for the local ordering observed in experiment, thereby highlighting the importance of ordering both for enhanced conductivity and carrier densities at oxide surfaces and at heterostructure interfaces.