Understanding the interactions between oxygen vacancies at SrTiO3 (001) surfaces

We examine the role of neutral divacancies on the electronic and atomic structure at SrTiO3 (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 TiO2-terminated one (0.38 eV), mainly due to the increased electrostatic screening at the ionic SrO layer compared to the covalently bonded TiO2 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 TiO2-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 TiO2- and SrO-terminated SrTiO3 (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 TiO2 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.