Oxygen vacancies in SrTiO$_{3}$ thin films at finite temperatures: A first-principles study

Epitaxially grown SrTiO$_{3}$ (STO) thin films are material enablers for a number of critical energy-conversion and information-storage technologies like electrochemical electrode coatings, solid oxide fuel cells and random access memories. Oxygen vacancies (${\rm V_{O}}$), on the other hand, are key defects to understand and tailor many of the unique functionalities realized in oxide perovskite thin films. Here, we present a comprehensive and technically sound ab initio description of ${\rm V_{O}}$ in epitaxially strained (001) STO thin films. The novelty of our first-principles study lies in the incorporation of lattice thermal excitations on the formation energy and diffusion properties of ${\rm V_{O}}$ over wide epitaxial strain conditions ($-4 \le \eta \le +4$%). We found that thermal lattice excitations are necessary to obtain a satisfactory agreement between first-principles calculations and the available experimental data on the formation energy of ${\rm V_{O}}$ for STO thin films. Furthermore, it is shown that thermal lattice excitations noticeably affect the energy barriers for oxygen ion diffusion, which strongly depend on $\eta$ and are significantly reduced (increased) under tensile (compressive) strain, also in consistent agreement with the experimental observations. The present work demonstrates that for a realistic theoretical description of oxygen vacancies in oxide perovskite thin films is necessary to consider lattice thermal excitations, thus going beyond standard zero-temperature ab initio approaches.