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Epitaxially grown SrTiO$_{3}$ (STO) thin films are material enablers for anumber of critical energy-conversion and information-storage technologies likeelectrochemical electrode coatings, solid oxide fuel cells and random accessmemories. Oxygen vacancies (${\rm V_{O}}$), on the other hand, are key defectsto understand and tailor many of the unique functionalities realized in oxideperovskite thin films. Here, we present a comprehensive and technically soundab initio description of ${\rm V_{O}}$ in epitaxially strained (001) STO thinfilms. The novelty of our first-principles study lies in the incorporation oflattice thermal excitations on the formation energy and diffusion properties of${\rm V_{O}}$ over wide epitaxial strain conditions ($-4 \le \eta \le +4$%). Wefound that thermal lattice excitations are necessary to obtain a satisfactoryagreement between first-principles calculations and the available experimentaldata on the formation energy of ${\rm V_{O}}$ for STO thin films. Furthermore,it is shown that thermal lattice excitations noticeably affect the energybarriers for oxygen ion diffusion, which strongly depend on $\eta$ and aresignificantly reduced (increased) under tensile (compressive) strain, also inconsistent agreement with the experimental observations. The present workdemonstrates that for a realistic theoretical description of oxygen vacanciesin oxide perovskite thin films is necessary to consider lattice thermalexcitations, thus going beyond standard zero-temperature ab initio approaches.

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