Strain modulated oxygen vacancy and polaron formation in rutile TiO₂

Strain is routinely used as a powerful method to achieve certain functional materials and the formation of oxygen vacancies (OVs) largely determines the material properties in many oxides like rutile TiO₂. In this work by hybrid functional (HSE06) calculations we find that strain can effectively modulate the formation of OVs in rutile . Biaxial tensile strain significantly lowers the formation energies of OVs and the concentrations of conduction electrons and OVs increase by several magnitudes, in consist with the semiconductor-to-metal transition observed in experiments. Biaxial compressive strain, however, increases the formation energies of OVs, in contrast with the continuum elastic model. The failure of the model is due to that strain changes the polaronic configurations as in the spin charge densities. The formation of OVs in rutile TiO₂ is intimately related with the formation of polarons, while the latter is favored under tensile strain but less favored under compressive strain, which may be a reasonable explanation for the discrepancy of OV formation energies under different strain types. This provides a new insight into the defect and polaron formations and their interplay with strain in rutile TiO₂ and possibly other similar materials.