Hybrid functional studies of the oxygen vacancy in TiO₂

The electronic and structural properties of the oxygen vacancy (V _O) in rutile TiO₂ are studied using generalized Kohn-Sham theory with the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. The HSE approach corrects the band gap and allows for a proper description of defects with energy levels close to the conduction band. According to the HSE calculations, V_O is a shallow donor for which the +2 charge state is lower in energy than the neutral and +1 charge states for all Fermi-level positions in the band gap. The formation energy of V ²⁺_O is relatively low in n -type TiO₂ under O-poor conditions but it rapidly increases with the oxygen chemical potential. This is consistent with experimental observations where the electrical conductivity decreases with oxygen partial pressure.