The electronic and structural properties of the oxygen vacancy (VO) in rutile TiO2 were studied using generalized Kohn-Sham theory with the Heyd-Scuseria-Ernzerhof hybrid functional for exchange and correlation. The Heyd-Scuseria-Ernzerhof approach corrects the band gap and allowed for a proper description of defects with energy levels close to the conduction band. According to the Heyd-Scuseria-Ernzerhof calculations, VO was a shallow donor for which the +2 charge state was lower in energy than the neutral and +1 charge states for all Fermi-level positions in the band gap. The formation energy of VO2+ was relatively low in n-type TiO2 under O-poor conditions but it rapidly increases with the oxygen chemical potential. This was consistent with experimental observations where the electrical conductivity decreases with oxygen partial pressure.

Hybrid Functional Studies of the Oxygen Vacancy in TiO2. A.Janotti, J.B.Varley, P.Rinke, N.Umezawa, G.Kresse, C.G.Van de Walle: Physical Review B, 2010, 81[8], 085212