The electronic and structural properties of the oxygen vacancy $\left(V_{\text{O}}\right)$ in rutile ${\text{TiO}}_2$ 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, $V_{\text{O}}$ 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 $V_{\text{O}}^{2+}$ is relatively low in $n$-type ${\text{TiO}}_2$ 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.

• Received 4 May 2009

DOI:https://doi.org/10.1103/PhysRevB.81.085212