We perform full-potential screened-hybrid density-functional theory calculations to compare the thermodynamic stability of neutral and charged states of the surface oxygen vacancy at the rutile ${\mathrm{TiO}}_2$(110) surface. Solid-state (QM/MM) embedded-cluster calculations are employed to account for the strong ${\mathrm{TiO}}_2$ polarization response to the charged defect states. Similarly to the situation for the bulk O vacancy, the +2 charge state ${\mathrm{V}}_{\mathrm{O}}^{2+}$ is found to be energetically by far the most stable. Only for Fermi-level positions very close to the conduction band, small polarons may at best be trapped by the charged vacancy. The large decrease in the ${\mathrm{V}}_{\mathrm{O}}^{2+}$ formation energy with decreasing Fermi-level position indicates strongly enhanced surface O vacancy concentrations for $p$-doped samples.

• Received 29 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075308