Surface and subsurface oxygen vacancies in anatase TiO 2 and differences with rutile

First-principles density-functional theory calculations in the generalized gradient approximation are carried out to study the relative stabilities of oxygen vacancies at surface and subsurface sites of anatase ${\text{TiO}}_{2}(101)$ and ${\text{TiO}}_{2}(001)$, and, for comparison, of the prototypical rutile ${\text{TiO}}_{2}(110)$ surface. Our results indicate that these defects are significantly more stable at subsurface than at surface sites in the case of anatase surfaces, whereas bridging oxygen sites are favored for O vacancies at rutile ${\text{TiO}}_{2}(110)$. Also, calculations of O-vacancy diffusion pathways at anatase ${\text{TiO}}_{2}(101)$ show that the energy barrier to diffuse from surface-to-subsurface sites is sufficiently low to ensure a rapid equilibration of the vacancy distribution at typical surface annealing temperatures. These results could explain why, experimentally, anatase surfaces are found to have a significantly lower defect concentration and/or to be more difficult to reduce than those of rutile.