Energetics and diffusion of intrinsic surface and subsurface defects on anatase TiO₂ (101)

We report on density functional theory (DFT) calculations of the formation energies and diffusion pathways of oxygen vacancies and Ti interstitials at and near the (101) surface and in the bulk of the anatase polymorph of TiO ₂. At the generalized gradient approximation level, both defects are found to be energetically more stable by ∼0.5 eV or more at bulk and subsurface sites than on the surface. Moreover, the energy barriers to diffuse from the surface to the bulk are rather low, while the opposite is true for the barriers to diffuse from the bulk to the surface. This indicates that similar to Ti interstitials, also oxygen vacancies should preferentially occur at subsurface rather than at surface sites. To substantiate these findings, additional DFT+U calculations have been performed using different values of U in the range 2.5≤U≤4.5 eV. These show small differences in the relative stabilities of surface and subsurface oxygen vacancies with subsurface vacancies being more stable at low U values and a crossover in stability taking place around U∼3 eV. Analogous calculations for the TiO₂ (110) surface of rutile show that surface bridging oxygen vacancies are largely favored with respect to subsurface vacancies for all values of U. Altogether, our results provide evidence of important differences between reduced anatase and rutile surfaces in agreement with recent experimental observations.