Effect of crystal field on the formation and diffusion of oxygen vacancy at anatase (101) surface and sub-surface

The intrinsic oxygen vacancy (O_v) in TiO₂ is a vital topic of semiconductor materials. Here, we use the first-principles calculations to explore the formation and diffusion properties of O_v at anatase (101) slab, combined with the crystal filed theory. The calculated result shows that O_v at subsurface is not only more stable than that at surface, but also prefers to cluster together at subsurface. The stability of O_v at subsurface is mainly attributed to the Ti3d orbitals in different crystal fields occupied by the excess electrons. Further calculation reveals that the O_v diffusion is greatly affected by the excess electrons. These results presented here show the importance of 3d orbitals in different crystal field, which should be helpful to understand the behavior of O_v at other transition metal oxide.