Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs

The structural and electronic properties of oxygen vacancies (V-Ox) and titanium interstitials (Ti-(i)) in the bulk of the rutile and anatase forms of TiO2 have been investigated with LSD-GGA+U ab initio simulations. In particular, formation energies of the charged and neutral forms of the V-Ox and Ti-(i) defects as well as the corresponding vertical and thermodynamic transition levels have been estimated. The achieved results can reconcile the apparent inconsistency of experimentally observed deep donor levels with the n-type conductivity observed in reduced TiO2. They show indeed that both defects give rise to vertical transition levels about 1 eV below the conduction band (CB), in agreement with experimental measures, and to thermodynamic transition levels close to the CB. That is, these defects behave as deep donors, when looking at vertical transitions, and as shallow donors, when the effects of the structural relaxations are taken into account. A major part of the explanation of this behavior is played by the polaron-like character of the defect states, which was already noted, but not deepened, in literature. Finally, it is shown that the application of the U correction to both Ti and O species gives qualitatively similar results, but with a better agreement to experimental findings, with respect to the application to Ti only. The former approach gives pretty similar results, for both rutile and anatase bulk properties, to those coming from HSE hybrid functional calculations.