Energetics of charged point defects in rutile TiO₂ by density functional theory

The defect formation energies of all possible charge states of point defects in TiO₂, including titanium interstitials, titanium vacancies and oxygen vacancies, are calculated in the phase space of temperature, oxygen partial pressure and Fermi level by combining density functional theory (DFT) and thermodynamic calculations. The point defect phase diagram illustrates that fully charged defects dominate in most regimes. The calculations not only give reasonable defect formation energies compared with prior experimental measurements, but also predict n-type TiO₂ at high T and low P_O2, and p-type TiO₂ at low T and high P_O2, which agrees well with experimental data. In addition, we evaluate methods for correcting the effects of artificial electrostatic interactions caused by periodic boundary conditions in the DFT calculations, including the electrostatic potential alignment correction (ΔV correction) and the Makov-Payne correction.