Charged Defect Formation Energies in TiO2 Using the Supercell Approximation
TiO2 has been intensively studied as a wide band-gap transition metal oxide partially due to the multi-valence nature of its cation. Here, density-functional theory calculations within the supercell approximation are carried out to determine the preferred charge state of point defects in rutile TiO2. The first component of this work is to investigate the dependence of the defect formation energies on supercell size and the electrostatic Makov-Payne correction. The results show that the Makov-Payne correction improves the convergence of defect formation energies as a function of supercell size for positively charged titanium interstitials and negatively charged titanium vacancies. However, in the case of positively charged oxygen vacancies, applying the Makov-Payne correction gives the wrong sign for the defect formation energy correction. This is attributed to the shallow nature of the transition levels for this defect in TiO2. Finally, we combine the calculated defect formation energies with thermodynamic data to evaluate the influence of temperature on the relative stabilities of point defects. The results indicate that when the Makov- Payne correction is applied, a stable charge transition occurs for titanium interstitials. In addition, as the temperature increases, the dominant point defect in TiO2 changes from oxygen vacancies to titanium interstitials.
J. He et al., "Charged Defect Formation Energies in TiO2 Using the Supercell Approximation", Advances in Science and Technology, Vol. 45, pp. 1-8, 2006