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.
Effective scheme to determine accurate defect formation energies and charge transition levels of point defects in semiconductors