Energetics of native defects in anatase TiO₂: a hybrid density functional study

The energetics and electronic structures of native defects in anatase TiO₂ are comprehensively studied using hybrid density functional calculations. We demonstrate that oxygen vacancies (V_O) and titanium interstitials (Ti_i) act as shallow donors, and can form at substantial concentrations, giving rise to free electrons with carrier densities from 10¹¹ to 10¹⁹ cm^-3 under oxygen-rich and oxygen-poor conditions, respectively. The titanium vacancies (V_Ti), identified as deep acceptors and induced hole carriers, are incapable of fully compensating for the free electrons originating from the donor-type defects at any oxygen chemical potential. Even under extreme oxygen-rich conditions, the Fermi level, which is determined from the charge neutrality condition among charge defects, electron and hole carriers, is located 2.34 eV above the valence band maximum, indicating that p-type conductivity can never be realized under any growth conditions without external doping. This is consistent with common observations of intrinsic n-type conductivity of TiO₂. At a typical annealing temperature and under a typical oxygen partial pressure, the carrier concentration is found to be approximately 5 × 10¹³ cm^-3.