First-principles calculations on TiO2 doped by N, Nd, and vacancy

First-principles density functional theory calculations have been carried out to investigate electronic structures of anatase TiO₂ with substitutional dopants of N, Nd, and vacancy, which replace O, Ti, and O, respectively. The calculation on N-doped TiO₂ with the local density approximation (LDA) demonstrates that N doping introduces some states located at the valence band maximum and thus makes the original band gap of TiO₂ smaller. Examining the effect of the strong correlation of Nd 4f electrons on the electronic structure of Nd-doped TiO₂, we have obtained the half-metallic ground state with the LDA and the insulating ground state with the LDA+U (Hubbard coefficient), respectively. In addition, the calculation on vacancy-doped TiO₂ with the LDA shows that a vacancy can induce some states in the band-gap region, which act as shallow donors.