First-principles energy band calculation for undoped and S-doped TiO2 with anatase structure

The electronic structure of S-doped TiO₂ with an optimized anatase structure was calculated within the framework of the density functional theory (DFT). For the calculation we built four kinds of supercells; type-A and B supercells consist of 12 and 48 atoms and a centered Ti atom is substituted for an S atom, while type-C and D supercells consist of 12 and 48 atoms and a centered O atom is substituted for an S atom. The supercells (type-B and D) were employed to adjust the S-concentration in TiO₂ to an experimental value of a few %. The changes of the lattice parameters are not significant in the type-A and B supercells. The phase transition from the tetragonal to the orthorhombic occurs in the type-C and D supercells. In the small supercell (type-A), S-related states are located in the range of −1.6 to 0 eV, and the S-states are band-like. In contrast, in the large supercell (type-B), S-related states appeared at about 0.9 eV above the top of the valence band, and the S-states are atomic-like. The localization of the S-related states is remarkable in the type-B supercell. In the type-D supercell, the S-related states were merged with the top of the valence band, and as a result the band-gap energy is narrowed by 0.7 eV. Despite a low S-concentration (3%) in the type-D supercell, the S-related states are somewhat band-like.