First-principles study for the atomic structures and electronic properties of PbTiO3 oxygen-vacancies (0 0 1) surface

The structural and electronic properties of fully-relaxed PbTiO₃ (0 0 1) oxygen-vacancy surface with PbO and TiO₂ terminations are investigated by first-principles calculations. In contrast to the perfect surface, the smaller surface rumples and interlayer distances have been found. The largest relaxation occurs on the second layer atoms not on the surface layer ones, and some in-gap Ti 3d states at about −1.1 eV below the Fermi-level are observed in the TiO₂-terminated surface caused by oxygen-vacancies. For the PbO-terminated surface, some in-gap Ti 3d states and Pb 6p states also move into the bulk midgap region to become partially occupied, and two different chemical states of the Pb 6s states were found. One is attributed to the bulk perovskite Pb atoms and another one is caused by the relaxation of surface Pb atoms. These theoretical results would give a good reference for the future experimental studies.