First-principles study of the atomic structures, electronic properties, and surface stability of BaTiO₃ (001) and (011) surfaces

The atomic structures, electronic properties, and surface stability of (001) and (011) surfaces of BaTiO₃ are studied by first-principles calculations. Four differently terminated BaTiO₃ surfaces are considered in this study, including (001)-BaO, (001)-TiO₂, (011)-BaTiO, and (011)-O₂ terminations. The relaxations and rumplings are calculated and discussed, finding that the first layer relaxes inwards, while the second layer relaxes outwards for (001) and (110) surfaces. The data obtained for electronic properties show that O_2p states in (001)-BaO/(001)-TiO₂ termination shift to the lower/higher energy region, leading to a wide/narrow band gap. And the new produced surface states are observed in (011) surface terminations, which is mainly attributed to the supplied electrons from outermost surface atoms, even O atoms are oxidized. Furthermore, the (001) surface of BaTiO₃ is found to be more stable than the (011) surface according to the predicted surface energy which is 0.86 and 2.92 J/m² for (001) and (011) surfaces, respectively. Of which, BaO termination is predicted to be more likely to cleavage from the (001) direction than the TiO₂ termination is.