Modeling the electrical conductivity in BaTiO3 on the basis of first-principles calculations

The dependence of the electrical conductivity on the oxygen partial pressure is calculated for the prototypical perovskite BaTiO₃ based on data obtained from first-principles calculations within density functional theory. The equilibrium point defect concentrations are obtained via a self-consistent determination of the electron chemical potential. This allows one to derive charge carrier concentrations for a given temperature and chemical environment and eventually the electrical conductivity. The calculations are in excellent agreement with experimental data if an accidental acceptor dopant level of 10¹⁷ cm³ is assumed. It is shown that doubly charged oxygen vacancies are accountable for the high-temperature n-type conduction under oxygen-poor conditions. The high-temperature p-type conduction observed at large oxygen pressures is due to barium vacancies and titanium-oxygen divacancies under Ti- and Ba-rich conditions, respectively. Finally, the connection between the present approach and the mass-action law approach to point defect thermodynamics is discussed.