Effect of donor (Nb) concentration on the bulk electrical resistivity of Nb-doped barium titanate

Abstract

The behavior of the bulk electrical resistivity of donor-doped ${\mathrm{BaTiO}}_3$ with the increase of donor concentration was investigated. A series of coarse-grained specimens with different donor concentrations were prepared by adjusting the oxygen partial pressure during sintering. Then they were heat treated in air for an extended period in order to reach the equilibrium defect distribution corresponding to each heating temperature, which was followed by fast cooling. The critical donor concentrations, beyond which the bulk resistivity increases abruptly, were experimentally evaluated and they were found to decrease with a decrease in the equilibrium temperature in air. Each defect and electron concentrations as a function of donor concentration were theoretically calculated based on the model that the resistivity anomaly is caused by the partially ionized cation vacancies ${\mathrm{(V}}_{\mathrm{Ti}}^{‴})$ at high temperature, which trap electrons, and become fully ionized cation vacancies ${\mathrm{(V}}_{\mathrm{Ti}}^{⁗})$ as specimens are cooled to room temperature. The results calculated could explain the experimentally observed behavior of the bulk resistivity versus donor concentration.