Quantitative calculation of barium vacancy formation mechanism effects on the room-temperature resistance and PTCR effect in donor-doped BaTiO3 ceramics

A modified barium vacancy formation mechanism in donor-doped barium titanate (BaTiO 3 ) ceramics is proposed. Assuming a uniform distribution of barium vacancies at sintering temperature and only oxygen partial pressure and sintering temperature related concentration of unionized barium vacancies, the electrical characteristics have been calculated by solving a differential equation about electron level. The room-temperature resistivity and positive temperature coefficient of resistivity (PTCR) behaviors of donor-doped BaTiO 3 semiconducting ceramics have been quantitatively computed. The results pointed out that the room-temperature resistivity changes as a U-type curve with an increase of donor concentration. Moreover, the PTCR effect of BaTiO 3 semiconductive ceramics was calculated quantitatively under different conditions. Theoretical and experimental results for BaTiO 3 semiconductive ceramics are compared and discussed.