Voltage effect in PTCR ceramics: Calculation by the method of tilted energy band

A numerical model for the calculation of the electrical characteristics of donor-doped BaTiO3 semiconducting ceramics is suggested. This paper established a differential equation about electron level on the base of Poisson equation, and solved the equation with Runge-Kutta method. Under extra electric field, electrical characteristics have been calculated by the method of tilted energy band. We have quantitatively computed the positive temperature coefficient of resistivity (PTCR) behavior of donor-doped BaTiO3 semiconducting ceramics and its voltage effect, and further obtained non-linear current-voltage characteristics with different grain sizes at different temperature. The results pointed out that the resistance jumping is reduced with increasing electric field applied; current and voltage relation follows Ohm's law below Curie temperature, and exhibits strong non-linear above Curie temperature; the non-linear coefficient shows a maximum value at temperature the resistivity reaches maximum and with grain size closed to depletion region width. The results are compared with experimental data.