Simulation of the Grain Boundary Effects in PTCR Ceramics
The positive temperature coefficient of resistivity (PTCR) behavior of semiconductive BaTiO3 ceramics is often explained by the Heywang model. However, Heywang model couldn’t explain some experimental phenomena of jump range more than 106. This paper considered that the migration of donors, electrons and holes has important influence on grain boundary effect. A differential equation about Fermi level was established on the base of Heywang model. By solving the equation the jump range can be calculated quantitatively. It was found that a potential well exists on the edge of grain due to the donor ionization, and the experimental phenomena of PTC jump range more than 106 could be explained.
Wei Pan and Jianghong Gong
C. Fang et al., "Simulation of the Grain Boundary Effects in PTCR Ceramics", Key Engineering Materials, Vols. 368-372, pp. 1692-1694, 2008