The mechanism of electrical breakdown of PTCR barium titanate ceramics is different from that of pure barium titanate ceramics. PTCR barium titanate is semiconductor at room temperature, so it is self heated under certain applied voltage, and then changed into an insulator.
As the applied voltage increased, the electrical breakdown was initiated when the specimen interior was heated above the temperature corresponding to the maximum resistance on the resistance -temperature curves by the joule heat. Therefore the electrical breakdown of PTCR $BaTiO_3$ ceramics is not purely electrical but electrically induced thermal breakdown.
The Influence of the microstructure and the grain boundary potential barrier layer on the electrical breakdown of barium titanate PTCR ceramics was studied. Various grain sized samples were prepared by adjusting the amount of Sb substitution to Ba site in barium titanate PTC ceramics. The sample which has large PTC effect($R_{max}$/$R_{min}$) and fine grain size was advantageous to withstand high applied voltage. The grain size effect has been understood that it is related to the number of the grain boundaries per unit thickness of the samples because the applied voltage drop is mainly across the potential barriers at grain boundary. But, the voltage dependence of single grain boundary potential barrier was more important. The voltage dependence of the grain boundary potential barrier layer was due to the grain boundary built-in potential not the depletion layer width as is expected by Heywang's model.
The breakdown voltage of PTCR $BaTiO_3$ ceramics is function of resistance-temperature curve, grain size, and grain boundary potential barrier height. Resistance-temperature curve is the factor related to the degree of heat accumulation when the external voltage is applied to the specimen and grain size is the factor related to the number of grain boundary layer per unit thickness of sample and grain boundary potentail barrier height is the factor related to the voltage dependence of resistance -temperature curve.
