The geometric dimensional effect, observed in ZnO varistors, is referred to as the responsible parameter for the change in bulk resistivity with the variation in the thickness of the varistor samples. The distribution of the ZnO grain size, and the distribution of the ZnO grain boundary breakdown voltage are statistically modeled. The thickness dependence of the bulk resistivity, obtained via computer simulation shows the dimensional effect. It was found that the critical thickness, dc, increases with the dispersive ratio of the ZnO grain length.

Our group has been also been involved in other simulation work relating to pulsed electrical breakdown in solids.  This includes typical wide-band gap semiconductors, ceramics and granular insulators.  For example, model studies of current conduction and breakdown in TiO₂ have been carried out.  Our simulation results indicate that electrical breakdown of TiO₂ under multiple pulsed conditions can occur at lower voltages as compared to quasi-DC biasing. This is in agreement with recent experimental data, and is indicative of a cumulative phenomena.  We have demonstrated that the lower breakdown voltages observed in TiO₂ under pulsed conditions, is a direct rise-time effect, coupled with successive de-trapping at the grain boundaries.

Breakdown strength versus TiO2 thickness for nano-crystalline and course-grained materials.

Time dependent free-electron density in TiO2. The applied voltage pulses are also shown for brevity.