The dimensional effect of breakdown field in ZnO varistors

The relationship between the breakdown electric field E_B (electric field corresponding to the current density 1 mA cm^-2) and thickness d for three types of Zinc oxide (ZnO) varistors were investigated. The geometric dimensional effect, observed in these varistors, is referred to as the responsible parameter for the change in E_B with the variation in the thickness of the varistor samples. The variation in the diameter of the ZnO grains and the corresponding aspect ratio due to the irregularity of each ZnO grain shape are used to characterize the microstructural heterogeneity of the resulting ZnO grain size distribution. The distribution of the ZnO grain size is statistically analysed, and thereby a model of the microstructure is proposed. The thickness dependence of the breakdown field, E_B, obtained via computer simulation shows a similar dimensional effect to the one observed experimentally. It was found that the critical thickness, d_c, increases linearly with the dispersive ratio of the ZnO grain length, and the corresponding slope (b₂) in the large thickness domain is directly proportional to the aspect ratio of the ZnO grains.