The relations among breakdown field E1mA/cm2 (electric field at 1 mA/cm2), nonlinear coefficient α (measured via current-voltage, I-V, characteristics), and change in breakdown field (ΔE1mA/cm2/E1 mA/cm2) (obtained via current impulse measurement), and thickness d of ZnO varistors were investigated. The dimensional effect refers to the variation in E1 mA/cm2, α, and ΔE1 mA/cm2/E1 mA/cm2 with thickness of the samples. The dispersion of the ZnO grain size and the aspect ratio of the ZnO grains are used in characterizing the microstructure to represent the degree of heterogeneity of the grain size distribution and irregularity of the shape of the ZnO grains. The distribution of the ZnO grain size is statistically analyzed and found that the critical thickness dc increases linearly with the dispersion of the ZnO grain size. The breakdown electric field can be empirically termed as E1 mA/cm2 ∝ exp(bd), where d is the thickness and b represents the transitional behavior for the curve of the E1 mA/cm2 versus d plot. Based on the inflecting response of this curve, b1 represents the small thickness domain prior to the inflection and b2 represents the large thickness domain in the post-inflection domain. It is observed that b2 is directly proportional to aspect ratio of the ZnO grains. Also it is revealed from the analysis that b1 increases with the increase in the critical electric field while b2 decreases with the increase in the critical electric field. Based on these observations it is suggested that the dimensional effect of ZnO varistors originates from the distribution of the grain size and proven via experiments involving the measurements of E1 mA/cm2, α, and ΔE1 mA/cm2/E1 mA/cm2. The dimensional effect is the macroscopic expression of population behavior of varistors that is consisting of the ZnO grains as well as the grain boundaries.
