  An attempt to determine theoretically the highly non-linear current-voltage
(I-V) characteristics of polycrystalline semiconductors, such as ZnO-based
varistors, is made from the electrical properties of individual grain
boundaries under dc bias. The role played by the fluctuations of double
Schottky barrier heights at grain interfaces on driving electrical breakdown
phenomena of macroscopic samples is pointed out in terms of a binary mixture
model. An alternative trial form for the double Schottky barrier height is
introduced to reproduce the breakdown voltage as well as the high non-linear
coefficient alpha, where I propto V^{alpha}. -------------
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