Nonlinear currents in Voronoi networks

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Abstract
A realistic model of transport properties of zinc oxide ceramic varistors is constructed from two-dimensional Voronoi networks, with a varying degree of disorder, and studied via computer simulations. The relationship between the current-voltage (I-V) characteristic of a single grain boundary and the I-V characteristic of the network has been determined. It is found that the breakdown voltage of the network decreases rapidly when the disorder increases. The ratio of the breakdown voltage per grain boundary, calculated from the average grain size, to the actual single barrier voltage approaches the value observed experimentally in the limit of a fully random network. Moreover, the difference between these two voltages obtained from the simulation has been expressed as a function of the standard deviation of the average grain size and compared with experimental curves, showing a very good agreement. It has been found that in the breakdown region varistor networks with nonuniform grain structure conduct the current almost exclusively through very narrow channels (paths). This current localization effect decays when the applied voltage becomes very high and the network enters the upturn region.