Nonlinear properties of ZnO ceramics as a function of threshold voltage and fraction of nonconducting grains

The important properties of ZnO nonlinear ceramic include its nonlinear coefficient, alpha, which is the derivative of the log of the current density with respect to the log of the field, the threshold voltage, energy absorption capability, etc. However the shape of alpha is also important. One would prefer that the ZnO "turn on" (become substantially conductive) very rapidly, while how it approaches its ultimate conductivity with voltage is less important. Both the threshold voltage and nonlinearity can be controlled, to some degree, by the fraction of nonconducting grains. In the present contribution, we use statistical approaches to study the effect of the fraction of nonconducting grains as a function of the element thickness (threshold voltage) to see how the properties change as the number of grains drops from the region of 1000, where the statistics are clearly "smooth" to the region of 30, where the effect of the standard deviation will be much greater