Dielectric breakdown in a thin oxide is presented in terms of an interacting particle system on a two-dimensional lattice. All edges in the system are initially assumed to be closed. An edge between two adjacent vertices will open according to an exponentially distributed random variable. Breakdown occurs at the time an open path connects the top layer of the lattice to the bottom layer. Using the extreme value theory, we show that the time until breakdown is asymptotically Weibull distributed.

The field distribution and the restraint effect of multipactor and plasma discharge on the periodic triangular surface have been theoretically and experimentally analyzed. It has been found by computational and simulative analysis that the periodic profile can quickly restrain or weaken multipactor and plasma discharge in low pressure within several microwave periods. Considering the field enhancement, increasing the slope angle, advancing the electric field, and lowering the frequency can enhance the multipactor suppression. X-band giga-watt high power microwave experiment with 20 ns short pulse was conducted. It was demonstrated that the periodic profile can effectively improve the breakdown threshold and slower the speed of tail erosion.