A percolation approach to dielectric breakdown statistics

The stochastic breakdown model proposed by Niemeyer et al. has been improved by taking the time evolution into account in the two-dimensional lattice system. A Markov process has been assumed in the breakdown process and 'time' has been defined reflecting the distribution of broken bonds in the cluster. The change of breakdown patterns with time predicts various aspects of breakdown phenomena. We have shown that the final breakdown path does not always form a straight line. We have proposed one of the possible origins. for the polarity problem and shown that the polarity difference is understood by the relative position of the damaged layer to the starting point of breakdown.