Statistical behavior of electrical breakdown in insulating polymers

A simulation model to investigate the statistical property of electrical breakdown is presented based on the field-assisted percolation model for dielectric breakdown, by expressing the disorder in morphology as randomly distributed trap barriers. The effects of sample area and large defects on the statistical property of breakdown are also studied, and the statistical behavior of the lifetime is investigated by considering the stochastic development of deteriorated regions. In addition an equation describing the breakdown probability in homogeneous materials is derived from percolation theory, which we show fits well to the simulation data. The breakdown probability is expressed in terms of trap distribution, and thus provides a way to connect the disorder in polymer morphology with the stochastic nature of breakdown.