Connection between disorder in morphology and stochastic nature of electrical breakdown in insulating polymers

Simulation model to investigate the statistical property of electrical breakdown is presented based on the field-assisted percolation model for dielectric breakdown, in which the disorder in morphology is expressed through randomly distributed trap barriers. In addition the effects of sample area and the presence of large defects are evaluated. Assuming that one simulation segment represents an actual length between tens of nano-metres up to 100nm, the simulated ß-value of Weibull-distribution in the sample sets with different thickness agrees very well with the experimental results of small-area samples with thickness ranging from 4μm to 14μm. An equation describing the breakdown probability in homogeneous materials is derived from percolation theory, which we show fits well to the simulation data. The large dispersion of breakdown strength in typical experiments is explained in terms of the domination of initial breakdown by the defect distribution and effective thickness. 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.