Dielectric breakdown model for polymer films

This paper describes a modified dielectric breakdown model (mDBM), to predict breakdown pathways in polymer films taking into consideration trapped charge and gaseous voids. Modeling components include: (1) accurate boundary integral equation method (BIEM) based on Green function formulations for grid-less, non-orthogonal, Poisson growth; (2) treatment of kernel singularities; (3) matrix algebra for extensibility, reuse, and rapid iterative computation; and (4) Monte Carlo statistics with inverse probability integral for tree branch growth. 2D and 3D versions of mDBM have been successfully validated against known data and closed-form solutions, viz. charge and capacitance calculations with agreement to within 3% of the theoretical. The versatility of the models has been demonstrated by results of test cases for throughfilm breakdown in the presence of trapped charge, gaseous void, and combination of trapped charge and gaseous void.