Size Effects of Electrical Breakdown in Quenched random Media

Abstract

Two percolation models for electrical breakdown in quenched random media, a fuse-wire network and a dielectric network, are introduced and studied. A combination of Lifshitz and scaling arguments leads to a size dependence given by $\frac{{V}_{b}}{L}\ensuremath{\sim}\frac{a(p)}{[1+b(p){(\mathrm{ln}L)}^{\ensuremath{\beta}}]}$, where $\frac{\ensuremath{\beta}=1}{(d\ensuremath{-}1)}$ for the fuse network and $\ensuremath{\beta}=1$ for the dielectric network. Simulations support this hypothesis in the 2D fuse network. We argue that any finite fraction of quenched defects qualitatively reduces the breakdown strength of a wide variety of electrical and mechanical systems in both two and three dimensions.