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 $\frac{V_b}{L}\sim \frac{a\left(p\right)\mathrm{}}{\mathrm{}[1+b(p\left)\mathrm{}{\left(\ln L\right)}^{\beta }\right]}$, where $\frac{\beta =1\mathrm{}}{\mathrm{}(d-1\mathrm{})\mathrm{}}$ for the fuse network and $\beta =1\mathrm{}$ 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.