J. Boksiner et Pl. Leath, DIELECTRIC-BREAKDOWN IN MEDIA WITH DEFECTS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(3), 1998, pp. 3531-3541
We investigate the breakdown held and geometry of breakdown paths of a
n electrical circuit model for dielectric breakdown in media with defe
cts of arbitrary residual resistivity. The circuit model consists of a
two-dimensional square lattice network of resistors that break down f
rom a high resistance to a lower (residual) resistance when the local
electric field exceeds a critical value. We consider infinite and semi
-infinite samples with a single cluster (needle) of defects as well as
samples with a finite concentration of defects from the dilute limit
to the percolation threshold. We find that for needle defects with non
zero residual resistivity, the breakdown field reaches a finite value
as the defects lengthen, causing the random lattice to reach the same
breakdown field in the thermodynamic limit. Furthermore, we find that
depending on the initial length of the seed defect and the residual re
sistivity, the breakdown either grows one dimensionally, or spreads wi
th a fractal dimension. We give the phase diagram and relevant exponen
ts for this crossover, and report similar behavior in random lattices
at dilute defect concentrations.