Dielectric breakdown in the presence of random conductors

Abstract

The potential distribution in a random conductor-insulator mixture is obtained here by numerically solving Laplace's equation on a lattice with arbitrary potential boundaries. A new algorithm is introduced for estimating the minimum insulation gap. The average breakdown voltage and the minimum gap for such lattices are estimated for different concentrations of conductors below percolation threshold. Detailed computer-simulation studies in two dimensions indicate that both the average breakdown voltage and the minimum gap variations near the percolation threshold are characterized by the same exponent, equal to the percolation correlation-length exponent.