Numerical modeling of nonohmic percolation conduction and Poole-Frenkel laws

Abstract

We present a numerical model that simulates the current-voltage (I-V) characteristics of materials exhibiting percolation conduction. The model consists of a two dimensional grid of exponentially different resistors in the presence of an external electric field. We obtained exponentially nonohmic I-V characteristics validating earlier analytical predictions and consistent with multiple experimental observations of the Poole-Frenkel laws in noncrystalline materials. The exponents are linear in voltage for samples smaller than the correlation length of percolation cluster L and square root in voltage for samples larger than L.