Numerical modeling of nonohmic percolation conduction and Poole Frenkel laws

TL;DR

This paper introduces a numerical model for simulating nonohmic percolation conduction and Poole-Frenkel laws, validating analytical predictions and experimental observations in disordered materials.

Contribution

The study develops a 2D resistor grid model that captures the nonlinear I-V behavior and size-dependent exponents of percolation conduction and Poole-Frenkel effects.

Findings

Exponential non-ohmic I-V characteristics validated.

Linear voltage dependence for small samples.

Square root voltage dependence for large samples.

Abstract

We present a numerical model that simulates the current-voltage (I-V) characteristics of materials that exhibit 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 non-ohmic I-V characteristics validating earlier analytical predictions and consistent with multiple experimental observations of the Poole-Frenkel laws in non-crystalline 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.