Effect of film thickness on the width of percolation threshold in metal-dielectric composites

TL;DR

This study investigates how film thickness influences the percolation threshold width in metal-dielectric composites by analyzing current distributions through cubic networks and identifying a power-law relationship in the 2D-3D crossover region.

Contribution

It introduces a method to quantify the percolation threshold width as a function of film thickness using Kirchhoff's equations and Levy statistics, revealing a power-law behavior.

Findings

Percolation width decreases with film thickness in the 2D-3D crossover.

Power-law exponent of the percolation width is approximately 0.36.

Current distribution tail analysis effectively characterizes percolation properties.

Abstract

The effect of thickness on the width of the percolation threshold in metal-dielectric composite films was examined. The distribution of current intensities through cubic networks of metal and dielectric components was determined using Kirchhoff's equations. From the tail of current distribution, the width of the percolation threshold was defined using L\'evy statistics, and determined as a function of the film thickness for a system size 100. In the 2D-3D crossover region, the percolation width decreases as a power-law with a power exponent of $ 0.36\pm 0.01$.