Effective medium theory for the electrical conductance of random resistor networks which mimic crack-template-based transparent conductive films

TL;DR

This paper develops an effective medium theory to predict the electrical conductance of random resistor networks mimicking crack-template-based transparent conductive films, revealing a specific conductance dependence on edge density.

Contribution

It introduces a theoretical model linking network structure to conductance, validated by numerical simulations, for networks resembling transparent conductive films.

Findings

Conductance scales as approximately 0.5852 times the square root of edge density.

The theoretical predictions agree with numerical results within 15%.

The model applies to networks produced by nano-imprinting technology.

Abstract

We studied random resistor networks produced with regular structure and random distribution of edge conductances. These networks are intended to mimic crack-template-based transparent conductive films as well some random networks produced using nano-imprinting technology. Applying an effective medium theory, we found out that the electrical conductance of such networks is $\approx 0.5852 \sqrt{n_E}$, where $n_E$ is the number density of conductive edges. This dependence is in agreement with numerical calculations in Voronoi networks, although the effective conductances are approximately 15\% larger.