Electrical conductivity of a random nanowire network: comparison of two-dimensional and quasi-three-dimensional models

TL;DR

This paper compares 2D and quasi-3D models of nanowire networks, highlighting overestimations in 2D models and proposing a simple modification to better reflect real contact saturation effects.

Contribution

It introduces a modification to the 2D model to accurately capture contact saturation, improving the estimation of electrical conductivity in nanowire networks.

Findings

2D models overestimate contact numbers and conductivity compared to quasi-3D models.

Electrical conductivity depends quadratically on density in 2D, linearly in 3D.

Proposed modification captures contact saturation effects in nanowire networks.

Abstract

Although the two-dimensional model of random networks of metallic nanowires or carbon nanotubes is widely used, it significantly overestimates the number of contacts between elements compared to quasi-three-dimensional models. This, within the mean-field approximation, leads to overestimates of the electrical conductivity, especially when the main contribution to the system's electrical conductivity comes from the contact resistances between the conductors. In the two-dimensional model, the system's electrical conductivity depends quadratically on the conductor density, whereas in the three-dimensional model, this dependence is linear. We propose a simple modification of a two-dimensional model, which can capture the saturation effect of the number of contacts per conductor in a real nanowire network.