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

Laboratory of Mathematical Modeling, Astrakhan Tatishchev State University - Astrakhan, Russia

Received: 3 February 2026
Accepted: 4 March 2026

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.