Effective medium theory for the electrical conductivity of random metallic nanowire networks

TL;DR

This paper develops an analytical model based on Foster's theorem to predict the electrical conductivity of dense random nanowire networks, simplifying the understanding of their conductive properties without extensive measurements.

Contribution

It introduces a novel approach using Foster's theorem to derive an analytical dependence of conductivity on key network parameters, extending effective medium theory for nanowire networks.

Findings

Derived an explicit formula for electrical conductivity based on network parameters.

Extended effective medium theory with Foster's theorem for regularized resistor networks.

Provided a method to predict conductivity without detailed system measurements.

Abstract

Interest in studying the conductive properties of networks made from randomly distributed nanowires is due to their numerous technological applications. Although the sheet resistance of such networks can be calculated directly, the calculations require many characteristics of the system (distributions of lengths, diameters and resistances of nanowires, distribution of junction resistance), the measurement of which is difficult. Furthermore, such calculations can hardly offer an analytical dependence of the sheet resistance on the basic physical parameters of the systems under consideration. Although various theoretical approaches offer such analytical dependencies, they are often based on more or less reasonable assumptions rather than rigorously proven statements. Here, we offer an approach based on Foster's theorem to reveal a dependence of the sheet resistance of dense nanowire networks on the main parameters of such networks. This theorem offers an additional perspective on the effective medium theory and extends our insight. Since the application of Foster's theorem is particularly effective for regular random resistor networks, we propose a method for regularizing resistor networks corresponding to random nanowire networks. We found an analytical dependence of the effective electrical conductivity on the main parameters of the nanowire network (reduced number density of nanowires, nanowire resistance, and resistance of contacts between nanowires).