Transparent electrodes based on mixtures of nanowires and nanorings: A mean-field approach along with computer simulation

TL;DR

This study combines a mean-field theoretical approach with computer simulations to analyze the electrical conductance of 2D nanowire and nanoring networks, revealing how their composition and contact resistances influence conductivity.

Contribution

It introduces a mean-field model for mixed nanowire and nanoring networks and validates it with Monte Carlo simulations, providing insights into their electrical behavior.

Findings

Conductance is insensitive to ring/stick ratio when wire and junction resistances are equal.

Network conductance varies linearly with ring/stick ratio when junction resistance dominates.

Mean-field predictions align well with Monte Carlo simulation results.

Abstract

We have studied the electrical conductance of two-dimensional (2D) random percolating networks of zero-width metallic nanowires (a mixture of rings and sticks). We toke into account the nanowire resistance per unit length and the junction (nanowire/nanowire contact) resistance. Using a mean-field approximation (MFA) approach, we derived the total electrical conductance of these nanowire-based networks as a function of their geometrical and physical parameters. The MFA predictions have been confirmed by our Monte Carlo (MC) numerical simulations. The MC simulations were focused on the case when the circumferences of the rings and the lengths of the wires were equal. In this case, the electrical conductance of the network was found to be almost insensitive to the relative proportions of the rings and sticks provided that the wire resistance and the junction resistance were equal. When the junction resistance dominated over the wire resistance, a linear dependency of the electrical conductance of the network on the proportions of the rings and sticks was observed.