Electrical conductivity of nanorod-based transparent electrodes: Comparison of mean-field approaches

TL;DR

This paper compares mean-field and resistor network models to predict electrical conductivity in nanorod-based transparent electrodes, finding the mean-field approach effective above twice the percolation threshold but slightly overestimating conductivity due to junction effects.

Contribution

It introduces a continuous mean-field model for nanorod networks and compares its predictions with resistor network simulations, highlighting its applicability and limitations.

Findings

Mean-field approximation works well for n > 2n_c.

Mean-field overestimates conductivity slightly.

Junction potential distribution causes overestimation.

Abstract

We mimic nanorod-based transparent electrodes as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We suppose that the number density (the number of objects per unit area of the surface) of these sticks exceeds the percolation threshold, i.e., the system under consideration is a conductor. We computed the electrical conductivity of random resistor networks vs the number density of conductive fillers for the wire-resistance-dominated case, for the junction-resistance-dominated case, and for an intermediate case. We also offer a consistent continuous variant of the mean-field approach. The results of the RRN computations were compared with this mean-field approach. Our computations suggest that, for a qualitative description of the behavior of the electrical conductivity in relation to the number density of conductive wires, the mean-field approximation can be successfully applied when the number density of the fillers $n > 2n_c$, where $n_c$ is the percolation threshold. However, note the mean-field approach slightly overestimates the electrical conductivity. We demonstrate that this overestimate is caused by the junction potential distribution.