Multiscale Electrical Response Assessment of Metal Nanowire Transparent Electrodes: A Computational Strategy
Authors: Grazioli Davide , Simone Angelo 
Published: February 2024

Transparent electrodes made of random distributions of metal nanowires (NWs) are appealing for optoelectronic devices, solar cells, light emitting diodes, and transparent heaters. While these electrodes are comparable to thin films in terms of electrical conductivity and transparency, their network structure allows limiting the amount of conductive material and makes them suitable for low-cost solution-based deposition methods, contributing to an overall costs reduction. Despite these advantages, an even material utilization at different length scales is difficult to achieve. The homogeneous distribution of electric current (electrical homogeneity) is indeed not guaranteed in nanowire electrodes but is crucial for the stability of the electrode and actually desirable in most applications. Despite the relevance of this feature, it is common practice to perform qualitative assessments at the electrode scale, overlooking local effects. To address this issue, we have developed a computational strategy to aid in the design of nanowire electrodes with improved electrical homogeneity.
We present a computational approach that allows an objective, quantitative, and systematic assessment of the electrical homogeneity. The approach enables a multiscale comparison of electrodes with different NW content and material properties. Nanowire electrodes are modeled as two-dimensional networks of stick and junction resistors (with resistance Rw and Rj, respectively) to simulate the electric conduction process. Electrodes are discretized into regular grids of squares and the electrical power of the network contained in each square is computed. The mismatch between the areal power density of the entire electrode and that of the squares provides a quantitative electrical homogeneity evaluation. Repeating the analysis with squares of different size yields an evaluation that spans across length scales. A scalar indicator, coined the homogeneity index, summarizes the results of the multiscale evaluation.
Parametric studies are performed by varying nanowire content and nanowire-to-junction resistance ratio Rw/Rj. We show that electrical homogeneity improves as i) NW density increases, and ii) junction resistance reduces. The ideal condition of negligible junction resistance (Rw >> Rj) leads to the best-case scenario and guarantees the highest rate of improvement of electrical homogeneity with NW content. Nevertheless, we observe that under condition Rw ≈ Rj the response of the system approaches the response of a system meeting the ideal condition Rw >> Rj (15% difference at most in terms of homogeneity index). We therefore conclude that reducing the junction resistance excessively (with the aim of achieving Rw/Rj > 1) may not always be a worthwhile strategy, as it results in only a marginal improvement in terms of electrical homogeneity.
The proposed strategy is employed to assess the electrical homogeneity of silver nanowire electrodes through the analysis of scanning electron microscopy images. Our results agree with the outcomes of the experimental assessment performed on the same electrodes.