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

Abstract

It is shown that the widely used two-dimensional model of random networks of metallic nanowires or carbon nanotubes significantly overestimates the number of contacts between elements compared to real systems, which, within the mean-field approach, leads to overestimated estimates of electrical conductivity, especially when the contact resistances between conductors make the main contribution to the electrical conductivity of the system. In the case of a two-dimensional model, the electrical conductivity of the system depends quadratically on the number density of conductors, whereas in the case of a three-dimensional model this dependence is linear.

Figures (3)

• Figure 1: Distribution of the number of contacts per conductor for various values of the number density of conductors according to the data from Ref. Daniels2021.
• Figure 2: Dependencies of the mean number of contacts on the number density of conductors for the 2D model \ref{['eq:meanNj']} and the Q3D model Daniels2021. Conductor orientations are uniformly distributed.
• Figure 3: Dependencies of electrical conductivity on the number density of conductors for the 2D and Q3D models, obtained within a mean-field-approach using formula \ref{['eq:MFAsigma-RC0']}. Conductor orientations are uniformly distributed. For the 2D model, the number of contacts per conductor was determined by formula \ref{['eq:meanNj']}, while for the Q3D, it was extracted from Ref. Daniels2021.