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

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.

arXiv comment10 pages, 9 figures, 52 references, extended and revised version of the invited talk presented during 34th Marian Smoluchowski Symposium on Statistical Physics http://www.smoluchowski.if.uj.edu.pl/

References in corpus (9)

• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Continuum Percolation Thresholds in Two Dimensions
• From percolating to dense random stick networks: Conductivity model investigation
• Effective resistance of random percolating networks of stick nanowires : functional dependence on elementary physical parameters
• Electrical conductance of two-dimensional composites with embedded rodlike fillers: an analytical consideration and comparison of two computational approaches
• Effect of tunneling on the electrical conductivity of nanowire-based films: computer simulation within a core--shell model
• Electrical conductivity of nanoring-based transparent conductive films: A mean-field approach
• Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm

Cited by in corpus (5)

• Random 2D nanowire networks: Finite-size effect and the effect of busbar/nanowire contact resistance on their electrical conductivity
• Percolation and electrical conduction in random systems of curved linear objects on a plane: computer simulations along with a mean-field approach
• Transparent electrodes based on mixtures of nanowires and nanorings: A mean-field approach along with computer simulation
• Electrical conductivity of random metallic nanowire networks: An analytical consideration along with computer simulation
• Electrical conductivity of a random nanowire network: comparison of two-dimensional and quasi-three-dimensional models