Electrical conductivity of random metallic nanowire networks: an analytical consideration along with computer simulation

The current interest in the study of the 2D systems of randomly deposited metallic nanowires is inspired by a combination of their high electrical conductivity with excellent optical transparency. Metallic nanowire networks show great potential for use in numerous technological applications. Although there are models that describe the electrical conductivity of the random nanowire networks through wire resistance, junction resistance, and number density of nanowires, they are either not rigorously justified or contain fitting parameters. We have proposed a model for the electrical conductivity in random metallic nanowire networks. We have mimicked such random nanowire networks as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We studied the electrical conductivity of these RRNs using a mean-field approximation. An analytical dependency of the electrical conductivity on the main physical parameters (the number density and electrical resistances of these wires and of the junctions between them) has been derived. Computer simulations have been performed to validate our theoretical predictions. We computed the electrical conductivity of the RRNs against the number density of the conductive fillers for the junction-resistance-dominated case and for the case where the wire resistance and the junction resistance were equal. The results of the computations were compared with this mean-field approximation. Our computations demonstrated that our analytical expression correctly predicts the electrical conductivity across a wide range of number densities.