Effective resistance of random percolating networks of stick nanowires: Functional dependence on elementary physical parameters

Abstract

We study by means of Monte Carlo numerical simulations the resistance of two-dimensional random percolating networks of stick, widthless nanowires. We use the multinodal representation [C. G. da Rocha et al., Nanoscale 7, 13011 (2015)] to model a nanowire network as a graph. We derive numerically from this model the expression of the total resistance as a function of all meaningful parameters, geometrical and physical, over a wide range of variation for each. We justify our choice of nondimensional variables by applying the Buckingham π-theorem. The effective resistance of 2D random percolating networks of nanowires is written as Req(ρ,Rc,Rm,w)=A(N,Ll∗)ρl∗+B(N,Ll∗)Rc+C(N,Ll∗)Rm,w, where N and Ll∗ are the geometrical parameters (number of wires and aspect ratio of electrode separation over wire length) and ρ, Rc, and Rm,w are the physical parameters (nanowire linear resistance per unit length, nanowire/nanowire contact resistance, and metallic electrode/nanowire contact resistance). The dependence of the resistance on the geometry of the network, on the one hand, and on the physical parameters (values of the resistances), on the other hand, is thus clearly separated, thanks to this expression, much simpler than the previously reported analytical expressions.