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

We study by means of Monte-Carlo numerical simulations the resistance of two-dimensional random percolating networks of stick, widthless nanowires. We use the multi-nodal representation (MNR) 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 non-dimensional variables applying Buckingham $\pi-$theorem. The effective resistance of 2D random percolating networks of nanowires is found to write as $R^{eq}(\rho,R_c,R_{m,w})=A\left(N,\frac{L}{l^{*}}\right) \rho l^* + B\left(N,\frac{L}{l^{*}}\right) R_c+C\left(N,\frac{L}{l^*} \right) R_{m,w}$ where $N$, $\frac{L}{l^{*}}$ are the geometrical parameters (number of wires, aspect ratio of electrode separation over wire length) and $\rho$, $R_c$, $R_{m,w}$ are the physical parameters (nanowire linear resistance per unit length, nanowire/nanowire contact resistance, metallic electrode/nanowire contact resistance). The dependence of the resistance on the geometry of the network, one 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.