Effective medium theory for the conductivity of disordered metallic nanowire networks

Motivated by numerous technological applications, there is current interest in the study of the conductive properties of networks made of randomly dispersed nanowires. The sheet resistance of such networks is normally calculated by numerically evaluating the conductance of a system of resistors but due to disorder and with so many variables to account for, calculations of this type are computationally demanding and may lack mathematical transparency. Here we establish the equivalence between the sheet resistance of disordered networks and that of a regular ordered network. Rather than through a fitting scheme, we provide a recipe to find the effective medium network that captures how the resistance of a nanowire network depends on several different parameters such as wire density, electrode size and electrode separation. Furthermore, the effective medium approach provides a simple way to distinguish the sheet resistance contribution of the junctions from that of the nanowires themselves. The contrast between these two contributions determines the potential to optimize the network performance for a particular application. An analytical model with dependance on all important underlying parameters to calculate the electrical properties of nanowire networks is presented.