Effective medium theory for the electrical conductance of random resistor networks which mimic crack-template-based transparent conductive films

We studied random resistor networks produced with regular structure and random distribution of edge conductances. These networks are intended to mimic crack-template-based transparent conductive films as well some random networks produced using nano-imprinting technology. Applying an effective medium theory, we found out that the electrical conductance of such networks is proportional to the square root of the number density of conductive edges. This dependence is in agreement with numerical calculations in Voronoi networks, although the effective conductances are about 15%.