A model to account for the field effect of the electrical conductance of discontinuous thin metal films

A series-connected islands model is proposed to account for the field effect of the electrical conductance of discontinuous thin metal films. It is assumed that the islands are all the same size but that their gap lengths have a gaussian distribution. Voltages applied between two adjacent islands differ from island to island depending on the gap length. The highest voltage is between the two islands that have the longest gap length to keep the current density constant. The results of computations show that the voltage between these two islands can be about a hundred times higher than the average voltage calculated from the voltage between the two electrodes and that the logarithm of the conductance depends almost linearly on the square root of the voltage between the two electrodes above a threshold voltage. At the highest voltage the conductance tends to saturate.