Clustering in Thin Au Films Near the Percolation Threshold

Abstract

A random mixture of conducting (fractional concentration p) and insulating (fractional concentration 1-p) material will abruptly exhibit electrical conduction at a critical concentration, p_c. While this idealized type of percolation problem is ideally suited for computer simulation studies and as a model for conductivity measurements in real systems, efforts have recently been made to examine these mixtures in thin metal films via transmission electron microscopy and to analyze the resulting micrographs using digital processing. In this way, detailed comparisons between the cluster formation in the metal film and the predictions of percolation theory can be directly made. We have made such comparisons in our studies of the thickness dependence of the resistance and microstructure of very thin metal films. While changes in the conductivity properties as a function of metal to insulator concentration have been interpreted in terms of percolation¹, these measurements are complicated by the presence of other conductivity mechanisms unrelated to percolation. Leakage between clusters either on the surface or through the bulk including quantum mechanical tunneling² can smear the percolation transition and add a temperature dependence to the conductivity. Detailed analysis of the TEM micrographs has been shown to be a reliable and informative way to compare the geometric properties of the clustered film with the theoretical predictions of percolation and scaling near the insulator-metal transition.