The Optical Properties of Semi-Continuous Metal Films: A Scaling Based Model

Abstract

ABSTRACTWe present a calculation of the optical properties of thin semi-continuous metal films near the percolative metal-insulator transition. The model is based on scaling assumptions, reflecting the fractal nature of these films. The film is divided into small squares of linear size L and the local complex conductivity of each square is calculated, using finite size scaling arguments and taking into account both ohmic resistance within the metallic clusters and intercluster capacitance. The size L, over which the finite size scaling is done, is related to the optical frequency by the anomalous diffusion relation, i.e. L(ω) α ωl/(2+θ). In this calculation two types of conductivities are found : good ones for the ‘metallic’ squares, showing that large clusters are present within these squares, and poor conductivities for ‘dielectric’ squares, where only small clusters are present. Moreover, the ‘metallic’ and ‘dielectric’ squares are not identical, thus a certain distribution of each type has to be considered. The width of the distribution is quite large close to the percolation threshold and decreases to zero when the film becomes homogeneous. The optical properties of the whole sample are obtained by summing the contribution from all squares, using a wide bimodal distribution function. Comparison with recent experimental results shows good agreement between this model and the experimental data.