ANALYSIS OF ISLAND-SIZE DISTRIBUTIONS IN ULTRATHIN METALLIC-FILMS

Ultrathin metallic films deposited on amorphous substrates show island growth until electrical percolation occurs. Scaling theory makes rather precise predictions about the deposition-time dependence of the island-size distributions and related properties. It is therefore important to be able to analyze experimental data in a quantitative way in order to be able to make a detailed comparison with theory. This paper addresses two aspects of the data analysis of island-size distributions. In the first, a robust method of presenting measurements in the form of continuous distributions (as opposed to histograms) is examined. In the second, we obtain a prescription for transforming chord distributions into diameter distributions. This transformation will be useful in cases where the islands are (or approximate to) regular droplets and when it is easier to measure chords than diameters. Relations between the moments of the chord and diameter distributions are obtained. To demonstrate the first method, it is used to extract the island-size distribution within a Pt/a-C film. A remarkably good match to a log-normal distribution is found without making any of the usual a priori assumptions. Comments on implications for scaling theory are made.