No abstract

The inverse power law has been used to describe the structures and the statistical distributions of discontinuous films of Au, Cu, and Mn on dielectric substrates. To this end, the rank of an island (k) was connected with its area (X) for the films with different coverage coefficients (metal contents) p. The dependencies of the island areas on the rank orders in a double-logarithmic plot are straight lines according to the Mandelbrot law. The slope of the straight line, determined as -1/µ, characterizes the distributions of the islands. One can distinguish three ranges of the critical index µ. For µ>2, the moments m1, m2 are finite; if the number of islands is large, the distribution of island areas tends towards a Gaussian or log-normal one. The films structures exhibit Euclidean character. When 1<µ<2, the moment m1 is finite, m2 is infinite; the islands become irregular in shape, and their areas may be described using Poisson distributions. For µ<1, the `hierarchization' of X is more pronounced, the moments m1, m2 are infinite, and the island areas are distributed according to a Lévy stable distribution (for example, Pareto's distribution). At the percolation threshold (phase transition), the infinite cluster appears and the inverse power law is no longer valid.

The optical properties of discontinuous copper films on quartz substrates at volume fractions ranging from 0.19 to 1.0 are investigated. The range of dielectric properties, the percolation threshold, and the range of metallic properties are determined. The transmittance spectra of copper films with low volume fractions are interpreted in terms of a modified Maxwell-Garnett theory.