The Anomalous Skin Effect in Metallic Films

Abstract

Fredholm integral equations of the second kind are formulated to describe the anomalous skin effect in metal films on dielectric substrates. An algorithm is developed for numerical solution of the equations based on the quadrature method. As a result of its use for processing published experimental data on the spectral ellipsometry of gold films of different thicknesses on a silicon substrate, the density, relaxation time of the conduction electrons, and dielectric constant of gold are uniquely determined. The dependence of the dielectric constant of gold films on their thickness noted in a number of experimental studies is explained by using a model of the normal Drude skin effect that does not take the excitation of space charge in the film into account when solving the inverse optical problems. The optical fields in gold films are studied for different probabilities of mirror reflection of electrons from the boundary of the films It is found that in sensors for biological solutions with a Kretschmann configuration, structures in which the probability of mirror reflection of electrons from the metallic film–liquid interface approaches unity are to be preferred.