Determination of thickness-dependent damping constant and plasma frequency for ultrathin Ag and Au films: nanoscale dielectric function

Abstract

This paper is devoted to determine an analytical expression for the thickness dependent complex dielectric function for the case of Ag and Au thin films. Free and bound electron contributions are dealt with independently. Using Drude model for the former and taking experimental refractive index values for Ag and Au thin films, we apply a previously developed method to determine for the first time damping constant and plasma frequency parameters for specific film thicknesses. Fitting separately each one of these parameters allowed us to find an analytical expression for their dependence on arbitrary film thickness and consequently for the free electron contribution. Concerning bound electrons, its contribution for small wavelengths is the same for all analyzed thicknesses and may be set equal to the bulk bound contribution. Taking these facts into account, the complex dielectric function is rewritten analytically, in terms of bulk dielectric function plus corrective film thickness dependent terms. From the fitting process for the damping constant we determine that electron scattering at the film boundary is mainly inelastic for both silver and gold thin films. It is also shown that, in accordance with theoretical studies, plasma frequency shows a red shift as the film thickness decreases.