Resonant guided elastic waves in an adsorbed slab: theoretical analysis of the density of states

Abstract

An isolated elastic slab presents an infinite number of guided vibrational modes. Upon its adsorption on a semi-infinite substrate some of them become resonant with the bulk modes of the substrate. Such resonances were initially studied by Brillouin and by inelastic helium-atom scattering. We present here an exact method for obtaining the total vibrational density of states of the adsorbed slab. This method is then applied to isotropic elastic media and gives a semi-analytical expression for the vibrational density of states. Detailed analysis for an Al slab on a W substrate and vice versa shows that the resonant modes appear in general as well defined peaks in the total density of states. The position of these peaks enables us to study the speed of the resonant modes as a function of the thickness of the slab or of the propagation vector parallel to the surface.