RESONANT GUIDED ELASTIC-WAVES IN AN ADSORBED SLAB - THEORETICAL-ANALYSIS OF THE DENSITY-OF-STATES

An isolated elastic slab presents an infinite number of guided vibrati onal modes. Upon its adsorption on a semi-infinite substrate some of t hem become resonant with the bulk modes of the substrate. Such resonan ces were initially studied by Brillouin and by inelastic helium-atom s cattering. We present here an exact method for obtaining the total vib rational density of states of the adsorbed slab. This method is then a pplied to isotropic elastic media and gives a semi-analytical expressi on for the vibrational density of states. Detailed analysis for an Al slab on a W substrate and vice versa shows that the resonant modes app ear in general as well defined peaks in the total density of states. T he position of these peaks enables us to study the speed of the resona nt modes as a function of the thickness of the slab or of the propagat ion vector parallel to the surface.