Resonant guided elastic waves in an adsorbed bilayer: Theoretical analysis of the density of states

We study resonant acoustic waves of sagittal polarization in a bilayer deposited on a substrate. Such resonances were initially studied by Brillouin light scattering in a buffer silica layer of a Si-${\mathrm{SiO}}_2$ bilayer on a Si substrate. Using a Green's-function method, we have obtained the local and total densities of states as a function of the frequency ω and the wave vector ${\mathbf{k}}_{\mathrm{\parallel }}$ parallel to the interfaces. When the velocities of sound in the buffer layer are higher than those in the topmost layer the former acts as a barrier between phonons of the topmost layer and those of the substrate; therefore well-confined resonant waves may exist in the higher slab, which appear as well-defined peaks in the density of states. The positions of these peaks enable us to study the speed of resonant modes as a function of the parallel wave vector and the thicknesses of the buffer and topmost layers. Specific applications of our analytical results are given in this paper for a GaAs-Si bilayer on a GaAs substrate.