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-SiO2 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 omega and the wave vector k(parallel to) 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.