Acoustic waves in solid and fluid layered materials

Abstract

This is a comprehensive theoretical survey of acoustic wave propagation in layered materials including elastic, viscoelastic and piezoelectric layers. The phonon modes are particularly emphasized in the case of periodic multilayered structures such as superlattices though other layered materials such as adsorbed layers and quasiperiodic structures are also discussed. Besides the bulk waves propagating in the whole materials, specific attention is paid to the effect of inhomogeneities within the perfect superlattice such as a free surface (with or without a cap layer), a superlattice/substrate interface and a defect layer embedded in the superlattice. Such inhomogeneities are usually present in actual device structures as a support (substrate) or as a protection (cap layer) for the superlattice; the defect layers offer the possibility of wave filtering and sometimes they can be introduced as an imperfection during the epitaxial growth process. The superlattices are considered as semi-infinite or finite size structures. The symmetry of the materials are chosen such that the transverse acoustic waves are decoupled from the sagittal one (i.e., those having components of the acoustic displacement in the sagittal plane formed by the propagation direction and the normal to the interfaces). A general rule about the existence of localized surface modes in elastic, viscoelastic and piezoelectric semi-infinite superlattices with a free surface is presented. The adsorption of a hard material on the top of the superlattice (cap layer) has been shown to be appropriate for detecting experimentally high frequency guided modes within the adsorbed layer. Also, the superlattice/substrate interface may exhibit interface modes which are without analogue in the case of an interface between two homogeneous media. For a finite size superlattice, due to the interaction between the surface, interface and bulk waves, different localized and resonant modes are obtained and their properties are investigated. In particular, the effect of a buffer layer embedded between the superlattice and the substrate in confining guided modes in the superlattice is highlighted. These results are obtained in the frame of a Green’s function formalism that enables us to deduce the dispersion curves, local and total densities of states, as well as the transmission and reflection coefficients and the corresponding phase times. In particular, an exact relation between the density of states and the phase times is pointed out. The application of elastic layered periodic structures as acoustic mirrors that exhibit total reflection of waves for all incident angles and polarizations in a given frequency range is indicated. These structures may also be used as acoustic filters when a defect layer is inserted within the finite size layered structure. A discussion is also included about some spectroscopic techniques used to probe the acoustic waves such as Raman and Brillouin light scattering and other acoustic techniques such as the surface acoustic waves and the picosecond laser techniques among others. A comparison of the theoretical results with experimental data available in the literature is also presented and the reliability of the theoretical predictions is indicated. Finally, other acoustic wave properties in quasiperiodic structures are briefly reviewed.