Sagittal Elastic Waves at the Interface between a Superlattice and a Substrate: Theoretical Analysis of the Density of States and Reflection Coefficientsrik

Abstract

We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the interface between a superlattice (SL) and a substrate. These modes appear as well‐defined peaks in the density of states, either inside the minigaps or inside the bulk bands of the SL and the substrate. It is shown that the interface modes strongly depend on the acoustic impedances of the substrate. Furthermore, a phonon incident on the superlattice from a substrate is partially reflected in the substrate, therefore the amplitudes and the phases of the reflection coefficients enable us to deduce the frequency ranges of the bulk bands and the minigaps of the superlattice as well as the frequency levels of the interface resonant modes. The densities of states and reflection coefficients, which are calculated as function of the frequency ω and the wave vector k∥(parallel to the interfaces), are obtained from an analytical determination of the Green's function for the superlattice/substrate interface. Specific application of our analytical results are given for a W/Al isotropic superlattice in contact with a substrate with different acoustic impedances.