Sagittal elastic waves at the interface between a superlattice and a substrate: theoretical analysis of the density of states and reflection coefficients

We investigate the existence and behavior of localized and resonant acousti c modes of sagittal polarization associated with the interface between a su perlattice (SL) and a substrate. These modes appear as well-defined peaks i n the density of states, either inside the minigaps or inside the bulk band s of the SL and the substrate. It is shown that the interface modes strongl y depend on the acoustic impedances of the substrate. Furthermore, a phonon incident on the superlattice from a substrate is partially reflected in th e substrate, therefore the amplitudes and the phases of the reflection coef ficients 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 interf ace resonant modes. The densities of states and reflection coefficients, wh ich are calculated as function of the frequency omega and the wave vector k (parallel to) (parallel to the interfaces), are obtained from an analytical determination of the Green's function for the superlattice/substrate inter face. Specific application of om analytical results are given for a W/Al is otropic superlattice in contact with a substrate with different acoustic im pedances.