A general model for analysis of acoustic phonons in piezoelectric super-lattices. Applicationto the (111)-AlAs/GaAs super-lattice

Abstract

A general model is established for the analysis of acoustic phononsin an arbitrarily oriented piezoelectric super-lattice (SL). Analyticalexpressions are derived allowing the dispersion relation, transmission(T) andreflection (R) properties of the phonons to be numerically calculated for any incidence angle. Numericalinvestigation is exemplified for the (111) GaAs/AlAs SL with incidence in the plane. The obtained band structures confirm that the stop bands for boththe shear horizontal and the coupled longitudinal and shear phonons appearinside the folded Brillouin zone, contrary to the (100) SL case in which theyappear at the zone centre and edges. Both classical dispersion curves andFloquet slowness diagrams are used to present the edges of the Brillouin zones.Locations and widths of the stop bands inside the folded zones, as well as theT and R rates taking into account mode conversion, are studied as a function of frequency andincidence angle.