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

A general model is established for the analysis of acoustic phonons in an arbitrarily oriented piezoelectric super-lattice (SL). Analytical expressions are derived allowing the dispersion relation, transmission (T) and reflection ( R) properties of the phonons to be numerically calculated for any incidence angle. Numerical investigation is exemplified for the (111) GaAs/AlAs SL with incidence in the (110) plane. The obtained band structures confirm that the stop bands for both the shear horizontal and the coupled longitudinal and shear phonons appear inside the folded Brillouin zone, contrary to the (100) SL case in which they appear at the zone centre and edges. Both classical dispersion curves and Floquet 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 the T and R rates taking into account mode conversion, are studied as a function of frequency and incidence angle.