Surface acoustic wave modes in two-dimensional shallow void inclusion phononic crystals on GaAs

The possibility to control supersonic acoustic wave propagation is intriguing, but when modeling phononic crystal devices, supersonic surface acoustic waves are mired by radiative attenuation and, hence, eschewed in many device designs. In this paper, we study supersonic surface acoustic wave modes in shallow hole phononic crystals computationally with respect to the three bulk wave sound barriers of cubic (001) GaAs. From a first principles modeling approach of linear elasticity, the finite element method, and with the aid of characterization parameters for systematic modal categorization, detailed nuances are observed for supersonic surface waves propagating along the [110]-direction of GaAs with a periodically patterned surface. Modes of interest are distinguished by possessing both strain energy and squared polarization ratios above defined thresholds. The square array of shallow inclusions imparts a metamaterial surface layer effect that results in marked changes in the dispersion, the bulk wave hybridization, and the modal interactions of the surface modes in the Gamma-X direction of the phononic crystal, which are characterized by their modal profiles and attenuation via bulk wave radiation. From these findings, we propose an extended sound cone concept to accommodate supersonic surface acoustic waves with low attenuation. Furthermore, at frequencies above the shear vertical bulk dispersion line, well-bounded surface acoustic wave modes are revealed, and the phenomenon of these supersonic modes with limited bulk wave coupling is explored. From these detailed band structures, the systematic method of mode characterization reveals deeper insights into modes that exist in shallow phononic crystals on cubic GaAs.