Quantized acoustic-phonon shear horizontal modes in an unbounded hexagonal nitride-based piezoelectric nanostructure

For the first time a quantum mechanics based theoretical description of acoustic-phonon shear horizontal modes in a class of piezoelectric media is proposed. The quantized acoustic modes that are needed in the transition from the microscale to the nanoscale are derived for a resonator with geometries of interest in optoelectronics and nanoelectronics. The acoustic-phonon frequency dispersion relations are obtained quantum mechanically for odd and even symmetry shear horizontal modes. It is shown that the derived dispersion relations are identical to the previously reported dispersion relations obtained classically as is expected. For each symmetry, the phonon-mode amplitude is derived in terms of the energy of the quantized vibrational mode, which is of great importance for modelling carrier-acoustic phonon interactions. Moreover, the product of quality factor and frequency (Q.f) have been estimated for AlN and GaN resonators by using the anharmonic phonon scattering theory. Furthermore, the electrical surface perturbation in the piezoelectric nanoresonator is studied and the resulting resonance frequency shift is determined.