Acoustic phonons propagating in semiconductor quantum wires and their mean-free-path

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In this work, we obtained normal acoustic phonon modes of rectangular quantum wires, applying an algorithm referred to as the xyz algorithm which is used in the ultrasonic sound spectroscopy. The normal modes are classified, according to the spatial symmetries of the rectangular wires, into the dilatational, shear/torsional, and flexural modes. The shear/torsional mode is not well defined for rectangular wires, but they are well defined for square wires.Dispersion curves of these modes have phonon subbands caused by the phonon confinement in the lateral direction of the wires. We investigated electron scattering by these acoustic phonon modes via the deformation potential and the suface vibrations induced by acoustic phonons. The latter is termed the ripple mechanism after the light scattering from vibrating surface. Paying special attention to coherence among the scattering events, we found the deformation potential and the ripple mechanism scatterings take place only for the dilatational phonon mode and therefore these two kinds of scatterings interfere to enhance scattering rates.Consequently, the scattering rates are more enhanced than the sum of individual contribution of these mechanisms to electron scatterings. This coherent interference between the deformation potential and the ripple mechanism scatterings is not peculiar to the rectangular quantum wires, but bring about for other systems with low spatial symmetries. This leads to the conclusion that the coherent interference between these two electron-phonon interaction is essential to the electron systems confined in the nanostructures, suggesting that the deformation potential can be empirically changed to incorporate the effect of the surface vibrations on the electron-phonon interaction.