Electron interaction with confined acoustic phonons in cylindrical quantum wires via deformation potential

The effects of phonon confinement on electron–acoustic-phonon scattering is studied in cylindrical semiconductor quantum wires. In the macroscopic elastic continuum model, the confined-phonon dispersion relations are obtained for several crystallographic directions with the two cardinal boundary conditions: free-surface and clamped-surface boundary conditions. The scattering rates due to the deformation potential interaction are obtained for these confined phonons and are compared with those of bulk-like phonons for a number of quantum wire materials. The results show that the inclusion of acoustic phonon confinement effects may be crucial for calculating accurate low-energy electron scattering rates in nanostructures. It is also demonstrated that the scattering rates may be significantly influenced by the direction of phonon propagation, especially for low-energy electrons. Furthermore, it has been found that there is a scaling rule governing the directional dependence of the scattering rates: the directions characterized by small Poisson ratios exhibit large scattering rates.