Electron--acoustic-phonon scattering in a rectangular quantum wire is studied. The Hamiltonian describing the deformation-potential interaction of confined acoustic phonons with carriers is derived by quantizing the appropriate, experimentally verified approximate compressional acoustic-phonon modes in a free-standing rectangular quantum wire. The scattering rate due to the deformation-potential interaction is obtained for GaAs quantum wires with a range of cross-sectional dimensions. The results demonstrate that a proper treatment of confined acoustic phonons may be essential to correctly model electron scattering rates at low energies in nanoscale structures.
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Yu et al. (1994) studied this question.