Electron-optical-phonon scattering rates in a rectangular semiconductor quantum wire

One-dimensional electron-optical-phonon interaction Hamiltonians in a rectangular quantum wire consisting of diatomic polar semiconductors are derived under the macroscopic dielectric continuum model. The scattering rates calculated in a GaAs square quantum wire show that when the quantum wire is free-standing in vacuum, the interaction by the surface-optical phonon modes is very strong and may dominate over other scattering processes, especially with dimensions of about 100 Å or less. When the wire is embedded in a polar semiconductor (AlAs to be specific), the scattering rates by the surface-optical phonon modes become generally smaller, but yet comparable to those by the confined longitudinal-optical modes as the wire dimension shrinks. A considerable decrease in the total scattering rate for optical phonons as a result of simple reduction in dimensionality is not observed in this study.