Phonon-limited mobility in a free-standing polar semiconductor quantum wire

A macroscopic continuum model is used to study the longitudinal optical phonons in a free-standing polar quantum wire with a rectangular cross section. The Frohlich Hamiltonian describing the electron-phonon interaction is then obtained and used to calculate the electron mobility governed by confined LO phonons by means of the memory function approach, neglecting electron-electron interaction. Numerical calculations are given for a GaAs quantum wire, showing that the mobility is enhanced at least by one order of magnitude in comparison with the bulk-LO-phonon-limited one. It is shown that the contribution of intersubband scattering is important in wires of large width at high temperature.