Theory of polar-optical-phonon scattering in a semiconductor quantum wire

The scattering rates of electrons due to the interaction with the polar-optical phonons in a quasi-one-dimensional semiconductor quantum wire are studied theoretically using a simple cylindrical wire model. Many-body effects on the electron-phonon interaction are included by calculating the leading-order polaronic self-energy. Analytical formulas for the scattering rates are derived using the simple model where the envelope function is assumed to be constant inside a cylindrical wire and zero outside. The most prominent feature of the many-body effects is that the phonon absorption process is enhanced while the emission process is suppressed for the low-energy electrons with increasing electron density as compared with those of the single-particle model. Polar scattering rates are reduced for the one-dimensional electron gas in a quantum wire by an order of magnitude as compared with those of the two-dimensional electron gas.