Modification of the three-phonon Umklapp process in a quantum wire

Abstract

We have investigated the modification of the three-phonon Umklapp process in a quantum wire caused by the effect of phonon confinement. Our formalism rigorously takes into account variations in phonon group velocity as well as the presence of an energy gap between the phonon modes due to the quantization of the radial phonon wave vector. Numerical calculations of the Umklapp relaxation rate were carried out for Si wires. Based on the obtained results we predict the suppression of the acoustic phonon modes decay at low temperatures that can lead to the unusual thermal conductivity increase. We also present a simplified empiric formula for the Umklapp relaxation rate calculation in a quantum wire.