Phonon-confinement effect on electron energy loss in one-dimensional quantum wires

We calculate, within the electron-temperature model, hot-electron intrasubband energy relaxation rates via LO-phonon emission in GaAs quantum wires, taking into account quantum degeneracy, dynamical screening, hot-phonon bottleneck, and, in particular, phonon confinement. Two prevailing macroscopic models of phonon confinement, namely, the slab or the electrostatic model and the guided or the mechanical model, are compared quantitatively. We find that the slab model, while giving relaxation rates comparable to the bulk-phonon emission rates, leads to an order of magnitude faster relaxation than the guided model. For reasonable parameter values, the hot-phonon-bottleneck effect is found to be the single most important physical mechanism determining energy relaxation. Numerical values for electronic-energy-loss rates in GaAs quantum wires are provided for both models of phonon confinement for a range of values of the relevant parameters, including confinement size, carrier density, hot-phonon lifetime, and electron temperature.