LO-phonon emission by hot electrons in one-dimensional semiconductor quantum wires

We provide a theoretical study of hot-electron energy loss via LO-phonon emission in GaAs quantum wires. Calculations are done for a model in which the hot-electron gas is described by a temperature T which is much higher than the lattice temperature. We take into account several relevant physical mechanisms such as quantum degeneracy, dynamic screening, quantum confinement, and hot-phonon bottleneck effect. We include the effects of quantum-wire phonon confinement using two prevailing boundary conditions, namely, the so-called electrostatic and the mechanical macroscopic models. The energy-loss rate calculated for the bulk LO-phonon emission is comparable to, but somewhat higher than, that due to slab (electrostatic) phonon emission, whereas the guided (mechanical) modes produce more than an order of magnitude slower energy relaxation than that due to the slab (electrostatic) or the bulk modes. Our results show that in the experimentally interesting electron-temperature range of 50–300 K, the hot-phonon bottleneck is the single most important quantitative effect provided the hot-phonon lifetime in GaAs quantum wires is comparable to that (∼5–7 ps) in the bulk GaAs. The numerical magnitudes of the quantum-wire hot-electron energy-loss rate due to LO-phonon emission are comparable to those in quantum-well structures under comparable conditions.