Monte Carlo study of electron relaxation in quantum-wire laser structures

Very-low threshold currents are expected to be achieved in quantum-wire lasers owing to the singularity in the density of states occurring at the bandedge. On the other hand, the high-speed modulation of quantum-wire lasers may be limited by carrier relaxation processes that are greatly affected by the reduction in the momentum space. In this paper, we calculate the electron relaxation times for GaAs/AlGaAs wires of various cross sections assuming that electrons are injected in a thermal distribution at the edge of the potential well formed by the barrier. The relaxation times are extracted from the time evolution of the carrier distribution as the electrons come to thermal equilibrium with the lattice. The Monte Carlo method is used to simulate the details of the relaxation process with the inclusion of electron-bulklike phonon, electron-electron and electron-hole interactions. We find that the electron relaxation times range from 120 ps for the 100×100 Å wire to 30 ps for the 200×200 Å wire for a carrier density of 10¹⁸ cm^-3. When the electron-hole interaction is included into the calculations, the equilibration time for the 100×100 Å wire is reduced to ≈50 ps. Screening effects are incorporated using the Thomas-Fermi formalism. At a carrier concentration of 10¹⁶ cm^-1, the equilibration times for the corresponding wire sizes are 20 and 5 ps. Thus, the relaxation time calculated within the limits of our model decreases with an increased wire cross section. This trend indicates the presence of a trade-off between speed and efficiency in quantum-wire lasers considering that the threshold current is decreased by reducing the wire cross section