Comparison of cooling rates for hot carriers in GaAs/AlAs quantum wells based on macroscopic and microscopic phonon models

Abstract

By using three analytical phonon models in quantum wells---the slab model, the guided-mode model, and the improved version of the Huang-Zhu model [Phys. Rev. B 38, 13 377 (1998)], ---and the phonon modes in bulk, the energy-loss rates of hot carriers due to the Fr\"ohlich potential scattering in GaAs/AlAs multiple quantum wells (MQW's) are calculated and compared to those obtained based on a microscopic dipole superlattice model. In the study, a special emphasis is put on the effects of the phonon models on the hot-carrier relaxation process when taking the hot-phonon effect into account. Our numerical results show that, the calculated energy-loss rates based on the slab model and on the improved Huang-Zhu model are almost the same when ignoring the hot-phonon effect; however, with the hot phonon effect considered, the calculated cooling rate as well as the hot phonon occupation number do depend upon the phonon models to be adopted. Out of the four analytical phonon models investigated, the improved Huang-Zhu model gives the results most close to the microscopic calculation, while the guided-mode model presents the poorest results. For hot electrons with a sheet density around ${10}^{12}/{\mathrm{cm}}^{2}$, the slab model has been found to overestimate the hot-phonon effect by more than 40% compared to the Huang-Zhu model, and about 75% compared to the microscopic calculation in which the phonon dispersion is fully included. Our calculation also indicates that Nash's improved version [J. Lumin. 44, 315 (1989)] is necessary for evaluating the energy-loss rates in quantum wells of wider well width, because Huang-Zhu's original analytical formulas are only approximately orthogonal for optical phonons associated with small in-plane wave numbers.