A rate equation formalism for electron and phonon dynamics in undoped quantum wells

Abstract

A theoretical investigation of the electron and phonon dynamics during intersubband transitions in undoped multiple GaAs-AlxGa1−xAs quantum well structures is presented within a rate equation formulation where particle and energy flow equations are derived from Boltzmann’s equation using Fermi statistics. This work focuses upon the role played by quantized polar optical phonons known as slab modes and interface modes. Photoexcited carrier behavior is analyzed in relation with recent Raman measurements and shows time constants for electron relaxation in agreement with experimental data.

Analysis of hot electron effects on intersubband Raman laser in modulation‐doped GaAs/AlGaAs coupled double quantum wells

“…So we accord to the time evolution scheme developed in Refs. [9,10] by averaging of the Boltzmann's equation over possible in-plane (transverse) energy distribution. In this modelled scheme, we assume the form of Fermi distribution function for hot electrons, and time variation of electron temperature T i and quasi-Fermi energy E fi .…”

“…These rate equations for particle number and average energy are de-rived from the Boltzmann's equation [9] using the Fermi statics combined with the stimulated resonant Raman term. The carrier scattering due to the confined LO phonons and interface (IF) optical phonon modes in CDQWs are taken into account in detail.…”

Hot electron effects in optically-pumped mid-infrared intersubband semiconductor laser

“…The transition probabilities for all types of electron-POP interactions are calculated for confined (slab) and interface POP phonon modes [8]. The electron dynamics is studied by using a rate equation formalism [9] under optical pumping. The electron density, electron temperature, quasi-Fermi level, and average electron relaxation time constant for each subband are determined as a function of the pumping intensity.…”

“…To simulate electron dynamics in the ACQW structure, we use a rate equation approach which is derived from Boltzmann's equation with Fermi statistics [9] and is less computer-intensive than the Monte-Carlo method. One major drawback of this approach is that the shape of the electron distribution function remains Fermi-like, whereas the Monte-Carlo method provides a distribution profile dictated by electron dynamics.…”