Electron population dynamics in optically pumped asymmetric coupled Ge/SiGe quantum wells: Experiment and models

n-type doped Ge quantum wells with SiGe barriers represent a promising heterostructure system for the development of radiation emitters in the terahertz range such as electrically pumped quantum cascade lasers and optically pumped quantum fountain lasers. The nonpolar lattice of Ge and SiGe provides electron-phonon scattering rates that are one order of magnitude lower than polar GaAs. We have developed a self-consistent numerical energy-balance model based on a rate equation approach which includes inelastic and elastic inter-and intra-subband scattering events and takes into account a realistic two-dimensional electron gas distribution in all the subband states of the Ge/SiGe quantum wells by considering subband-dependent electronic temperatures and chemical potentials. This full-subband model is compared here to the standard discrete-energy-level model, in which the material parameters are limited to few input values (scattering rates and radiative cross sections). To provide an experimental case study, we have epitaxially grown samples consisting of two asymmetric coupled quantum wells forming a three-level system, which we optically pump with a free electron laser. The benchmark quantity selected for model testing purposes is the saturation intensity at the 1!3 intersubband transition. The numerical quantum model prediction is in reasonable agreement with the experiments and therefore outperforms the discrete-energy-level analytical model, of which the prediction of the saturation intensity is off by a factor 3.