Abstract
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.
Highlights
Quantum cascade lasers (QCL) are based on intersubband transitions (ISBTs) among discrete energy states in quantum wells (QWs), and their operating principle is not limited to direct bandgap material systems [1]
ACQW samples were grown epitaxially on low-impurity concentration Si (100) with the ultra-high-vacuum chemical vapor deposition (UHV-CVD) technique
We have grown and optically characterized a set of asymmetric-coupled Ge/SiGe quantum wells designed as three-level systems for optical pumping and absorption-saturation experiments in the THz range
Summary
Quantum cascade lasers (QCL) are based on intersubband transitions (ISBTs) among discrete energy states in quantum wells (QWs), and their operating principle is not limited to direct bandgap material systems [1]. QWs has to comply with in order to be suitable for QCL development are a high quality of the heterostructure; a band offset compatible with the target emitted photon energy; and a small effective mass of carriers (holes or electrons). For the active region, imposes the growth of strain-symmetrized Ge/SiGe heterostructures where tensile strained SiGe is used as the barrier material and compressive Ge QWs confine the electrons at the L-point minimum of the conduction band of Ge. The maximum band offset that can be obtained at the L-point with strain-symmetrised Ge/SiGe heterostructures with designs doable in practice for QCL is around 100 meV, limiting possible laser emission to photon energies in the terahertz (THz) range below about 30 meV. Non-radiative lifetimes in Ge/SiGe QWs may be slightly longer than in equivalent designs realized in an AlGaAs/GaAs material system, due to the nonpolar nature of the Ge and SiGe lattices
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