Electron Population Dynamics in Optically Pumped Asymmetric Coupled Ge/SiGe Quantum Wells: Experiment and Models

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.

Terahertz absorption-saturation and emission from electron-doped germanium quantum wells

“…2(g)), thereby normalizing for the pump-dependent silicon wafer transimssion. From the ∆T/T 0 calculated from numerical simulations we obtain a saturation fluence F p,sat,num = 17 × 10 −8 J/cm 2 [40], which we use as a rough estimate of the optimal pump intensity in a ISBT-PL emission experiment.…”

“…2(c)-(e). This procedure is motivated by the fact that F p,sat is weakly doping-and temperature-dependent as it is determined only by the ISBT absorption cross-section and by the non-radiative lifetimes [40]. While fitting all the data of Figs.…”

Intersubband Transition Engineering in the Conduction Band of Asymmetric Coupled Ge/SiGe Quantum Wells

“…Electrically pumped QCLs and optically pumped quantum fountains realized in the SiGe material system also benefit from the absence of polar longitudinal optical phonons inducing the long-range polarization field (Fröhlich interaction) which strongly couples to charge carriers and limits their non-radiative lifetimes in III-V compounds [7]. Being only mediated by the short-range deformation potential, electron-phonon coupling in non-polar semiconductors is much weaker [19,20] and, as a consequence, SiGe ISB lasers are expected to have a wider temperature operational range, reaching room temperature for n-type Ge/SiGe QCLs [21]. Also, the emission bandwidth would widen, extending inside the reststrahlen band (5-10 THz) of forbidden light propagation caused, in III-V materials, by strong light absorption by optical phonons in this spectral range [7].…”

Disentangling elastic and inelastic scattering pathways in the intersubband electron dynamics of n -type Ge/SiGe quantum fountains

“…Although one of the main challenges in the realization of SiGe devices is their large lattice mismatch with the Si substrate, the growth of high-quality Ge/SiGe QW heterostructures featuring a large number of module repetitions has been recently made available thanks to the high degree of control achieved in the deposition process [14][15][16]. The observation of narrow ISBT absorption peaks in the 4-12 THz range [6,[17][18][19][20] and the very recent measurement of photoluminescence emission in the THz range [21], confirm that n-type Ge/SiGe QWs are excellent candidates for the realization of a silicon-compatible THz emitter.…”