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We present a theoretical investigation of guided second harmonic generation at THz frequencies in SiGe waveguides embedding n-type Ge/SiGe asymmetric coupled quantum wells to engineer a giant second order nonlinear susceptibility. A characteristic of the chosen material system is the existence of large off-diagonal elements in the χ 2 tensor, coupling optical modes with different polarization. To account for this effect, we generalize the coupled-mode theory, proposing a theoretical model suitable for concurrently resolving every second harmonic generation interaction among guide-sustained modes, regardless of which χ 2 tensor elements it originates from. Furthermore, we exploit the presence of off-diagonal χ 2 elements and the peculiarity of the SiGe material system to develop a simple and novel approach to achieve perfect phase matching without requiring any fabrication process. For a realistic design of the quantum heterostructure we estimate second order nonlinear susceptibility peak values of ∼7 and ∼1.4 × 105 pm/V for diagonal and off diagonal χ 2 elements, respectively. Embedding such heterostructure in Ge-rich SiGe waveguides of thicknesses of the order of 10–15 μm leads to second harmonic generation efficiencies comprised between 0.2 and 2 %, depending on the choice of device parameters. As a case study, we focus on the technologically relevant frequency of 7.1 THz, yet the results we report may be extended to the whole 5–20 THz range.

A parabolic potential that confines charge carriers along the growth direction of quantum wells semiconductor systems is characterized by a single resonance frequency, associated to intersubband transitions. Motivated by fascinating quantum optics applications leveraging on this property, we use the technologically relevant SiGe material system to design, grow, and characterize n-type doped parabolic quantum wells realized by continuously grading Ge-rich Si1−x Gex alloys, deposited on silicon wafers. An extensive structural analysis highlights the capability of the ultra-high-vacuum chemical vapor deposition technique here used to precisely control the quadratic confining potential and the target doping profile. The absorption spectrum, measured by means of Fourier transform infrared spectroscopy, revealed a single peak with a full width at half maximum at low and room temperature of about 2 and 5 meV, respectively, associated to degenerate intersubband transitions. The energy of the absorption resonance scales with the inverse of the well width, covering the 2.5–5 THz spectral range, and is almost independent of temperature and doping, as predicted for a parabolic confining potential. On the basis of these results, we discuss the perspective observation of THz strong light–matter coupling in this silicon compatible material system, leveraging on intersubband transitions embedded in all-semiconductor microcavities.

High-quality n-type continuously graded Ge-rich Si1−xGex parabolic quantum wells with different doping levels were grown by using ultrahigh-vacuum chemical vapor deposition on Si(001) substrates. A thorough structural characterization study highlights an ideal parabolic compositional profile. THz intersubband absorption has been investigated in modulation-doped samples and samples directly doped in the wells. The comparison of experimental absorption data and theoretical calculations allowed us to quantify the impact of electron correlation effects on the absorption resonances in the different doping conditions and for electron sheet densities in the (1 ÷ 6) × 10 11 cm−2 range. A single optical resonance is present in modulation doped samples. Its peak energy and line shape are independent of temperature-induced variations of the electron distribution in the subbands up to 300 K, in agreement with the generalized Kohn theorem. This achievement represents a relevant step forward for the development of CMOS compatible optoelectronic devices in the THz spectral range, where thermal charge fluctuations play a key role. [ABSTRACT FROM AUTHOR]

We report electroluminescence originating from L-valley transitions in n-type Ge/Si0.15Ge0.85 quantum cascade structures centered at 3.4 and 4.9 THz with a line broadening of Δ f / f ≈ 0.2. Three strain-compensated heterostructures, grown on a Si substrate by ultrahigh vacuum chemical vapor deposition, have been investigated. The design is based on a single quantum well active region employing a vertical optical transition, and the observed spectral features are well described by non-equilibrium Green's function calculations. The presence of two peaks highlights a suboptimal injection in the upper state of the radiative transition. Comparison of the electroluminescence spectra with a similar GaAs/AlGaAs structure yields one order of magnitude lower emission efficiency. [ABSTRACT FROM AUTHOR]

n-type Ge/SiGe terahertz quantum cascade lasers are investigated using non-equilibrium Green's functions calculations. We compare the temperature dependence of the terahertz gain properties with an equivalent GaAs/AlGaAs quantum cascade laser design. In the Ge/SiGe case, the gain is found to be much more robust to temperature increase, enabling operation up to room temperature. The better temperature robustness with respect to III–V is attributed to the much weaker interaction with optical phonons. The effect of lower interface quality is investigated and can be partly overcome by engineering smoother quantum confinement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

n-type Ge/SiGe asymmetric coupled quantum wells represent the building block of a variety of nanoscale quantum devices, including recently proposed designs for a silicon-based THz quantum cascade laser. In this paper, we combine structural and spectroscopic experiments on 20-module superstructures, each featuring two Ge wells coupled through a Ge-rich SiGe tunnel barrier, as a function of the geometry parameters of the design and the P dopant concentration. Through a comparison of THz spectroscopic data with numerical calculations of intersubband optical absorption resonances, we demonstrated that it is possible to tune, by design, the energy and the spatial overlap of quantum confined subbands in the conduction band of the heterostructures. The high structural/interface quality of the samples and the control achieved on subband hybridization are promising starting points towards a working electrically pumped light-emitting device. [ABSTRACT FROM AUTHOR]