Room temperature operation of n-type Ge/SiGe terahertz quantum cascade lasers predicted by non-equilibrium Green's functions

Abstract

n-type Ge/SiGe terahertz quantum cascade laser are investigated using non-equilibrium Green's functions calculations. We compare the temperature dependence of the terahertz gain properties with an equivalent GaAs/AlGaAs QCL 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 via multiple barrier heights.Terahertz (THz) quantum cascade lasers (QCLs) have been demonstrated with different III-V materials including GaAs/AlGaAs 1 , InGaAs/AlInAs 2,3 , InGaAs/GaAsSb 4 and InAs/AlAsSb 5 .In the past decade however, relatively small progress has been reported to increase the maximum operating temperature (presently 200 K) despite substantial efforts of design optimization 6-8 . The rationale for the quenching of THz laser emission above this temperature is due to the very effective electron-phonon (e-phonon) interaction, typical of III-V materials. Indeed in polar lattices the longitudinal optical (LO) phonons induce a long-range polarization field which strongly couples to the charge carriers (Fröhlich interaction). The THz transitions are typically designed to be well below the optical phonon energy (30-36 meV), so that at low temperature the upper laser state is protected against scattering by emission of LO-phonons. With increasing temperature however, the thermally activated electrons in the subband of the upper lasing state gain enough in-plane kinetic energy to access this scattering channel 9 . This non-radiative relaxation of carriers reduces the population inversion and is responsible for quenching of the laser emission with increasing temperature as the gain drops below the cavity losses. This fast non-radiative channel cannot easily be overcome by design engineering, as there is a necessary trade-off between selectivity and speed of the carrier injection in such closely spaced energy levels.To overcome this limitation, QCLs based on crystals having large optical phonon energy such as GaN or ZnO have recently been proposed 10 . As an alternative strategy, non-polar material systems are attractive because of their weaker e-phonon interaction. Indeed in these crystals the e-phonon coupling is controlled by the deformation potential which due to its short range is much less effective than the Fröhlich interaction. SiGe alloys fulfill this requirement and also have the great advantage of being non-toxic materials fully compatible with silicon technology. Among different configurations (electron or hole based, Si or Ge rich regimes) 11-14 , theoretical studies have indicated n-type Ge/SiGe heterostructures where charge transport is associated to L electrons, as the most promising architecture 15-17 . Experimentally, sharp THz absorption peaks, related to intersubband transitions in n-typ...

Atomic-Scale Insights into Semiconductor Heterostructures: From Experimental Three-Dimensional Analysis of the Interface to a Generalized Theory of Interfacial Roughness Scattering

“…The NEGF simulations are performed using the nextnano.QCL package, which calculates the quantum transport through layered heterostructures. The scattering processes are treated within the selfconsistent Born approximation, including phonons, charged impurities, electron-electron, interface roughness, and alloy disorder [21,24,25]. We neglected hot-phonon effects assuming a Bose-Einstein statistics at the lattice temperature.…”

“…Moreover, aiming at reducing the computational time, the electronelectron interaction is calculated exploiting a mean-field approximation, as discussed in Ref. 21 , where the interest reader can find a detailed description of the model and of its approximations. The gain is calculated self-consistently within the linear response theory following Ref.…”

“…As a relevant example, we discuss here the impact of the IFR scattering on the performances of a n-type Ge/SiGe quantum cascade laser grown on top of a Si(001) substrate, featuring a composition profile quite similar to the one of the ACQW samples here investigated. This choice is motivated by the fact that QCL systems are a prototypical case-study to assess the role of IFR scattering [6,37,38], owing to the inherently large number of heterointerfaces featured by this class of devices, and by the technological relevance of a Si-based THz source, suitable for room temperature operation [20,21].…”

“…4, we quantitatively compare the maximum gain as a function of Δ calculated using the generalized model of IFR scattering described in this paper (solid lines) with that predicted by the abrupt uncorrelated interface approach (dashed lines), as done in Refs. [21] and [39] [Fig. 5(c)].…”

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

“…For accurate QCL designs, a numerical quantum model of electron state population dynamics out of equilibrium is required. Since an electrically pumped Ge/SiGe QCL has been designed but not realized yet [9][10][11], optically pumped devices may offer an easier experimental test bench to assess the performances of models with out-of-equilibrium intersubband (ISB) population dynamics. For optically pumped lasers, electrical contacts are not required, thus eliminating most of the device processing steps and related difficulties [12], and besides, much simpler active layer QW stacks are needed compared to QCLs.…”