We developed a time-dependent density-matrix model to study photon-assisted (PA) electron transport in quantum cascade lasers. The Markovian equation of motion for the density matrix in the presence of an optical field is solved for an arbitrary field amplitude. Level-broadening terms emerge from microscopic Hamiltonians and supplant the need for empirical parameters that are often employed in related approaches. We show that, in quantum cascade lasers with diagonal design, photon resonances have a pronounced impact on electron dynamics around and above the lasing threshold, an effect that stems from the large spatial separation between the upper and lower lasing states. With the inclusion of PA tunneling, the calculated current density and output power are in good agreement with experiment.
Bosonic cascade lasers are terahertz (THz) lasers based on stimulated radiative transitions between bosonic condensates of excitons or exciton-polaritons confined in a trap. We study the interaction of an incoming THz pulse resonant in frequency with the transitions between neighboring energy levels of the cascade. We show that at certain optical pump conditions the cascade becomes transparent to the incident pulse: it neither absorbs nor amplifies it, in the mean field approximation. The populations of intermediate levels of the bosonic cascade change as the THz pulse passes, nevertheless. In…
Book chapter on multiscale electrothermal simulation of midinfrared quantum cascade lasers. To appear in Handbook of Optoelectronic Device Modeling and Simulation, Taylor and Francis Books, 2017. Editor: Joachim Piprek.
We analyze the peculiar case where the free carrier absorption arising from LO phonon absorption-assisted transitions becomes negative and therefore turns into a gain source for quantum cascade lasers. Such an additional source of gain exists when the ratio between the electronic and the lattice temperatures is larger than one, a condition that is usually fulfilled in quantum cascade lasers. We find a gain of few cm$^{-1}$'s at 200K. We report the development of a terahertz quantum cascade laser operating in the negative free carrier absorption regime.
We propose a concept of a quantum cascade laser based on transitions of bosonic quasiparticles (excitons and exciton-polaritons) in a parabolic potential trap in a semiconductor microcavity. This laser would emit terahertz radiation due to bosonic stimulation of excitonic transitions. Dynamics of a bosonic cascade is strongly different from the dynamics of a conventional fermionic cascade laser. We show that populations of excitonic ladders are parity-dependent and quantized if the laser operates without an external terahertz cavity.
THz quantum cascade lasers based on a novel buried cavity geometry are demonstrated by combining double-metal waveguides with proton implantation. Devices are realised with emission at 2.8 THz, displaying ultra low threshold currents of 19 mA at 4K in both pulsed and continuous wave operation. Thanks to the semiconductor material on both sides of the active region and to the narrow width of the top metal strip, the thermal properties of these devices have been greatly improved. A decrease of the thermal resistance by over a factor of two compared to standard ridge double-metal lasers of simila…
Quantum cascade lasers made of nanowire axial heterostructures are proposed. The dissipative quantum dynamics of their carriers is theoretically investigated using non-equilibrium Green functions. Their transport and gain properties are calculated for varying nanowire thickness, from the classical-wire regime to the quantum-wire regime. Our calculation shows that the lateral quantum confinement provided by the nanowires allows an increase of the maximum operation temperature and a strong reduction of the current density threshold compared to conventional terahertz quantum cascade lasers.
A model of sequential resonant tunneling transport between two-dimensional subbands that takes into account explicitly elastic scattering is investigated. It is compared to transport measurements performed on quantum cascade lasers where resonant tunneling processes are known to be dominating. Excellent agreement is found between experiment and theory over a large range of current, temperature and device structures.
A comprehensive model for the photon number fluctuations and the current noise in quantum cascade lasers is presented. It is shown that the photon intensity noise in quantum cascade lasers exhibits little amplitude squeezing even when noise in the drive current is suppressed below the shot noise value. This is in contrast to interband semiconductor diode lasers in which the laser intensity noise can be squeezed well below the shot noise limit by high impedance suppression of fluctuations in the drive current. The theoretical model presented in this paper self-consistently accounts for the supp…
A Schottky diode integrated into a terahertz quantum cascade laser waveguide couples directly to the internal laser fields. In a multimode laser, the diode response is correlated with both the instantaneous power and the coupling strength to the diode of each lasing mode. Measurements of the rectified response of diodes integrated in two quantum cascade laser cavities at different locations indicate that the relative diode position strongly influences the laser-diode coupling.
We present a method for self-consistently including the optical cavity field into Monte Carlo-based carrier transport simulations. This approach allows for an analysis of the actual lasing operation in quantum cascade lasers, considering effects such as gain saturation and longitudinal mode competition. Simulation results for a terahertz quantum cascade laser are found to be consistent with experiment.
Using the effective mass and rectangular potential approximations, the theory of electron dynamic conductivity is developed for the plane multilayer resonance tunnel structure placed into a constant electric field within the model of open nanosystem, and oscillator forces of quantum transitions within the model of closed nanosystem. For the experimentally produced quantum cascade laser with four-barrier active band of separate cascade, it is proven that just the theory of dynamic conductivity in the model of open cascade most adequately describes the radiation of high frequency electromagnetic…
We report gain calculations for a quantum cascade laser using a fully self-consistent quantum mechanical approach based on the theory of nonequilibrium Green functions. Both the absolute value of the gain as well as the spectral position at threshold are in excellent agreement with experimental findings for T=77 K. The gain strongly decreases with temperature.
We present a viewpoint of the transport process in quantum cascade laser structures in which spatial transport of charge through the structure is a property of coherent quantum-mechanical wavefunctions. In contrast, scattering processes redistribute particles in energy and momentum but do not directly cause spatial motion of charge.
We study the rapid decrease of peak gain in resonant-phonon THz Quantum Cascade Lasers with increasing temperature. The effect of various microscopic scattering processes on the gain profile as a function of temperature is discussed. We argue that increased broadening, primarily due to increased impurity scattering, and not diminishing population inversion, is the main reason for the reduction of peak gain.
In a recent Letter [Appl. Phys. Lett. 82, 1015 (2003)], Williams et al. reported the development of a terahertz quantum cascade laser operating at 3.4 THz or 14.2 meV. We have calculated and analyzed the gain spectra of the quantum cascade structure described in their work, and in addition to gain at the reported lasing energy of ~= 14 meV, we have discovered substantial gain at a much lower energy of around 5 meV or just over 1 THz. This suggests an avenue for the development of a terahertz laser at this lower energy, or of a two-color terahertz laser.
We have investigated the time-resolved vibrational properties of terahertz quantum cascade lasers by means of ultra-fast laser spectroscopy. By the observation of the acoustic folded branches, and by analyzing the involved phonon modes it is possible to extract accurate structural information of these devices, which are essential for their design and performance.
We report on our study of the luminescence spectra of a quantum cascade laser in the presence of an external magnetic field tilted from the direction perpendicular to the electron plane. The effect of the tilted field is to allow novel optical transitions because of the coupling of intersubband-cyclotron energies. We find that by tuning the applied field, one can get optical transitions at different energies that are as sharp as the zero-field transitions.
Silicon-based quantum cascade lasers (QCLs) offer the prospect of integrating coherent THz radiation sources with silicon microelectronics. Theoretical studies have proposed a variety of n-type SiGe-based heterostructures as design candidates, however the optimal material configuration remains unclear. In this work, an optimization algorithm is used to design equivalent THz QCLs in three recently-proposed configurations [(001) Ge/GeSi, (001) Si/SiGe and (111) Si/SiGe], with emission frequencies of 3 and 4 THz. A systematic comparison of the electronic and optical properties is presented. A sem…
We present a comparative analysis of a set of GaAs-based THz quantum cascade lasers, based on longitudinal-optical phonon scattering depopulation, by using an ensemble Monte Carlo simulation, including both carrier-carrier and carrier-phonon scattering. The simulation shows that the parasitic injection into the states below the upper laser level limits the injection efficiency and thus the device performance at the lasing threshold. Additional detrimental effects playing an important role are identified. The simulation results are in reasonable agreement with the experimental findings.
The linewidth in intersubband transitions can be significantly reduced below the sum of the lifetime broadening for the involved states, if the scattering environment is similar for both states. This is studied within a nonequilibrium Green function approach here. We find that the effect is of particular relevance for a recent, relatively low doped, THz quantum cascade laser.
The method of nonequilibrium Greens functions allows for a spatial and energetical resolution of the electron current in Quantum Cascade Lasers. While scattering does not change the spatial position of carriers, the entire spatial evolution of charge can be attributed to coherent transport by complex wave functions. We discuss the hierarchy of transport models and derive the density matrix equations as well as the hopping model starting from the nonequilibrium Greens functions approach.
Resonant phonon depopulation terahertz quantum cascade lasers based on vertical and diagonal lasing transitions are systematically compared using a well established ensemble Monte Carlo approach. The analysis shows that for operating temperatures below 200 K, diagonal designs may offer superior temperature performance at lasing frequencies of about 3.5 THz and above; however, vertical structures are more advantageous for good temperature performance at lower frequencies.
We show that mid infrared transmission spectroscopy of a quantum cascade laser provides clear cut information on changes in charge location at different bias. Theoretical simulations of the evolution of the gain/absorption spectrum for the $λ\sim$ 7.4 $μ$m InGaAs/AlInAs/InP quantum cascade laser have been compared with the experimental findings. Transfer of electrons between the ground states in the active region and the states in the injector goes in hand with a decrease of discrete intersubband absorption peaks and an increase of broad high-energy absorption towards the continuum delocalised…
A quantum cascade laser where the quantum wells in the active regions are replaced by quantum dots with their atom-like discrete energy levels is an interesting system to study novel features in optical spectroscopy. We study structures suitable for diagonal lasing transitions in coupled dots, and vertical lasing transitions in a single dot, in the active regions of the laser device. The luminescence spectra as a function of electron number and dot size show that for diagonal transitions, a significant amount of blue-shift in the emission spectra can be achieved by increasing electron populati…
The luminescence spectra of a quantum cascade laser in a strong magnetic field is influenced significantly by the presence of disorder (charged or neutral) in the system. An externally applied magnetic field parallel to the electron plane causes a red shift of the luminescence peak in the absence of any disorder potential. Our results indicate that the disorder potential tends to cancel that red shift and causes a rapid decrease of the luminescence peak. A similar behavior was observed in a recent experiment on QCL in a parallel magnetic field.
We report three-well, resonant-phonon depopulation terahertz quantum cascade lasers with semi-insulating surface-plasmon waveguides and reduced active region (AR) thicknesses. Devices with thicknesses of 10, 7.5, 6, and 5 μm are compared in terms of threshold current density, maximum operating temperature, output power and AR temperature. Thinner ARs are technologically less demanding for epitaxial growth and result in reduced electrical heating of devices. However, it is found that 7.5-μm-thick devices give the lowest electrical power densities at threshold, as they represent the optimal trad…
We characterized the DC transport response of a diode embedded in a THz quantum cascade laser as the laser current was changed. The overall response is described by parallel contributions from the rectification of the laser field due to the non-linearity of the diode I-V and from thermally activated transport. Sudden jumps in the diode response when the laser changes from single mode to multi-mode operation, with no corresponding jumps in output power, suggest that the coupling between the diode and laser field depends on the spatial distribution of internal fields. The results demonstrate con…
Transport and gain properties of a resonant-phonon terahertz quantum cascade laser are calculated using nonequilibrium Green's functions. Impurity scattering is shown to be responsible for contrasting nonlinear effects in the transport and the gain properties. For typical doping concentrations, the current density is found to be weakly sensitive to the impurity scattering strength. In contrast, the calculated gain is found to be very sensitive to the impurity scattering strength. This difference is attributed to the strong momentum dependence of the long-range coupling to charged impurities. S…
Detailed simulations for Terahertz quantum cascade lasers based on two-well designs are presented. We reproduce the maximal operation temperatures observed and attribute the degradation with temperature to the occupation of parasitic levels and thermal backfilling. Furthermore, we demonstrate that the current injection can be conveniently studied by using EZ states, which combine energy selectivity and spatial localisation. Improving the injection allows to achieve higher maximal operation temperatures around 265 Kelvin.
Quantum cascade lasers (QCLs) are high-power coherent light sources in the midinfrared and terahertz parts of the electromagnetic spectrum. They are devices in which the electronic and lattice systems are far from equilibrium, strongly coupled to one another, and the problem bridges disparate spatial scales. We present our ongoing work on the multiphysics and multiscale simulation of far-from-equilibrium transport of charge and heat in midinfrared QCLs.
A midinfrared quantum cascade laser with high wall-plug efficiency is analyzed by means of an ensemble Monte Carlo method. Both the carrier transport and the cavity field dynamics are included in the simulation, offering a self-consistent approach for analyzing and optimizing the laser operation. It is shown that at low temperatures, photon emission and absorption can govern the carrier transport in such devices. Furthermore, we find that photon-induced scattering can strongly affect the kinetic electron distributions within the subbands. Our results are validated against available experimenta…
Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different THz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of THz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement.
Phase-locking an array of quantum cascade lasers is an effective way to achieve higher output power and beam shaping. In this article, based on Talbot effect, we show a new-type phase-locked array of mid-infrared quantum cascade lasers with an integrated spatial- filtering Talbot cavity. All the arrays show stable in-phase operation from the threshold current to full power current. The beam divergence of the array device is smaller than that of a single-ridge laser. We use the multi-slit Fraunhofer diffraction mode to interpret the far-field radiation profile and give a solution to get better …
Gain in current-driven semiconductor heterostructure devices is calculated within the theory of nonequilibrium Green functions. In order to treat the nonequilibrium distribution self-consistently the full two-time structure of the theory is employed without relying on any sort of Kadanoff-Baym Ansatz. The results are independent of the choice of the electromagnetic field if the variation of the self-energy is taken into account. Excellent quantitative agreement is obtained with the experimental gain spectrum of a quantum cascade laser. Calculations for semiconductor superlattices show that the…
Although most work toward the realization of group IV quantum cascade lasers (QCLs) has focused on valence-band transitions, there are many desirable properties associated with the conduction band. We show that the commonly cited shortcomings of n-type Si/SiGe heterostructures can be overcome by moving to the (111) growth direction. Specifically, a large band offset and low effective mass are achievable and subband degeneracy is preserved. We predict net gain up to lattice temperatures of 90 K in a bound-to-continuum QCL with a double-metal waveguide, and show that a Ge interdiffusion length o…
The gain spectrum of a terahertz quantum cascade laser is analysed by a non equilibrium Green's functions approach. Higher harmonics of the response function were retrievable, providing a way to approach nonlinear phenomena in quantum cascade lasers theoretically. Gain is simulated under operation conditions and results are presented both for linear response and strong laser fields. An iterative way of reconstructing the field strength inside the laser cavity at lasing conditions is described using a measured value of the level of the losses of the studied system. Comparison with recent experi…
Based on an ensemble Monte Carlo analysis, we show that Coulomb interactions play a dominant role in bound-to-continuum terahertz quantum cascade lasers and thus require careful modeling. Coulomb interactions enter our simulation in the form of space charge effects as well as Coulomb scattering events. By comparison to a full many-subband Coulomb screening model, we show that simplified approaches produce considerable deviations for such structures. Also the spin dependence of electron-electron scattering has to be adequately considered. Moreover, we demonstrate that iterative Schrödinger-Pois…
We investigate room temperature lasing of terahertz quantum cascade lasers using quantum dot chains as active material suitable for wireless communication and imaging technologies. Bandstructure calculations for such extended systems of coupled quantum dots are made possible by a novel 'linear combination of quantum dot orbitals'--method, based on single quantum dot wavefunctions. Our results demonstrate strong vertical-emission of coupled quantum dots, reduced phonon coupling and in-plane scattering, enabling room-temperature lasing with significantly reduced threshold current densities.
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 co…
The link between the inversion gain of quantum cascade structures and the Bloch gain in periodic superlattices is presented. The proposed theoretical model based on the density matrix formalism is able to treat the gain mechanism of the Bloch oscillator and Quantum cascade laser on the same footing by taking into account in-plane momentum relaxation. The model predicts a dispersive contribution in addition to the (usual) population-inversion-dependent intersubband gain in quantum cascade structures and - in the absence of inversion - provides the quantum mechanical description for the dispersi…
We investigate the effects of nonequilibrium phonon dynamics on the operation of a GaAs-based midinfrared quantum cascade laser over a range of temperatures (77--300 K) via a coupled ensemble Monte Carlo simulation of electron and optical-phonon systems. Nonequilibrium phonon effects are shown to be important below 200 K. At low temperatures, nonequilibrium phonons enhance injection selectivity and efficiency by drastically increasing the rate of interstage electron scattering from the lowest injector state to the next-stage upper lasing level via optical-phonon absorption. As a result, the cu…
By including elements of the density matrix formalism, the semiclassical ensemble Monte Carlo method for carrier transport is extended to incorporate incoherent tunneling, known to play an important role in quantum cascade lasers (QCLs). In particular, this effect dominates electron transport across thick injection barriers, which are frequently used in terahertz QCL designs. A self-consistent model for quantum mechanical dephasing is implemented, eliminating the need for empirical simulation parameters. Our modeling approach is validated against available experimental data for different types…
Within the model of rectangular potentials and different effective masses of electrons in different elements of plane two-barrier resonance tunnel structure there is developed a theory of spectral parameters of quasi-stationary states and active conductivity for the case of mono-energetic electronic current interacting with electromagnetic field. It is shown that the two-barrier resonance tunnel structure can be utilized as a separate or active element of quantum cascade laser or detector. For the experimentally studied In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As nano-system it is establ…
We have obtained a closed-form expression for the threshold of Risken-Nummedal-Graham-Haken (RNGH) multimode instability in a Fabry-Pérot (FP) cavity quantum cascade laser (QCL). This simple analytical expression is a versatile tool that can easily be applied in practical situations which require analysis of QCL dynamic behavior and estimation of its second threshold. Our model for a FP cavity laser accounts for the carrier coherence grating and carrier population grating as well as their relaxation due to carrier diffusion. In the model, the RNGH instability threshold is analyzed using a seco…
We present a systematic comparison of the results from our non-equilibrium Green's function formalism with a large number of AlGaAs-GaAs terahertz quantum cascade lasers previously published in the literature. Employing identical material and simulation parameters for all samples, we observe that discrepancies between measured and calculated peak currents are similar for samples from a given group. This suggests that the differences between experiment and theory are partly due to a lacking reproducibility for devices fabricated at different laboratories. Varying the interface roughness height …
Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simula…
We present an experimental study of the turn-on delay in pulsed mid-infrared quantum cascade lasers. We report the unexpectedly long delay time depending on the pumping current, which does not agree with conventional theoretical predictions for step-like excitation. Similar behavior has been observed in InP- and InAs-based QCLs emitting near 8$μ$m. Numerical simulations performed using a model based on rate equations for excitation by current pulses with non-zero rise time provide fair agreement with our observations.
We show a phase-locked array of three quantum cascade lasers with an integrated Talbot cavity at one side of the laser array. The coupling scheme is called diffraction coupling. By controlling the length of Talbot to be a quarter of Talbot distance (Zt/4), in-phase mode operation can be selected. The in-phase operation shows great modal stability under different injection currents, from the threshold current to the full power current. The far-field radiation pattern of the in-phase operation contains three lobes, one central maximum lobe and two side lobes. The interval between adjacent lobes …
Quantum Cascade Lasers (QCLs) are generally designed to avoid negative differential conductivity (NDC) in the vicinity of the operation point in order to prevent instabilities. We demonstrate, that the threshold condition is possible under an inhomogeneous distribution of the electric field (domains) and leads to lasing at an operation point with a voltage bias normally attributed to the NDC region. For our example, a Terahertz QCL operating up to the current maximum temperature of 199 K, the theoretical findings agree well with the experimental observations. In particular, we experimentally o…
A density matrix theory of electron transport and optical gain in quantum cascade lasers in an external magnetic field is formulated. Starting from the general quantum kinetic treatment, we describe the intra- and inter-period electron dynamics at the non-Markovian, Markovian and Boltzmann approximation levels. Interactions of electrons with longitudinal optical phonons and classical light field are included in the present description. The non-Markovian calculation for a prototype structure reveals significantly different gain spectra in terms of linewidth and additional polaronic features in …
