Simplified density-matrix model applied to three-well terahertz quantum cascade lasers

Dupont, Emmanuel; Fathololoumi, Saeed; Liu, H. C.

doi:10.1103/physrevb.81.205311

Cited by 112 publications

(126 citation statements)

References 44 publications

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“…Simultaneously, simulations have been performed for a large variety of samples with different models. These can be based on rate equations for the electron densities, 3,4 Monte-Carlo simulations of the Boltzmann equation for the occupations of the k-states in the individual subbands, [5][6][7][8] density matrix calculations, [9][10][11][12][13] which have been also done k-resolved, 7,14,15 as well as nonequilibrium Green's functions (NEGF). [16][17][18][19][20] While the published results from either scheme typically agree well with experimental data, it is not clear how the choices of parameters (in particular, interface roughness (IFR) distributions and band offsets), specific approximations (such as screening models or various model-specific assumptions as subband temperatures), or model complexity affect the results.…”

Section: Introductionmentioning

confidence: 99%

Simulating terahertz quantum cascade lasers: Trends from samples from different labs

Winge

Franckié

Wacker

2016

Journal of Applied Physics

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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 for different devices, we find that the peak current under lasing operation hardly changes, so that differences in interface quality appear not to be the sole reason for the lacking reproducibility.

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Section: Introductionmentioning

confidence: 99%

Simulating terahertz quantum cascade lasers: Trends from samples from different labs

Winge

Franckié

Wacker

2016

Journal of Applied Physics

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“…Combined with the fact that the optimization parameters are typically trade-offs for one another, the task is very complex. Here, typically simpler rate equation or density matrix models are used in order to more quickly sweep the parameter space [21][22][23] , while more advanced models, such as non-equilibrium Green's functions (NEGF) or Monte-Carlo, are used to validate and analyze the final designs 13,[24][25][26] . In contrast, in this work we will employ an advanced model directly at the optimization stage.…”

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confidence: 99%

Two-well quantum cascade laser optimization by non-equilibrium Green's function modelling

Franckié

Bosco

Beck

et al. 2018

Applied Physics Letters

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We present a two-quantum well THz intersubband laser operating up to 192 K. The structure has been optimized with a non-equilibrium Green's function model. The result of this optimization was confirmed experimentally by growing, processing and measuring a number of proposed designs. At high temperature (T > 200 K), the simulations indicate that lasing fails due to a combination of electron-electron scattering, thermal backfilling, and, most importantly, re-absorption coming from broadened states.Terahertz quantum cascade lasers (QCLs) 1 are interesting candidates for a wide variety of potential applications 2,3 . However, to date, their operation is limited to ∼200 K 4 and the necessity of cryogenic cooling hinders a widespread use of these devices. In the last decade, significant scientific effort has been directed towards identifying the main temperaturedegrading mechanisms 5-8 , as well as finding optimized QCL designs 9-14 . The degrading mechanisms include thermal backfilling 3,15 , thermally activated LO phonon emission [6][7][8]16 , increased broadening [17][18][19] , and carrier leakage into continuum states 20 . When numerically optimizing a design, it is important to take all of these effects into consideration, in order to ensure a close correspondence between the model and the real device. Combined with the fact that the optimization parameters are typically trade-offs for one another, the task is very complex. Here, typically simpler rate equation or density matrix models are used in order to more quickly sweep the parameter space 21-23 , while more advanced models, such as non-equilibrium Green's functions (NEGF) or Monte-Carlo, are used to validate and analyze the final designs 13,[24][25][26] . In contrast, in this work we will employ an advanced model directly at the optimization stage. Specifically, we shall use a NEGF model 27 , capable of accurately simulating experimental devices 13,26,28 and including the most general treatment of scattering, from all relevant processes.The goal of the optimization is to achieve the highest possible operating temperature. Thus, the gain of the active medium should be maximized at high lattice temperature, and simultaneously the external losses minimized. The key figures for gain are inversion, oscillator strength, and line width 29 . These are mainly controlled by the doping density, the energy difference E ex between the lower laser level ll and the extractor state e, and the width of the two barriers: the laser and injection barriers. Population inversion increases with doping, although a too high level promotes detrimental effects, such as electron-electron scattering. E ex , which is chosen to be close to the LO phonon resonance E LO in order to have a short ll lifetime, and the laser frequency ω are mainly determined by the well widths. The laser barrier width determines the oscillator strength, which at the same time affects inversion; a more vertical transition

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“…The pulse is made as strong as possible in order to get a good signal to noise ratio but it is not known how the system dynamics are affected by such a measurement. The simulation of THz QCLs relies on a consistent treatment of tunneling and scattering, either by hybrid density matrix/rate equation schemes [9][10][11][12][13] or more evolved nonequilibrium Green's function (NEGF) theory. [14][15][16][17] Here, we present an extension of our NEGF scheme 18 towards the treatment of high intensities inside the QCL, going beyond linear response to an external electromagnetic field.…”

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confidence: 99%

Nonlinear response of quantum cascade structures

Winge

Lindskog

Wacker

2012

Applied Physics Letters

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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 experimental data from time-domain-spectroscopy indicates that the experimental situation is beyond linear response.Comment: 4 pages, 3 figures included in text, to appear in Applied Physics Letter

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Simplified density-matrix model applied to three-well terahertz quantum cascade lasers

Cited by 112 publications

References 44 publications

Simulating terahertz quantum cascade lasers: Trends from samples from different labs

Simulating terahertz quantum cascade lasers: Trends from samples from different labs

Two-well quantum cascade laser optimization by non-equilibrium Green's function modelling

Nonlinear response of quantum cascade structures

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