Nonequilibrium Green’s Function Model for Simulation of Quantum Cascade Laser Devices Under Operating Conditions

Wacker, Andreas; Lindskog, M.; Winge, David O.

doi:10.1109/jstqe.2013.2239613

Cited by 96 publications

(87 citation statements)

References 52 publications

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“…Therefore, we performed simulations with our NEGF scheme 21 for a wide range of different published THz QCLs using precisely the same parameters and model approach and document all results in this paper. This allows to monitor the quality of our simulation scheme.…”

Section: Introductionmentioning

confidence: 78%

“…30 In their complete theoretical formulation, the self energies of the NEGF models are functions of both momentum and energy, but in our implementation they are effectively treated as only energy dependent. This is done by evaluating the scattering matrix elements at a set of representative momentum transfers 21 and reduces the computational effort to an accessible level. Throughout this work, we use the typical momentum transfers k 0 equivalent to E 0 k ¼ 6:3 meV for intra-subband scattering at 77 K lattice temperature.…”

Section: Model and Estimatesmentioning

confidence: 99%

“…The second typical energy E 0 k 0 ¼ E 0 k þ DE is then chosen to reflect the level difference DE as discussed in Ref. 21.…”

Section: Appendix A: Asymptotic Behavior Of the Self-energiesmentioning

confidence: 99%

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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: 78%

Section: Model and Estimatesmentioning

confidence: 99%

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

Winge

Franckié

Wacker

2016

Journal of Applied Physics

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“…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.…”

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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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“…35,36 The factor k in the summation, effective for non-nearest-neighbour scattering, originates from the scatterings from any QCL period left of the central period into any period right of it, or vice versa. Once again, we introduce the "tight-binding" approximation assuming that only the nearest neighbours interact, and set P ¼ 2.…”

Section: B the Self-consistent Rate Equation Modelmentioning

confidence: 99%

Genetic algorithm applied to the optimization of quantum cascade lasers with second harmonic generation

Gajic

Radovanović

Milanović

et al. 2014

Journal of Applied Physics

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A computational model for the optimization of the second order optical nonlinearities in GaInAs/AlInAs quantum cascade laser structures is presented. The set of structure parameters that lead to improved device performance was obtained through the implementation of the Genetic Algorithm. In the following step, the linear and second harmonic generation power were calculated by self-consistently solving the system of rate equations for carriers and photons. This rate equation system included both stimulated and simultaneous double photon absorption processes that occur between the levels relevant for second harmonic generation, and material-dependent effective mass, as well as band nonparabolicity, were taken into account. The developed method is general, in the sense that it can be applied to any higher order effect, which requires the photon density equation to be included. Specifically, we have addressed the optimization of the active region of a double quantum well In 0.53 Ga 0.47 As/Al 0.48 In 0.52 As structure and presented its output characteristics. V C 2014 AIP Publishing LLC. [http://dx

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Nonequilibrium Green’s Function Model for Simulation of Quantum Cascade Laser Devices Under Operating Conditions

Cited by 96 publications

References 52 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

Genetic algorithm applied to the optimization of quantum cascade lasers with second harmonic generation

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