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

Abstract

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

Thermoelectrically cooled THz quantum cascade laser operating up to 210 K

“…The discrepancy between the optimized (nominal) structure and the best (3.5% thinner) structure (which is also better in the NEGF model under a detailed analysis) can be explained by the restrictions imposed to the optimization, since the best structure operates at a higher bias (56 mV/period) and photon energy (16.5 meV). In accordance with previous results 22 , including a rudimentary form of electron-electron scattering 29 in the model (not shown) the current density changes negligibly while the gain is almost halved and red shifted by 1 meV at 200 K.We also find that the temperature degradation of the presented design is dominated by level broadening. 22 Laser spectra with the device operating on a Peltier cooler were performed using a commercial FTIR (Bruker Vertex 80V) equipped with a DTGS room temperature detector, making such setup fully cryogenic free.…”

“…In accordance with previous results 22 , including a rudimentary form of electron-electron scattering 29 in the model (not shown) the current density changes negligibly while the gain is almost halved and red shifted by 1 meV at 200 K.We also find that the temperature degradation of the presented design is dominated by level broadening. 22 Laser spectra with the device operating on a Peltier cooler were performed using a commercial FTIR (Bruker Vertex 80V) equipped with a DTGS room temperature detector, making such setup fully cryogenic free. Spectra measured at different temperatures with a resolution of 0.2 cm −1 are reported in Fig.3(a).…”

“…The scattering assisted (SA) injection design 15 , also with 4 active states per period, achieves similar performance. The minimum number of active states is three, limited by the electrical stability of the laser 11,16 , and has been realized in two-quantum well designs 17,20,21 with close-torecord temperature performance achieved recently 22,23 . In fact, one might see the two quantum well active region as the structure closest to the original proposal from Kazarinov and Suris 24 which satisfies the electrical stability condition.…”

“…Nonequilibrium Green's function (NEGF) modeling has proven to be a powerful tool for optimizing THz QCL designs 22 . Owing to the significant computation times that come with such a complex model, we have performed a systematic optimization using the NEGF model of Ref.…”

“…We optimized the maximum gain at a lattice temperature of 300 K, varying all four layers of the two-well design in a region around the best one from Ref. 22. In order to keep a manageable computing time, we limited the optimization to a photon energy of ω = 16 meV and a bias of 52.5 mV/period (encompassing one LO phonon and one photon emission per period).…”