Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green's functions

Abstract

We study the operation of an 8.5 µm quantum cascade laser based on GaInAs/AlInAs lattice matched to InP using three different simulation models based on density matrix (DM) and nonequilibrium Green's function (NEGF) formulations. The latter advanced scheme serves as a validation for the simpler DM schemes and, at the same time, provides additional insight, such as the temperatures of the sub-band carrier distributions. We find that for the particular quantum cascade laser studied here, the behavior is well described by simple quantum mechanical estimates based on Fermi's golden rule. As a consequence, the DM model, which includes second order currents, agrees well with the NEGF results. Both these simulations are in accordance with previously reported data and a second regrown device

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

“…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.…”

“…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.…”

Monte Carlo modeling applied to studies of quantum cascade lasers

“…Models entirely based on density matrix approach have been successfully used by various authors (Willenberg et al 2003;Kumar and Hu 2009;Weber et al 2009;Dupont et al 2010;Terazzi and Faist 2010;Lindskog et al 2014). Their main advantage, when compared to MC simulations, is proper accounting of electron resonant tunneling through quantum barriers and dephasing processes.…”

Quantum Transport Simulation of High-Power 4.6-μm Quantum Cascade Lasers

“…Electron transport in GaAs-based quantum cascade lasers in both mid-IR and THz regimes has been successfully simulated via semiclassical (rate equations [19][20][21] and Monte Carlo [22][23][24][25]) and quantum techniques (density matrix [26][27][28][29][30], nonequilibrium Green's functions (NEGF) [31], and lately Wigner functions [32]). InP-based mid-IR QCLs have been addressed via semiclassical [33] and quantum transport approaches (8.5-µm [34] and 4.6-µm [35,36] devices). Short-wavelength structures [8] have very thin wells and barriers, so coherent transport in them has pronounced coherent features, which cannot be addressed semiclassically.…”

“…Density-matrix approaches offer a good compromise: they have considerably lower computational overhead than NEGF but are still capable of describing coherent-transport features. Unfortunately, density-matrix techniques commonly employ phenomenological dephasing times [27,30,34,37].…”