Robust Density Matrix Simulation of Terahertz Quantum Cascade Lasers

Abstract

A common setback to electron transport models for quantum cascade laser active regions is the inability to freely simulate widely varying designs. One solution to this problem is to use a density matrix formalism with a generalized treatment of scattering, wherein the well-defined energy eigenbasis is used, and the relative simplicity of the density matrix can be taken advantage of for rapid simulations. We have developed such a model from first principles in the past, and now built a simulator for terahertz quantum cascade lasers that calculates a fully selfconsistent solution to the coupled problem of bandstructure, lasing field strength, and space charge. This level of depth enables us to examine the model's performance across much of the design space and operating temperatures, for which we find generally good agreement. Areas for future improvement of the model are discussed, particularly the treatment of electron-electron scattering and continuum leakage. The model also enables us to make qualitative insights into the microscopic workings of the active regions, such as the non-equilibrium subband distributions and their response to the optical field, and the possibility for using two sequential optical transitions.

Broadband continuous single-mode tuning of a short-cavity quantum-cascade VECSEL

“…2h); the two modes are not observed to lase simultaneously. Such behavior is consistent with the Stark shift of intersubband transitions with applied field and/or the contribution of multiple intersubband transitions to the gain spectra for this active material 31 . Neither the length of the external cavity, nor the relative position of the output coupler can be measured directly with the equipment available, but this information can be inferred from the observed FSR at the edges of the tuning range.…”

Prospects of temperature performance enhancement through higher resonant phonon transition designs in GaAs-based terahertz quantum-cascade lasers

“…In previous work [42] we demonstrated the efficiency of DM model by simulating several million devices. These simulations relied on the capability of our [31,35] and similar [37] models to predict the cut-off temperature of different designs for any number of states per module.…”

“…We employ scattering mechanism calculation that is described in detail in [39] we use equithermal subband approximation for solving the kinetic balance equation and obtaining the electron temperature. This approach [30,44] transforms the kinetic balance equation into a minimization problem with one unknown, rather than the nonlinear system [37,45] with subband temperatures as the unknowns. Therefore our model consists of iterative algorithm (the Schrödinger-Poission solver) nested within the minimization algorithm for determination of electron temperature.…”

“…In terms of transport models [29], the semi-classical rate-equation (RE) models [30] neglect coherence effects and quantum mechanical dephasing and may generate non-physical output [31], while quantum models as Wigner function [32] and non-equilibrium Green's function approaches [33,34], although most general, suffer from very high computational cost. The density matrix (DM) models [31,[35][36][37][38] offer the compromise with moderate computational requirements that provide reasonable description of THz QCL operation [37].…”

“…These scattering mechanisms are treated through the perturbation theory via Fermi-golden rule [39]. The robustness of similar model is discussed in [37], however here we focus on its ability of predicting cut-off temperature reliably and discuss devices for high temperature performance.…”