Monte-Carlo-based spectral gain analysis for THz quantum cascade lasers
📝 Abstract
Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different THz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of THz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement.
💡 Analysis
Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different THz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of THz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement.
📄 Content
Monte-Carlo-based spectral gain analysis for THz quantum cascade lasers
Christian Jirauschek1,2,a) and Paolo Lugli2
1Emmy Noether Research Group “Modeling of Quantum Cascade Devices“, TU München, Arcisstraße 21, D-80333 München, Germany 2Institute for Nanoelectronics, TU München, Arcisstraße 21, D-80333 München, Germany a)Author to whom correspondence should be addressed. Electronic mail: jirauschek@tum.de
(Dated: 15 June 2011, published as J. Appl. Phys. 105, 123102 (2009))
Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different THz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of THz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement.
I. INTRODUCTION
The quantum cascade laser (QCL) has become an important source of coherent radiation in the mid-infrared, and its frequency range has been extended to the THz region.1 However, especially in the THz regime the functionality of QCLs is still quite limited, especially considering the temperature performance. Further improvement requires a thorough understanding of the carrier transport processes in the device, as provided by detailed simulations. Self-consistent Monte Carlo (MC) carrier transport simulations are a well- established tool to analyze and optimize QCL structures.2-11 Usually such simulations focus on transport properties and level occupations. However, the optical gain achieved in the structure not only depends on the population inversion between upper and lower laser level and the corresponding oscillator strength, but is also affected by the linewidth of the lasing transition. In semiclassical approaches like three-dimensional (3D) MC simulations or rate equation descriptions, the lifetime broadening due to carrier transitions between the different quantum states can be self-consistently evaluated, while collisional broadening due to pure dephasing and cancellation effects due to nondiagonal dephasing contributions can only be considered in fully quantum mechanical approaches.12-16 On the other hand, the MC approach allows for an inclusion of intercarrier scattering (beyond the mean-field approximation), which has up to now not been achieved for comparable quantum mechanical simulations of QCLs,12-16 due to the significantly increased computational complexity as compared to single-electron processes like electron-impurity interaction. Electron-electron scattering dominates the intrasubband dynamics and thus greatly influences the kinetic electron distributions within the subbands, and can also strongly affect the intersubband transport, especially for closely spaced energy levels, low temperatures or high doping densities.17 Besides, due to the relative computational efficiency of the MC approach, also other effects can be fully considered where often approximations have to be used in quantum mechanical simulations, such as neglecting the momentum dependence of scattering mechanisms.12 Typically, in 3D MC simulations the spectral gain is evaluated in a phenomenological way, using parameters like the experimentally measured spontaneous emission linewidth.5,9 This prevents self-consistent gain modeling which can be crucial for analyzing and understanding experimental results. In contrast, in quantum mechanical simulations of QCLs like the nonequilibrium Green’s functions (NEGF) or density matrix approach, gain is routinely computed in a self- consistent manner.12-16 In this context, it is desirable to combine the strengths of fully three-dimensional MC simulations, like the inclusion of electron-electron scattering, with a self-consistent gain analysis. One example is the analysis of the temperature performance of THz structures, where not only the reduced inversion,11 but also the increased broadening of the gain profile plays a role.15 Here, MC simulations can bring valuable insights, e.g., by evaluating the role of all important scattering mechanisms, including electron- electron interaction. Also, the relative computational efficiency as compared to NEGF simulations allows us to evaluate a larger parameter field, or to refrain from approximations that are often used in quantum mechanical simulations. For example, the momentum dependence of the scattering matrix elements plays a major role especially for high operating temperatures, an effect often neglected in NEGF simulations to keep the computational effort reasonable.12 We self-consistently extract the gain spectra of bound- to-continuum and resonant phonon depopulation THz QCLs
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