Regardless of all the success of Mid Infrared Quantum Cascade Lasers (QCLs), they still do not operate at room temperature in the THz range. The main temperature degrading mechanism for THz QCLs is not known in time of writing this abstract and it is still a topic of debate by the community [S. Khanal et al, J. Opt. 16 094001, 2014]. This is a challenge to theory and it is crucial to treat all possible scattering channels with the same mathematical footing. A summary of different methods for simulating these structures is found in [C. Jirauschek et al, Appl. Phys. Rev. 1 011307, 2014]. In this work we include and study the effects of electron-electron scattering via the Single Plasmon Pole Approximation (SPPA). In this approximation we capture both the static limit as well as dynamic effects. This gives an energy dependent (non-local in time) interaction beyond the Hartree-Fock approximation. This has been studied in a similar model with promising results [T. Schmielau and M.F. Pereira, Appl. Phys. Lett. 95 231111, 2009], and with this work we want to adapt the idea into the model described in Ref. [A. Wacker et a, IEEE Journal of Sel. Top. in Quantum Electron.,19 1200611, 2013]. We start by summarizing the theory underlying the SPPA and we show how it is implemented in the context of our formalism, by showing good agreement with the results for a four well quantum cascade laser [M. Amanti et al, New J. Phys. 11 125022, 2009].
David O. Winge, Martin Franckie, Claudio Verozzi, Andreas Wacker, and Mauro F. Pereira, "A simple approach for electron-electron scattering in nonequilibrium Green's function simulations
(Conference Presentation)," Proc. SPIE 9934, Terahertz Emitters, Receivers, and Applications VII, 99340B (Presented at SPIE Nanoscience + Engineering: August 28, 2016; Published: 3 November 2016); https://doi.org/10.1117/12.2238613.5167075329001.
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