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Microscopic theory of hot-carrier relaxation in semiconductor-based quantum-cascade lasers
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6.The basic idea is to identify a three-level quantum structure: Carriers are injected into the upper level (level three) which is “metastable”, i.e., weakly coupled to the lower levels; in contrast, carriers in the intermediate level (level two) can relax very fast into the lowest level (level one). As a result, we have , thus realizing the desired intersubband lasing between levels three and two
7.C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulations (Springer, Wien, 1989).
8.This is based on a time-step separation between injection/loss and scattering contributions [see Eq. (2)] similar to the generalized MC technique used for the analysis of coherent vs incoherent phenomena in photoexcited semiconductors [T. Kuhn and F. Rossi, Phys. Rev. Lett. 69, 977 (1992);
8.T. Kuhn and F. Rossi, Phys. Rev. B 46, 7496 (1992)].
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10.For such GaAs-based MQW structure the carrier injection has been modeled in terms of a 3D Fermi–Dirac velocity distribution into level three only [see Eq. (2)] while for the sake of simplicity a k-independent loss function has been considered. In our simulation, carriers are injected into level three and extracted from level one with best efficiency. In real structures this injection/loss process strongly depends on the operative conditions (mainly current and temperature) of the device in a nontrivial way. In the present scheme, however, a phenomenological modeling of this dependence would in any case be questionable.
11.Note the different time scales in Figs. 2(a) and 2(b) which correspond to the different values of the escape time .
12.As discussed in Ref. 5, carrier-optical phonon scattering depends strongly on the in-plane momentum transfer.
13.Contrary to interband gain spectra, we deal with very sharp peaks, whose line width is not affected by in-plane parabolic dispersion.
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