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论文范文
1. Introduction Capturing and subsequent relaxation of hot carriers (quasi-electrons and holes) in nanoscale QD are of central importance for practical applications of QD systems, for example, in lasers [1] single photon emitters [2] and photodetectors with unique properties [3, 4]. The discussion of the corresponding rate is controversial. It is long known that a singular spectrum in QD inhibits incoherent emission of phonons suppressing the most effective relaxation mechanism [5], so the term phonon bottleneck was coined. Indeed, experiments [6, 7] demonstrate a rapid enhancement of the relaxation rate when interlevel spacing coincides with phonon energy. However, in many experiments the bottleneck did not reveal itself and the relaxation rate was comparable or even faster than provided by phonons in bulk systems [8–15] possibly indicating the role of the continuous spectrum [16–19]. Further studies lead to a conclusion that the processes of capturing and relaxation can be separated and that the relaxation is likely to be defined by different mechanisms in specific situations for both capture and relaxation [13, 18, 20, 21]. Several relaxation scenarios were proposed to explain these experimental results: phonon-assisted tunnelling to impurity states [22], decay of the LO phonons [23], and several Auger-like mechanisms which included particle collisions [24], QD coupling with the WL plasma excitations [25], phonon-assisted intradot Auger interactions [26], and Auger interactions between excitons in the dot and in a localized state of the wetting layer [27]. Experimentally observed dependence of the relaxation rate on the number of created excitons prompted the conclusion that Auger-like processes are likely to play a role when exciton density is cm−2, while other mechanisms are dominant at smaller density [13, 20, 28]. Calculations of the rate due to WL carrier collisions [24, 29, 30] and plasma excitations [25] demonstrated that these mechanisms become important at cm−2 leaving the phonon-assisted intradot Auger interaction mechanism [26] as the likely candidate to explain the experimentally observed relaxation at lower densities [13]. However, as we show below, the Coulomb interaction between delocalized WL and trapped carriers can provide an efficient relaxation mechanism yielding a high relaxation rate even for as low as cm−2 density when the resonant scattering of the WL carriers is considered. This mechanism is general and could be applied to describe relaxation to deep states in a general gaseous system. Here we apply it to the QD systems. In the discussion we calculate the rate for two models of the confining potential: a rectangular model for which analytical results are obtained and a parabolic potential for which we do numerical simulations. Qualitative agreement between the two models is demonstrated, showing the results are not very sensitive to details of the chosen model. By substituting standard parameters for the InGaAs dot systems we obtain relaxation rate which agrees with experiments. 2. Relaxation Rate Scattering of delocalized WL carriers induces transitions of the trapped carrier between the QD states leading to relaxation in the system the rate of which is obtained from the scattering cross-section as 
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