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Quantum dots
System of ideal quantum dots with Coulomb interaction
A. M. Mandel^{a}, V. B. Oshurko^{ba}, S. M. Pershin^{b} ^{a} Moscow State Technological University "Stankin"
^{b} Wave Research Center of Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow
Abstract:
The wave functions of singleelectron states localised on a system of singlelevel ideal quantum dots in a semiconductor matrix are constructed. The standard Kane theory, which describes the renormalisation of the effective mass of electrons in bulk III – V semiconductors, is transformed, for the first time as far as we know, for smallsize quantum dots. The renormalised electron mass in a quantum dot depends on its ground state energy, which, in turn, depends on this mass. Thus, a selfconsistent problem is obtained for calculating the electron binding energy. The radius of the Debye screening of the Coulomb interaction in a system of quantum dots is calculated at room temperature. The Coulomb repulsion of electrons localised on dots limits from above the possible number of filled dots. The condition is formulated for the optimal concentration of quantum dots. A classical distribution function for the probability of quantum dot filling is constructed. It is found the state, where electrons fill exactly half the maximum possible number of filled dots, exhibits the minimal energy (and therefore the most stable), the condition being fairly universal. In particular, it can be used to estimate the limiting efficiency of quantumdot diode lasers.
Keywords:
system of singlelevel ideal quantum dots, Coulomb interaction, binding energy, transformation of Kane's theory for small quantum dots, critical size of ideal dots, Debye radius in the system of dots, distribution function over the number of filled dots, condition of optimal filling.
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Quantum Electronics, 2019, 49:5, 505–511
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Received: 21.09.2018 Revised: 21.12.2018
Citation:
A. M. Mandel, V. B. Oshurko, S. M. Pershin, “System of ideal quantum dots with Coulomb interaction”, Kvantovaya Elektronika, 49:5 (2019), 505–511 [Quantum Electron., 49:5 (2019), 505–511]
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http://mi.mathnet.ru/eng/qe17032 http://mi.mathnet.ru/eng/qe/v49/i5/p505
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This publication is cited in the following articles:

A. M. Mandel, V. B. Oshurko, S. M. Pershin, S. G. Veselko, E. E. Karpova, A. A. Scharts, P. V. Aristarkhov, Bull. Lebedev Phys. Inst., 47:10 (2020), 296–299

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