Modeling of the Electronic Structure of Semiconductor Nanoparticles

Vasily B. Novozhilov (), Valeria L. Bodneva, Kairat S. Kurmangaleev, Boris V. Lidskii, Vladimir S. Posvyanskii and Leonid I. Trakhtenberg
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Vasily B. Novozhilov: Institute of Sustainable Industries and Liveable Cities, Victoria University, Melbourne, VIC 8001, Australia
Valeria L. Bodneva: N.N. Semenov Federal Research Centre of Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., Building 1, Moscow 119991, Russia
Kairat S. Kurmangaleev: N.N. Semenov Federal Research Centre of Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., Building 1, Moscow 119991, Russia
Boris V. Lidskii: N.N. Semenov Federal Research Centre of Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., Building 1, Moscow 119991, Russia
Vladimir S. Posvyanskii: N.N. Semenov Federal Research Centre of Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., Building 1, Moscow 119991, Russia
Leonid I. Trakhtenberg: N.N. Semenov Federal Research Centre of Chemical Physics, Russian Academy of Sciences, 4 Kosygina St., Building 1, Moscow 119991, Russia

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface of a nanoparticle. The numerical modeling of the sensor effect is carried out in two steps. First, the number of charged oxygen atoms on the surface of the nanoparticle N O − is determined. This value is found by solving a system of nonlinear algebraic equations, where the unknowns are the stationary points of this system describing the processes on the surface of a nanoparticle. The specific form of such equations is determined by the type of nanoparticles and the mechanism of chemical reactions on the surface. The second step is to calculate the electron density inside the nanoparticle ( n c ( r ) ) , which gives the minimum free energy. Mathematically, this second step reduces to solving a boundary value problem for a nonlinear integro-differential equation. The calculation results are compared with experimental data on the sensor effect.

Keywords: sensors; conduction; calculus of variations; extremals; boundary value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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