Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings

The results of mathematical modeling of stationary physical processes in the electron-hole plasma of the active region (i-region) of integral p-i-n-structures are presented. The mathematical model is written in the framework of the hydrodynamic thermal approximation, taking into account the phenomen...

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Autores principales:	Andrii Bomba, Igor Moroz, Mykhailo Boichura
Formato:	article
Lenguaje:	EN RU UK
Publicado:	PC Technology Center 2021
Materias:	asymptotic series boundary layer correction conformal mappings singularity electron-hole plasma p-i-n-structure Technology (General) T1-995 Industry HD2321-4730.9
Acceso en línea:	https://doaj.org/article/65a3d31073e34301b534fff37530d67a
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spelling	oai:doaj.org-article:65a3d31073e34301b534fff37530d67a2021-11-08T08:04:06ZConstructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings1729-37741729-406110.15587/1729-4061.2021.243097https://doaj.org/article/65a3d31073e34301b534fff37530d67a2021-10-01T00:00:00Zhttp://journals.uran.ua/eejet/article/view/243097https://doaj.org/toc/1729-3774https://doaj.org/toc/1729-4061The results of mathematical modeling of stationary physical processes in the electron-hole plasma of the active region (i-region) of integral p-i-n-structures are presented. The mathematical model is written in the framework of the hydrodynamic thermal approximation, taking into account the phenomenological data on the effect on the dynamic characteristics of charge carriers of heating of the electron-hole plasma as a result of the release of Joule heat in the volume of the i-th region and the release of recombination energy. The model is based on a nonlinear boundary value problem on a given spatial domain with curvilinear sections of the boundary for the system of equations for the continuity of the current of charge carriers, Poisson, and thermal conductivity. The statement of the problem contains a naturally formed small parameter, which made it possible to use asymptotic methods for its analytical-numerical solution. A model nonlinear boundary value problem with a small parameter is reduced to a sequence of linear boundary value problems by the methods of perturbation theory, and the physical domain of the problem with curvilinear sections of the boundary is reduced to the canonical form by the method of conformal mappings. Stationary distributions of charge carrier concentrations and the corresponding temperature field in the active region of p-i-n-structures are obtained in the form of asymptotic series in powers of a small parameter. The process of refining solutions is iterative, with the alternate fixation of unknown tasks at different stages of the iterative process. The asymptotic series describing the behavior of the plasma concentration and potential in the region under study, in contrast to the classical ones, contain boundary layer corrections. It was found that boundary functions play a key role in describing the electrostatic plasma field. The proposed approach to solving the corresponding nonlinear problem can significantly save computing resourcesAndrii BombaIgor MorozMykhailo BoichuraPC Technology Centerarticleasymptotic seriesboundary layer correctionconformal mappingssingularityelectron-hole plasmap-i-n-structureTechnology (General)T1-995IndustryHD2321-4730.9ENRUUKEastern-European Journal of Enterprise Technologies, Vol 5, Iss 5 (113), Pp 51-61 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU UK
topic	asymptotic series boundary layer correction conformal mappings singularity electron-hole plasma p-i-n-structure Technology (General) T1-995 Industry HD2321-4730.9
spellingShingle	asymptotic series boundary layer correction conformal mappings singularity electron-hole plasma p-i-n-structure Technology (General) T1-995 Industry HD2321-4730.9 Andrii Bomba Igor Moroz Mykhailo Boichura Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
description	The results of mathematical modeling of stationary physical processes in the electron-hole plasma of the active region (i-region) of integral p-i-n-structures are presented. The mathematical model is written in the framework of the hydrodynamic thermal approximation, taking into account the phenomenological data on the effect on the dynamic characteristics of charge carriers of heating of the electron-hole plasma as a result of the release of Joule heat in the volume of the i-th region and the release of recombination energy. The model is based on a nonlinear boundary value problem on a given spatial domain with curvilinear sections of the boundary for the system of equations for the continuity of the current of charge carriers, Poisson, and thermal conductivity. The statement of the problem contains a naturally formed small parameter, which made it possible to use asymptotic methods for its analytical-numerical solution. A model nonlinear boundary value problem with a small parameter is reduced to a sequence of linear boundary value problems by the methods of perturbation theory, and the physical domain of the problem with curvilinear sections of the boundary is reduced to the canonical form by the method of conformal mappings. Stationary distributions of charge carrier concentrations and the corresponding temperature field in the active region of p-i-n-structures are obtained in the form of asymptotic series in powers of a small parameter. The process of refining solutions is iterative, with the alternate fixation of unknown tasks at different stages of the iterative process. The asymptotic series describing the behavior of the plasma concentration and potential in the region under study, in contrast to the classical ones, contain boundary layer corrections. It was found that boundary functions play a key role in describing the electrostatic plasma field. The proposed approach to solving the corresponding nonlinear problem can significantly save computing resources
format	article
author	Andrii Bomba Igor Moroz Mykhailo Boichura
author_facet	Andrii Bomba Igor Moroz Mykhailo Boichura
author_sort	Andrii Bomba
title	Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
title_short	Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
title_full	Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
title_fullStr	Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
title_full_unstemmed	Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
title_sort	constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings
publisher	PC Technology Center
publishDate	2021
url	https://doaj.org/article/65a3d31073e34301b534fff37530d67a
work_keys_str_mv	AT andriibomba constructingandanalyzingmathematicalmodelofplasmacharacteristicsintheactiveregionofintegratedpinstructuresbythemethodsofperturbationtheoryandconformalmappings AT igormoroz constructingandanalyzingmathematicalmodelofplasmacharacteristicsintheactiveregionofintegratedpinstructuresbythemethodsofperturbationtheoryandconformalmappings AT mykhailoboichura constructingandanalyzingmathematicalmodelofplasmacharacteristicsintheactiveregionofintegratedpinstructuresbythemethodsofperturbationtheoryandconformalmappings
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Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings

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