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

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.243097

Keywords:

asymptotic series, boundary layer correction, conformal mappings, singularity, electron-hole plasma, p-i-n-structure

Abstract

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

Author Biographies

Andrii Bomba, National University of Water and Environmental Engineering

Doctor of Technical Sciences, Professor

Department of Computer Science and Applied Mathematics

Igor Moroz, National University of Water and Environmental Engineering

PhD, Associate Professor

Department of Computer Science and Applied Mathematics

Mykhailo Boichura, National University of Water and Environmental Engineering

PhD

Research Department

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Published

2021-10-31

How to Cite

Bomba, A., Moroz, I., & Boichura, M. (2021). 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. Eastern-European Journal of Enterprise Technologies, 5(5 (113), 51–61. https://doi.org/10.15587/1729-4061.2021.243097

Issue

Vol. 5 No. 5 (113) (2021): Applied physics

Section

Applied physics

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Copyright (c) 2021 Andrii Bomba, Igor Moroz, Mykhailo Boichura

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