scholarly journals 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

2021 ◽  
Vol 5 (5 (113)) ◽  
pp. 51-61
Author(s):  
Andrii Bomba ◽  
Igor Moroz ◽  
Mykhailo Boichura
Keyword(s):  
Mathematical Model ◽  
Perturbation Theory ◽  
Active Region ◽  
Small Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Asymptotic Series ◽  
Charge Carriers ◽  
Electron Hole ◽  
Electron Hole Plasma

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

scholarly journals THE DIFFUSION-DRIFT PROCESS WITH ACCOUNT HEATING AND RECOMBINATION IN THE p-i-n DIODES ACTIVE REGION MATHEMATICAL MODELING BY THE PERTURBATION THEORY METHODS

2021 ◽  
pp. 29-35
Author(s):  
A. Ya. Bomba ◽  
I. P. Moroz
Keyword(s):  
Plasma Concentration ◽  
Active Region ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Concentration Distribution ◽  
Boundary Value ◽  
Charge Carriers ◽  
Electron Hole ◽  
Electron Hole Plasma

With prolonged transmission of an electric current through the semiconductor devices, in a particular p-i-n diodes, an electron-hole plasma of their active region is heated. This paper presents the theoretical studies results of the plasma heating effect by the Joule heat release in the p-i-n diode volume and the charge carriers recombination energy release on the plasma concentration distribution in the p-i-n diodes active region. The mathematical model is proposed for predicting the electron-hole plasma stationary concentration distribution and the temperature field in the i-region of the bulk p-i-n diodes in the form of a nonlinear boundary value problem in a given area for the equations system, which consist of the charge carrier current continuity equations, the Poisson and the thermal conductivity. It is shown that the differential equations of the model contain a small parameter in such a way that the Poisson equation is singularly perturbed and the heat conduction equation is regularly perturbed. An approximate solution of the problem posed is obtained in the form of the corresponding asymptotic series in powers of the small parameter. The asymptotic serieses, which describes the behavior of the plasma concentration and potential in the investigated region, containing near-boundary corrections to ensure the fulfillment of the boundary conditions. The terms of these series are found as a result of solving a sequence of boundary value problems, obtained as a result of splitting the original problem, for systems of linear differential equations. The boundary value problem for a nonlinear heat equation is reduced to a sequence of problems for the corresponding linear inhomogeneous equations. The process of refining solutions is iterative. The stabilization of the process is ensured by the existence of negative feedback in the system (as the temperature rises, the mobility of charge carriers decreases).

scholarly journals THE OPTIMIZATION OF THE SHAPE AND SIZE OF THE INJECTION CONTACTS OF THE INTEGRATED P-I-N-STRUCTURES ON THE BASE OF USING THE CONFORMAL MAPPING METHOD

2021 ◽  
Vol 1 (1) ◽  
pp. 14-28
Author(s):  
A. Ya. Bomba ◽  
I. P. Moroz ◽  
M. V. Boichura
Keyword(s):  
Mathematical Model ◽  
Active Region ◽  
Conformal Mapping ◽  
Mapping Method ◽  
Internal Boundary ◽  
Electron Hole ◽  
Hole Plasma ◽  
Conformal Mapping Method ◽  
Electron Hole Plasma ◽  
Control Devices

Context. P-i-n-diodes are widely used in a microwave technology to control the electromagnetic field. The field is controlled by the formation of an electron-hole plasma in the region of an intrinsic semiconductor (i-region) under the influence of a control current. The development of control devices on p-i-n-diodes has led to the emergence of integral p-i-n-structures of various types, the characteristics of which (for example, switching speed, switched power level, etc.) exceed the similar characteristics of volume diodes. The properties of p-i-n-structures are determined by a number of processes: the diffusion-drift charge transfer process, the recombination-generation, thermal, injection, and the so on. Obviously, these processes should be taken into account (are displayed) in the mathematical model of the computer-aided design system for control devices of a microwave systems. Integrated process accounting leads to the formulation of complex tasks. One of them is the task of optimizing the shape, geometric dimensions and placement of the injected contacts (an active region). Objective. The goal of the work is the development of a mathematical model and the corresponding software of the process of a microwave waves interaction with electron-hole plasma in an active region of the surface-oriented integral p-i-n-structures with ribbon-type freeform contacts to optimize an active region shape and its geometric dimensions. Method. The main idea of the developed algorithm is to use the conformal mapping method to bring the physical domain of the problem to canonical form, followed by solving internal boundary value problems in this area for the ambipolar diffusion equation and the wave equation using numerical-analytical methods (the finite difference method; partial domains method using projection boundary conditions similar to the Galerkin method). The optimization algorithm is based on a phased solution of the following problems (the shape and geometric dimensions of the active region are specified at each stage): a computational grid of nodes for the physical regions of the problem is being found, in an active region the carriers concentration distribution is being determined and the energy transmitted coefficient in the system under study is being calculated, which is used in the proposed optimization functional. The extreme values of the functional are found by the uniform search method. Results. The proposed mathematical model and the corresponding algorithm for optimizing the shape and geometric dimensions of the active region (i-region) of integrated surface-oriented p-i-n-structures expands the tool base for the design of semiconductor circuits of microwave frequencies (for example, similar to CST MICROWAVE STUDIO). Conclusions. An algorithm has been developed to optimize the shape and geometrical dimensions of the active region of integrated surface-oriented p-i-n-structures with in-depth contacts intended for switching millimeter-wave electromagnetic signals. The universality of the algorithm is ensured by applying the method of conformal transformations of spatial domains. The example of the application of the proposed algorithm to search for the optimal sizes of wedge-shaped (in cross-section) contacts of silicon structures is considered.

scholarly journals Quantum many-body effects on Rydberg excitons in cuprous oxide

2021 ◽  
Author(s):  
D. Semkat ◽  
H. Fehske ◽  
H. Stolz
Keyword(s):  
Perturbation Theory ◽  
Oscillator Strength ◽  
Cuprous Oxide ◽  
Many Body ◽  
Electron Hole ◽  
First Order ◽  
Electron Hole Plasma ◽  
Plasma Line ◽  
Many Body Effects ◽  
First Order Perturbation

AbstractWe investigate quantum many-body effects on Rydberg excitons in cuprous oxide induced by the surrounding electron-hole plasma. Line shifts and widths are calculated by full diagonalisation of the plasma Hamiltonian and compared to results in first order perturbation theory, and the oscillator strength of the exciton lines is analysed.

Interface Dynamics of Melt Instabilities on Semiconductor Surface

2007 ◽  
Vol 129 ◽  
pp. 137-143
Author(s):  
Bogdan Datsko ◽  
Vitaliy Meleshko ◽  
Zbigniew Świątek ◽  
Ivan Mohylyak ◽  
Lidia Lityńska-Dobrzyńska ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Computer Simulation ◽  
Threshold Power ◽  
Semiconductor Surface ◽  
Surface Dynamics ◽  
Electron Hole ◽  
Interface Dynamics ◽  
Electron Hole Plasma ◽  
Surface Patterns

At uniform excitation of semiconductors by laser radiation with pre-threshold power, locally melted regions are formed on irradiated surfaces. This is induced by thermo diffusive instability of a distribution of uniformly generated electron-hole plasma. The shapes of locally melted regions give rise to a great variety of interesting surface patterns. A mathematical model of the surface dynamics, when the instability of the melt front arises along a chosen wave vector, is proposed. The results of computer simulation of interface dynamics of solitary melted region are compared with experimental data.

scholarly journals On a nonlinear boundary value problem involving a small parameter

1962 ◽  
Vol 2 (4) ◽  
pp. 425-439 ◽  
Author(s):  
A. Erdéyi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Small Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Boundary Value Problem ◽  
Image Position

In this paper we shall discuss the boundary value problem consisting of the nonlinear ordinary differential equation of the second order, and the boundary conditions.

scholarly journals Сверхбыстрая динамика электронно-дырочной плазмы в полупроводниковых нитевидных нанокристаллах -=SUP=-*-=/SUP=-

2018 ◽  
Vol 52 (1) ◽  
pp. 23
Author(s):  
В.Н. Трухин ◽  
А.Д. Буравлев ◽  
И.А. Мустафин ◽  
Г.Э. Цырлин ◽  
J.P. Kakko ◽  
...  
Keyword(s):  
Vapor Phase ◽  
Temporal Dynamics ◽  
Semiconductor Nanowires ◽  
Charge Carriers ◽  
Thz Radiation ◽  
Electron Hole ◽  
Hole Plasma ◽  
Organic Vapor ◽  
Electron Hole Plasma ◽  
Metal Organic

AbstractExperimental results obtained in a study of the effect of electron–hole plasma on the generation of terahertz (THz) radiation in semiconductor nanowires grown by metal-organic vapor-phase epitaxy (MOVPE) are presented. It is shown that the temporal dynamics of photoexcited charge carriers in semiconductor nanowires is determined by the transport of carriers, both electrons and holes, and by the time of capture of electrons and holes at surface levels.

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