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
Highlights
IntroductionP-i-n-diodes (diodes with a wide base) are widely used for switching the electromagnetic field [1, 2]
In microwave technology, p-i-n-diodes are widely used for switching the electromagnetic field [1, 2]
The operation of switching p-i-n-diodes is based on the possibility of creating, under the influence of the control current, a highly concentrated electron-hole plasma in the active region (n-region) of the diode
Summary
P-i-n-diodes (diodes with a wide base) are widely used for switching the electromagnetic field [1, 2]. The basic characteristics of switches based on p-i-n-diodes – the level of the switched power of the microwave signal, the modulation depth, the speed of response – determine the concentration of the electron-hole plasma in the active region, the pulse density, energy (averaged characteristics of the plasma) and the design of the p-i-n-diodes. The main ones are injection of charge carriers from highly doped bands through n-i and p-i junctions, electron-hole diffusion and drift, recombination processes in the bulk and on the surface of the n-region, energy transfer of electrons and holes to the crystal lattice, and the like. These processes are described by nonlinear mathematical models
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