<p>We propose a procedure for the mathematical modeling of the volt-ampere characteristic of a semiconductor bulk diode based on the systematic approach to the investigation of studied electronic devices and the analysis of the physical processes in these devices by the methods of perturbation theory. Stationary current flows under the action of applied drops of potential in the high-alloy, contact, and active domains of the diode are treated in the hydrodynamic approximation. The process of modeling of the volt-ampere characteristics is reduced to finding the distributions of the concentrations of charge carriers and potential in the structural elements of the analyzed system. The proposed mathematical model is based on the customary nonlinear singularly perturbed system of the equations of continuity for electron-hole currents and the Poisson equation with appropriate boundary conditions. As specific features of the proposed approach, we can mention the representation of the solution of the posed nonlinear problem in the form of asymptotic series constructed by the method of boundary corrections in perturbation theory and taking into account the influence of barriers <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(p-i$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>-</mo> <mi>i</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$n-i$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>-</mo> <mi>i</mi> </mrow> </math></EquationSource> </InlineEquation> junctions) on the formation of electron-hole plasma in the active domain of the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$p-i-n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>-</mo> <mi>i</mi> <mo>-</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>-diode. The boundary corrections found in the process of solving play a key role in describing the distribution of electrostatic fields in the analyzed system and make it possible to clarify, for the first time, important details of the process of conduction of electron-hole currents in the diode. The obtained results correlate with the available data of experimental investigations.</p>

Methods of Perturbation Theory in the System Modeling of the Volt-Ampere Characteristics of p − i − n-diode

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发表日期：

2025年10月1日

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A. Ya. Bomba,
I. P. Moroz

摘要

We propose a procedure for the mathematical modeling of the volt-ampere characteristic of a semiconductor bulk diode based on the systematic approach to the investigation of studied electronic devices and the analysis of the physical processes in these devices by the methods of perturbation theory. Stationary current flows under the action of applied drops of potential in the high-alloy, contact, and active domains of the diode are treated in the hydrodynamic approximation. The process of modeling of the volt-ampere characteristics is reduced to finding the distributions of the concentrations of charge carriers and potential in the structural elements of the analyzed system. The proposed mathematical model is based on the customary nonlinear singularly perturbed system of the equations of continuity for electron-hole currents and the Poisson equation with appropriate boundary conditions. As specific features of the proposed approach, we can mention the representation of the solution of the posed nonlinear problem in the form of asymptotic series constructed by the method of boundary corrections in perturbation theory and taking into account the influence of barriers $(p-i$ $(p - i$ and $n-i$ $n - i$ junctions) on the formation of electron-hole plasma in the active domain of the $p-i-n$ $p - i - n$ -diode. The boundary corrections found in the process of solving play a key role in describing the distribution of electrostatic fields in the analyzed system and make it possible to clarify, for the first time, important details of the process of conduction of electron-hole currents in the diode. The obtained results correlate with the available data of experimental investigations.