Global existence for the system of the macroscopic balance equations of charge transport in semiconductors

Блохин, А. М.; Bushmanov, R.S.; Romano, Vittorio

doi:10.1016/j.jmaa.2004.10.024

Cited by 6 publications

(7 citation statements)

References 39 publications

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“…Following [5] - [7], we write down the quasilinear nonstationary system of moment equations mentioned above for the one-dimensional case and in a dimensionless form (the reduction to a dimensionless form is described in [6,7]): these functions are given in [6,7]). In this work we will construct a computational algorithm for finding the approximate solutions the ballistic diode composite problem (see [5] - [7] and Fig.…”

Section: Problem Statementmentioning

confidence: 99%

“…In this work we will construct a computational algorithm for finding the approximate solutions the ballistic diode composite problem (see [5] - [7] and Fig. 1), which is well-known in semiconductor physics The problem is stated as follows.…”

Section: Problem Statementmentioning

confidence: 99%

“…Considering the Poisson equation as an ordinary differential equation (with parameter t ) for potential with boundary conditions (3), we obtain (see [5] - [7] …”

Section: Remarkmentioning

confidence: 99%

“…Note, that due to (7), the number of boundary conditions on each bound corresponds exactly to a number of outgoing characteristics (we have two outgoing characteristics and two boundary conditions for each boundary).…”

Section: Remarkmentioning

confidence: 99%

See 3 more Smart Citations

The construction of one class of numerical algorithms in ballistic diode problem

Блохин

Семисалов

2009

2009 International School and Seminar on Modern Problems of Nanoelectronics, Micro- And Nanosystem Technologies

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Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

“…Considering the Poisson equation as an ordinary differential equation (with parameter t ) for potential with boundary conditions (3), we obtain (see [5] - [7] …”

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

The construction of one class of numerical algorithms in ballistic diode problem

Блохин

Семисалов

2009

2009 International School and Seminar on Modern Problems of Nanoelectronics, Micro- And Nanosystem Technologies

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“…Note also that various mathematical aspects of the model [1,2] related to the stability of the equilibrium state for a 1-D n + − n − n + silicon ballistic diode were studied in [22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Strong discontinuities for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Блохин

2008

Quart. Appl. Math.

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Abstract.For the balance equations of charge transport in semiconductors based on the maximum entropy principle (see Anile and Romano (1999) and Romano (2000)), we derive and study the Rankine-Hugoniot jump conditions. Introduction.In the hierarchy of macroscopic models of charge transport in semiconductors beyond the drift-diffusion equations [3,4,5] and the energy-transport models [6,7,8], one finds the hydrodynamical models that are obtained from an infinite set of moment equations of the Boltzmann Transport Equation by a suitable truncation procedure (see [9,10] for a complete review on the mathematical modelling for semiconductors).It is well known that moment systems require a closure assumption in order to yield a closed system of evolution equations. In [1, 2] the balance equations for density, momentum, energy, and energy flux of electrons have been considered for silicon and, by using the maximum entropy principle (MEP) for the closure, explicit constitutive relations for the stress tensor, the flux of energy flux tensor, and production terms have been obtained both in the parabolic and the Kane dispersion relation approximations for the energy conduction bands. The model fits into Extended Thermodynamics [10,11,12] and Levermore's theory of moments [13] and does not contain any fitting parameters. The validity of the constitutive equations has been checked in [14,15] and the general mathematical properties have been studied in [16], where it has been shown that the evolution equations form a hyperbolic system in the physically relevant region of the field space. Applications of the model have been presented in [15,16] for 1-D problems and in [17] for a 2-D simulation of a silicon MESFET (metal semiconductor field effect transistor). At last, the mathematical aspects of the model related to the stability of the equilibrium state for a 2-D silicon MESFET have been investigated in [18].In the present paper, we continue the study of the system of balance equations proposed in [1,2]. We are interested in piecewise smooth solutions of this system with smooth parts separated by a surface of strong discontinuity. Using a standard approach

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Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Блохин

Bushmanov

Rudometova

et al. 2006

Nonlinear Analysis: Theory, Methods & Applications

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Global existence for the system of the macroscopic balance equations of charge transport in semiconductors

Cited by 6 publications

References 39 publications

The construction of one class of numerical algorithms in ballistic diode problem

The construction of one class of numerical algorithms in ballistic diode problem

Strong discontinuities for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors

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