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

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

doi:10.1016/j.na.2005.09.045

Cited by 16 publications

(20 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [17,18], 2D numerical simulations were performed for the silicon MESFET (metal semiconductor field effect transistor). Mathematical aspects of the model related to the stability of the equilibrium state for the 2D silicon MESFET were studied in [19]. Following [9,10,19,20], we write down the quasilinear nonstationary system of moment equations in the 2D case and in a dimensionless form (the process of reduction to a dimensionless form was detailed in [19,20]):…”

Section: Introductionmentioning

confidence: 99%

“…the coefficients c, c 11 , c 12 , c 21 , c 22 in (1.1) are smooth functions of the energy E (their explicit form is technically complicated, but for the parabolic band it can be found in [19,20]); ρ = ρ(x, y) is the doping density, and β > 0 is a constant (see [19,20]). …”

Section: Introductionmentioning

confidence: 99%

“…The detailed description of such a semiconductor transistor with electron conductivity is given in [19,22]. Its schematic sketch is given on Fig.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

Блохин

Tkachev

2010

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

We prove the local-in-time well-posedness of the initial boundary value problem for a system of quasilinear equations. This system is used for finding numerical stationary solutions of the hydrodynamical model of charge transport in the silicon MESFET (metal semiconductor field effect transistor). The initial boundary value problem has the following peculiarities: the quasilinear system is not a Cauchy-Kovalevskaya-type system; the boundary is a non-smooth curve and has angular points; nonlinearity of the problem is mainly connected with squares of gradients of the unknown functions. By using a special representation for the solution of a model problem we reduce the original problem to an integro-differential system. The local-in-time existence of a weakened generalized solution of this system is then proved by the fixed-point argument.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

Блохин

Tkachev

2010

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 97%

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

Блохин

2008

Quart. Appl. Math.

View full text Add to dashboard Cite

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

show abstract

Some Formal Properties of the Hydrodynamical Model

Camiola

Mascali

Romano

2020

Mathematics in Industry

View full text Add to dashboard Cite

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

Cited by 16 publications

References 24 publications

Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

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

Some Formal Properties of the Hydrodynamical Model

Contact Info

Product

Resources

About