The quasineutral limit problem in semiconductors sciences

Ling Hsiao

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 249-256
  • ISSN: 1120-6330

Abstract

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The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.

How to cite

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Hsiao, Ling. "The quasineutral limit problem in semiconductors sciences." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 249-256. <http://eudml.org/doc/252399>.

@article{Hsiao2004,
abstract = {The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.},
author = {Hsiao, Ling},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Quasineutral limit; Drift-diffusion model; Semiconductors; quasineutral limit; drift-diffusion model; semiconductors; electrical current transport; a priori estimates},
language = {eng},
month = {12},
number = {3-4},
pages = {249-256},
publisher = {Accademia Nazionale dei Lincei},
title = {The quasineutral limit problem in semiconductors sciences},
url = {http://eudml.org/doc/252399},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Hsiao, Ling
TI - The quasineutral limit problem in semiconductors sciences
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 249
EP - 256
AB - The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.
LA - eng
KW - Quasineutral limit; Drift-diffusion model; Semiconductors; quasineutral limit; drift-diffusion model; semiconductors; electrical current transport; a priori estimates
UR - http://eudml.org/doc/252399
ER -

References

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  2. GASSER, I., The initial time layer problem and the quasineutral limit in a nonlinear drift diffusion model for semiconductors. Nonlinear Differential Equations Appl., 8(3), 2001, 237-249. Zbl0980.35158MR1841258DOI10.1007/PL00001447
  3. GASSER, I. - HSIAO, L. - MARKOWICH, P.A. - WANG, S., Quasi-neutral limit of a nonlinear drift diffusion model for semiconductors. J. Math. Anal. Appl., 268(1), 2002, 184-199. Zbl1016.82034MR1893201DOI10.1006/jmaa.2001.7813
  4. GASSER, I. - LEVERMORE, C.D. - MARKOWICH, P.A. - SCHMEISER, C., The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model. European J. Appl. Math., 12(4), 2001, 497-512. Zbl1018.82024MR1852311DOI10.1017/S0956792501004533
  5. HSIAO, L. - JU, Q. - WANG, S., The asymptotic behavior of global smooth solutions to the multidimensional hydrodynamic model for semiconductors. Math. Methods Appl. Sci., 26, 2003, 1187-1210. Zbl1027.35071MR2002977DOI10.1002/mma.410
  6. HSIAO, L. - MARKOWICH, P. - WANG, S., The asymptotic behavior of global smooth solutions to the multidimensional hydrodynamic model for semiconductors. J. Diff. Eqns., 192, 2003, 111-133. Zbl1045.35088MR1987086DOI10.1016/S0022-0396(03)00063-9
  7. HSIAO, L. - MARKOWICH, P.A. - WANG, S., Quasineutral limit of a standard drift diffusion model for semiconductors. Sci. China Ser. A, 45(1), 2002, 33-41. Zbl1054.82031MR1894957
  8. HSIAO, L. - WANG, S., Quasineutral limit of a nonlinear drift diffusion model for semiconductors: the fast diffusion case. Advances in Math., vol. 32, no. 5, 2003, 615-622. Zbl1016.82034MR2057508
  9. HSIAO, L. - WANG, S., Quasineutral limit of a transient p - n junction model for semiconductors. Preprint. 
  10. HSIAO, L. - WANG, S. - ZHAO, H., Asymptotic behaviour of global smooth solutions to the multidimensional hydrodynamic model for semiconductors. Math. Methods Appl. Sci., 25(8), 2002, 663-700. Zbl1010.35071MR1900649DOI10.1002/mma.307
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  14. MARKOWICH, P.A. - RINGHOFER, C.A. - SCHMEISER, C., Semiconductor Equations. Springer-Verlag, Vienna1990. Zbl0765.35001MR1063852DOI10.1007/978-3-7091-6961-2
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  17. VAN ROOSBROECK, W., Theory of flow of electrons and holes in germanium and other semiconductors. Bell Syst. Tech. J., 29, 1950, 560-607. 

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