Skip to main content

Kinetic models for semiconductors

  • Chapter
  • First Online:
Nonequilibrium Problems in Many-Particle Systems

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1551))

  • 487 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Illner, H. Lange and P.F. Zweifel, Global existence and uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems, preprint.

    Google Scholar 

  2. F. Brezzi and P.A. Markowich, The three-dimensional Wigner-Poisson problem: Existence, uniqueness and approximation, Math Meth. Appl. Sci. 14 35–62

    Google Scholar 

  3. V.I. Tatarskii, The Wigner representation of quantum mechanics, Sov. Phys.Usp.26(1983), 311–327

    Article  MathSciNet  Google Scholar 

  4. K. Takahashii, Distribution functions in classical and quantum mechanics, Progr. of Theor. Phys. Suppl. 98 (1989), 109–156

    Article  MathSciNet  Google Scholar 

  5. P.A. Markowich, C. Ringhofer and C. Schmeiser, “Semiconductor Equations”, Springer Verlag, Wien-New York, 1990

    Book  MATH  Google Scholar 

  6. P.A. Markowich, N.J. Mauser, The classical limit of a self-consistent Quantum-Vlasov equation in 3-d, Math Meth. Appl. Sci. (to appear) (1992)

    Google Scholar 

  7. R. Di Perna and P.L. Lions, Global solutions of Vlasov-Poisson type equations, CERE-MADE preprint Nr. 8824.

    Google Scholar 

  8. J. Simon, Compact sets in the spaces Lp((0,T);B), Anal. Math Pura. Appl. 166 (1987), 65–97.

    MATH  Google Scholar 

  9. P.L Lions and T. Paul, Sur les mesures de Wigner, preprint, CREMADE, Universite de Paris-Dauphine, (1992).

    Google Scholar 

  10. F. Nier, A stationary Schrödinger-Poisson System arising from the Modelling of Electronic Devices, Forum Math. 25, 489–510, (1991).

    MathSciNet  MATH  Google Scholar 

  11. F. Nier, A variational Formulation of Schrödinger-Poisson Systems in Dimension d ≤ 3, submitted, (1991).

    Google Scholar 

  12. J. Dolbeault, Stationary States in Plasma Physics; Maxwellian Solutions of the Vlasov-Poisson System, M 3 AS, 1, 183–208, (1991).

    MathSciNet  Google Scholar 

  13. L. Desvillettes & J. Dobbeault On long time asymptotics of the Vlasov-Poisson-Boltzmann Equation, to appear in Math. Models and Meth. in Appl. Sci., (1992)

    Google Scholar 

  14. A. Arnold, P.A. Markowich and N. Mauser, The One-Dimensional Periodic Bloch-Poisson Equation, M 3 AS, 1, 83–112, (1991).

    MathSciNet  Google Scholar 

  15. P.A. Markowich, Boltzmann Distributed Quantum Steady States and their Classical Limit, to appear in Forum Math., (1991).

    Google Scholar 

  16. U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary value ODEs, Trans. Math. Soft. 7 (1981), 209–222.

    Article  MATH  Google Scholar 

  17. U. Ascher, P Markowich, P.Pietra and C. Schmieser, A Phase plane analysis of transonic solutions for the hydrodynamic semiconductor model, to appear in M 3 AS

    Google Scholar 

  18. P. Degond and P.A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Letters 3 (3), (1990), 25–86.

    Article  MathSciNet  MATH  Google Scholar 

  19. P. Degond and P.A. Markowich, A steady state potential flow model for semiconductors, to appear in Annali di Matematica Pura ed Applicata.

    Google Scholar 

  20. I.M. Gamba, Stationary transonic solutions for a one-dimensional hydrodynamic model for semiconductors, Technical Report #143, Center for Applied Mathematics, Purdue University.

    Google Scholar 

  21. I.M. Gamba, Boundary layer formation for viscosity approximations in transonic flow, Technical Report #149, Center for Applied Mathematics, Purdue University.

    Google Scholar 

  22. P.A. Markowich, “The Stationary Semiconductor Device Equations”, Springer-Verlag, Heidelberg, (1986).

    Book  Google Scholar 

  23. P.A. Markowich and P. Pietra, A non-isentropic Euler-Poisson model for a collisionless plasma, to appear in Math. Meth. Appl. Sci., 1993.

    Google Scholar 

  24. P.A. Markowich, C. Ringhofer and C. Schmeiser, “Semiconductor Equations”, Springer Verlag, Wien-New York, (1990).

    Book  MATH  Google Scholar 

  25. J. Smoller, “Shock Waves and Reaction-Diffusion Equations”, Springer-Verlag, New York, Heidelberg, Berlin, (1980).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Carlo Cercignani Mario Pulvirenti

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this chapter

Cite this chapter

Markowich, P.A. (1993). Kinetic models for semiconductors. In: Cercignani, C., Pulvirenti, M. (eds) Nonequilibrium Problems in Many-Particle Systems. Lecture Notes in Mathematics, vol 1551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090930

Download citation

  • DOI: https://doi.org/10.1007/BFb0090930

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56945-9

  • Online ISBN: 978-3-540-47832-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics