Time-Depending Solutions to Spherical Harmonic Equations for Semiconductor Devices

  • C. Drago
  • A. Majorana
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


In this paper we consider two models derived from the semiconductor Boltzmann equation by using the spherical harmonic expansion method. The first model contains only two terms of the expansion, the second also the third term. We look for space-homogeneous solutions to two Cauchy problems. Numerical results are found using a simple difference scheme and a comparison between the two models is shown.


Cauchy Problem High Electric Field Spherical Harmonic Expansion Velocity Overshoot Hydrodynamical Velocity 
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  1. 1.
    Ferry D. K. (1982) Fundamental aspects of hot electron phenomena. In: Paul W. (Ed.) Handbook on Semiconductors Vol. I, North-Holland Publishing Company, 563–597Google Scholar
  2. 2.
    Smith H., Jensen H. H. (1989) Transport Phenomena. Oxford Univ. Press, New YorkGoogle Scholar
  3. 3.
    Jacoboni C., Lugli P. (1989) The Monte Carlo Method for Semiconductor Device Simulation. Springer-Verlag, New YorkCrossRefGoogle Scholar
  4. 4.
    Ventura D., Gnudi A., Baccarani G. (1995) A Deterministic Approach to Solution of the BTE in Semiconductors. Rivista del Nuovo Cimento 18, 1–33CrossRefGoogle Scholar
  5. 5.
    Rahmat K., Whithe J., Antoniadis D. A. (1996) Simulation of Semiconductor Devices Using a Galerkin/Spherical Harmonic Expansion Approach to Solving the Coupled Poisson-Boltzmann System. IEEE Trans. Computer-Aided Design 15, 1181–1196CrossRefGoogle Scholar
  6. 6.
    Drago C., Majorana A. (2000) The Velocity Overshoot in Semiconductors according to a transport model derived from the Boltzmann Equation. Transp. Theory Stat. Phys. 29, 805–823MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • C. Drago
    • 1
  • A. Majorana
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversity of CataniaCataniaItaly

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