Abstract
Different approaches to the solution of the kinetic transport models discussed in Chapter 1 are possible. Although several promising attempts towards a numerical solution have been undertaken in the recent past (we only mention particle methods [2.10] and spectral methods [2.13]), the application of numerical methods remains to be a formidable task in general. Apart from that, solutions of the kinetic equations contain in many cases (e.g. close to equilibrium) a good deal of redundant information.
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References
G. Baccarani, M. R. Wordeman: An Investigation of Steady-State Velocity Overshoot Effects in Si and GaAs Devices. Solid State Electr. 28, 407–416 (1985).
K. Bløotekjaer: Transport Equations for Electrons in Two-Valley Semiconductors. IEEE Trans. Electron. Devices ED-17, 38–47 (1970).
C. Cercignani: The Boltzmann Equation and Its Applications. Springer-Verlag, New York (1988).
G. Frosali: Functional-Analytic Techniques in the Study of Time-Dependent Electron Swarms in Weakly Ionized Gases. Preprint, Istituto di Matematica, Università di Ancona (1988).
C. L. Gardner, J. W. Jerome, D. J. Rose: Numerical Methods for the Hydrodynamic Device Model: Subsonic Flow. Presented at the meeting on Mathematische Modellierung und Simulation elektrischer Schaltungen, Oberwolfach (1988).
R. N. Hall: Electron-Hole Recombination in Germanium. Physical Review 87, 387 (1952).
W. Hänsch, M. Miura-Mattausch: The Hot-Electron Problem in Small Semiconductor Devices. J. Appl. Phys. 80, 650–656 (1986).
W. Hänsch, C. Schmeiser: Hot Electron Transport in Semiconductors. ΖAMΡ 40, 440–455 (1989).
D. Hubert: Math. Ann. 72, 562 (1912).
B. Niclot, P. Degond, F. Poupaud: Deterministic Particle Simulations of the Boltzmann Transport Equation of Semiconductors. J. Comp. Phys. 78, 313–350 (1988).
F. Poupaud: Etude Mathematique et Simulations Numeriques de Quelques Equations de Boltzmann. Thesis, Univ. Paris 6 (1988).
F. Poupaud: Runaway Phenomena and Fluid Approximation Under Strong Electric Field in Semiconductor Theory. Manuscript, Laboratoire de Mathématiques, Université de Nice (1988).
C. A. Ringhofer: A Spectral Method for Numerical Simulation of Quantum Tunneling Phenomena. SI AM J. Numer. Anal. (1989) (to appear).
W. Shockley: Problems Related to P-N Junctions in Silicon. Solid State Electr. 2, 35–67 (1961).
W. Shockley, W. T. Read: Statistics of the Recombinations of Holes and Electrons. Physical Review 87, 835–842 (1952).
S. Selberherr: Analysis and Simulation of Semiconductor Devices. Springer-Verlag, Wien-New York (1984).
S. M. Sze: Physics of Semiconductor Devices, 2nd edn. John Wiley & Sons, New York (1981).
W. V. van Roosbroeck: Theory of Flow of Electrons and Holes in Germanium and Other Semiconductors. Bell Syst. Techn. J. 29, 560–607 (1950).
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© 1990 Springer-Verlag Wien
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Markowich, P.A., Ringhofer, C.A., Schmeiser, C. (1990). From Kinetic to Fluid Dynamical Models. In: Semiconductor Equations. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6961-2_3
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DOI: https://doi.org/10.1007/978-3-7091-6961-2_3
Publisher Name: Springer, Vienna
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