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  • 1
    Electronic Resource
    Electronic Resource
    An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theory (1994)
    Springer
    Numerische Mathematik 68 (1994), S. 239-262 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65M06, 82C40, 82C80, 82D10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We propose a finite difference scheme to approximate the Fokker-Planck collision operator in 3 velocity dimensions. The principal feature of this scheme is to provide a decay of the numerical entropy. As a consequence, it preserves the collisional invariants and its stationary solutions are the discrete Maxwellians. We consider both the whole velocity-space problem and the bounded velocity problem. In the latter case, we provide artificial boundary conditions which preserve the decay of the entropy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050059
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A mathematical analysis of quantum transport in three-dimensional crystals (1991)
    Springer
    Annali di matematica pura ed applicata 160 (1991), S. 171-191 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present an existence and uniqueness result for a quantum transport model in three dimensional crystals. The model consists of a quantum transport (Wigner) equation posed on the phase space consisting of a discrete position variable and a «continuous» wave vector, which is restricted to a bounded domain inR 3 (first Brillouin zone of the crystal). The potential is modeled self-consistently by a discrete Poisson equation (Coulomb interaction). Also we investigate the limits of solutions of this model as the grid spacing tends to zero and show that they converge to the solution of a quantum transport model posed on the «fully continuous» phase space. The transport model derived by this limiting procedure treats the band diagram of the crystal in a semi-classical way and the potential energy term quantum mechanically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01764126
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  • 3
    Electronic Resource
    Electronic Resource
    A steady state potential flow model for semiconductors (1993)
    Springer
    Annali di matematica pura ed applicata 165 (1993), S. 87-98 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a three-dimensional steady state irrotational flow model for semiconductors which is based on the hydrodynamic equations. We prove existence and local uniqueness of smooth solutions under a smallness assumptions on the data. This assumption implies subsonic flow of electrons in the semiconductors device.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01765842
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On a mathematical model for hot carrier injection in semiconductors (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1193-1212 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a collisionless transport model for electrons in a semiconductor, and we perform an asymptotic analysis for low temperatures or large applied biases. We derive analytic relations for the built-in potential and for the current which flows through the structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171503
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