\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Analysis of a diffusive effective mass model for nanowires

Abstract Related Papers Cited by
  • We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking into account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain.
    Mathematics Subject Classification: Primary: 35Q40, 76R99, 49K20, 82D80; Secondary: 81Q10.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    N. W. Ashcroft and N. D. Mermin, "Solid State Physics,'' Saunders College Publishing, 1976.

    [2]

    J.-P. Aubin, Un théor\`eme de compacité, C. R. Acad. Sci. Paris, 256 (1963), 5042-5044.

    [3]

    N. Ben Abdallah and L. Barletti, Quantum transport in crystals : Effective-mass theorem and k.p Hamiltonians, Comm. Math. Phys., 307 (2011), 567-607.

    [4]

    N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors J. Math. Phys., 37 (1996), 3306-3333.doi: 10.1063/1.531567.

    [5]

    N. Ben Abdallah, C. Jourdana and P. PietraAn effective mass model for the simulation of ultra-scaled confined devices, preprint, IMATI-CNR 10PV11/7/0.

    [6]

    N. Ben Abdallah and F. Méhats, On a Vlasov-Schrödinger-Poisson model, Comm. Partial Differential Equations, 29 (2004), 173-206.

    [7]

    N. Ben Abdallah and F. Méhats, Semiclassical analysis of the Schrödinger equation with a partially confining potential, J. Math. Pures Appl. (9), 84 (2005), 580-614.doi: 10.1016/j.matpur.2004.10.004.

    [8]

    N. Ben Abdallah, F. Méhats and N. Vauchelet, Diffusive transport of partially quantized particles: Existence, uniqueness and long-time behaviour, Proc. Edinb. Math. Soc. (2), 49 (2006), 513-549.doi: 10.1017/S0013091504000987.

    [9]

    N. Ben Abdallah and M. L. Tayeb, Diffusion approximation for the one dimensional Boltzmann-Poisson system, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1129-1142.doi: 10.3934/dcdsb.2004.4.1129.

    [10]

    C. Heitzinger and C. Ringhofer, A transport equation for confined structures derived from the Boltzmann equation, Comm. Math. Sci., 9 (2011), 829-857.

    [11]

    A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,'' Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006.

    [12]

    A. Jüngel, "Transport Equations for Semiconductors,'' Lecture Notes in Physics, 773, Springer-Verlag, Berlin, 2009.

    [13]

    J.-L. Lions, "Équations Différentielles Opérationnelles et Problèmes aux Limites,'' Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.

    [14]

    P. A. Markowich, C. A. Ringhofer and C. Schmeiser, "Semiconductor Equations,'' Springer-Verlag, Vienna, 1990.doi: 10.1007/978-3-7091-6961-2.

    [15]

    N. Masmoudi and M. L. Tayeb, Diffusion limit of a semiconductor Boltzmann-Poisson system, SIAM J. Math. Anal., 38 (2007), 1788-1807.doi: 10.1137/050630763.

    [16]

    M. S. Mock, "Analysis of Mathematical Models of Semiconductor Devices,'' Advances in Numerical Computation Series, 3, Boole Press, Dún Laoghaire, 1983.

    [17]

    P. Pietra and N. Vauchelet, Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, J. Comp. Elec., 7 (2008), 52-65.doi: 10.1007/s10825-008-0253-z.

    [18]

    F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), 293-317.

    [19]

    N. Vauchelet, Diffusive limit of a two dimensional kinetic system of partially quantized particles, J. Stat. Phys., 139 (2010), 882-914.doi: 10.1007/s10955-010-9970-3.

    [20]

    N. Vauchelet, Diffusive transport of partially quantized particles: $L\log L$ solutions, Math. Models Methods Appl. Sci., 18 (2008), 489-510.doi: 10.1142/S0218202508002759.

    [21]

    T. Wenckebach, "Essential of Semiconductor Physics,'' Wiley, Chichester, 1999.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(87) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return