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Multi-Scale Modeling of Quantum Semiconductor Devices

In: Analysis, Modeling and Simulation of Multiscale Problems

Author

Listed:
  • Anton Arnold

    (Technische Universität Wien, Institut für Analysis und Scientific Computing)

  • Ansgar Jüngel

    (Universität Mainz, Institut für Mathematik)

Abstract

Summary This review is concerned with three classes of quantum semiconductor equations: Schrödinger models, Wigner models, and fluid-type models. For each of these classes, some phenomena on various time and length scales are presented and the connections between micro-scale and macro-scale models are explained. We discuss Schrödinger-Poisson systems for the simulation of quantum waveguides and illustrate the importance of using open boundary conditions. We present Wigner-based semiconductor models and sketch their mathematical analysis. In particular we discuss the Wigner-Poisson-Focker-Planck system, which is the starting point of deriving subsequently the viscous quantum hydrodynamic model. Furthermore, a unified approach to derive macroscopic quantum equations is presented. Two classes of models are derived from a Wigner equation with elastic and inelastic collisions: quantum hydrodynamic equations and their variants, as well as quantum diffusion models.

Suggested Citation

  • Anton Arnold & Ansgar Jüngel, 2006. "Multi-Scale Modeling of Quantum Semiconductor Devices," Springer Books, in: Alexander Mielke (ed.), Analysis, Modeling and Simulation of Multiscale Problems, pages 331-363, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35657-8_12
    DOI: 10.1007/3-540-35657-6_12
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