Multi-Scale Modeling of Quantum Semiconductor Devices

Anton Arnold () and Ansgar Jüngel ()
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Anton Arnold: Technische Universität Wien, Institut für Analysis und Scientific Computing
Ansgar Jüngel: Universität Mainz, Institut für Mathematik

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 331-363 from Springer

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.

Keywords: Wigner Function; Collision Operator; Open Quantum System; Tunneling Diode; Quantum Waveguide (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_12

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DOI: 10.1007/3-540-35657-6_12

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