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Multi-scale modeling of quantum semiconductor devices
 

Summary: Multi-scale modeling of quantum
semiconductor devices
Anton Arnold1
and Ansgar J¨ungel2
1
Institut f¨ur Analysis und Scientific Computing, Technische Universit¨at Wien,
Wiedner Hauptstr. 8, A-1040 Wien, Austria
2
Institut f¨ur Mathematik, Universit¨at Mainz, Staudingerweg 9, D-55099 Mainz,
Germany
anton.arnold@tuwien.ac.at, juengel@mathematik.uni-mainz.de
Summary. This review is concerned with three classes of quantum semiconductor
equations: Schr¨odinger 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 Schr¨odinger-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

  

Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien
Jüngel, Ansgar - Institut für Analysis und Scientific Computing, Technische Universität Wien

 

Collections: Computer Technologies and Information Sciences; Mathematics