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Title: Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals
Authors: Dreyer, WolfgangDruet, Pierre-ÉtienneKlein, OlafSprekels, Jürgen
Issue Date: 2012
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1689, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations ...
Keywords: Czochralski method; crystal growth; traveling magnetic fields; radiative heat transfer; nonlinear PDE systems; Navier–Stokes equations; MHD equations; Maxwell’s equations; well-posedness; optimal control; first-order necessary optimality conditions; numerical simulation
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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