TY - GEN A1 - Dreyer, Wolfgang A1 - Druet, Pierre-Étienne A1 - Klein, Olaf A1 - Sprekels, Jürgen T1 - Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals N2 - 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. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years. KW - Czochralski method KW - crystal growth KW - traveling magnetic fields KW - radiative heat transfer KW - nonlinear PDE systems KW - Navier-Stokes equations KW - MHD equations Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1086 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-10868 ER -