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Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals

Please always quote using this URN:urn:nbn:de:0296-matheon-10868
  • 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.

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Metadaten
Author:Wolfgang Dreyer, Pierre-Étienne Druet, Olaf Klein, Jürgen Sprekels
URN:urn:nbn:de:0296-matheon-10868
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/23
Release Date:2012/02/23
Tag:Czochralski method; MHD equations; Navier-Stokes equations; crystal growth; nonlinear PDE systems; radiative heat transfer; traveling magnetic fields
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q30 Navier-Stokes equations [See also 76D05, 76D07, 76N10]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q61 Maxwell equations
45-XX INTEGRAL EQUATIONS / 45Gxx Nonlinear integral equations [See also 47H30, 47Jxx] / 45G05 Singular nonlinear integral equations
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Wxx Magnetohydrodynamics and electrohydrodynamics / 76W05 Magnetohydrodynamics and electrohydrodynamics
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A20 Heat and mass transfer, heat flow
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A22 Stefan problems, phase changes, etc. [See also 74Nxx]
Preprint Number:929
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