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Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals. (English) Zbl 1257.35181

Summary: 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., silicon (Si) or gallium arsenide (GaAs) 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.

MSC:

35Q82 PDEs in connection with statistical mechanics
35Q61 Maxwell equations
45G05 Singular nonlinear integral equations
76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
80A22 Stefan problems, phase changes, etc.

Software:

PARDISO; Triangle; pdelib
PDFBibTeX XMLCite
Full Text: DOI

References:

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