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1998 Modelling of the Czochralski flow
Jan Franců
Abstr. Appl. Anal. 3(1-2): 1-40 (1998). DOI: 10.1155/S1085337598000426


The Czochralski method of the industrial production of a silicon single crystal consists of pulling up the single crystal from the silicon melt. The flow of the melt during the production is called the Czochralski flow. The mathematical description of the flow consists of a coupled system of six P.D.E. in cylindrical coordinates containing Navier-Stokes equations (with the stream function), heat convection-conduction equations, convection-diffusion equation for oxygen impurity and an equation describing magnetic field effect.

This paper deals with the analysis of the system in the form used for numerical simulation. The weak formulation is derived and the existence of the weak solution to the stationary and the evolution problem is proved.


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Jan Franců. "Modelling of the Czochralski flow." Abstr. Appl. Anal. 3 (1-2) 1 - 40, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0993.76084
MathSciNet: MR1700275
Digital Object Identifier: 10.1155/S1085337598000426

Primary: 76D05 , 76Rxx
Secondary: 35Q10 , 46E35

Keywords: Czochralski method , existence theorem , mathematical modelling , operator equation , Rothe method , single crystal growth , viscous flow , Weak solution , weighted Sobolev spaces

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 1-2 • 1998
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