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Axisymmetric and 3-D Numerical Simulations of the Effects of a Static Magnetic Field on Dissolution of Silicon into Germanium

F. Mechighel1,2,3, N. Armour4, S. Dost4, M. Kadja3
University of Limoges, SPCTS UMR CNRS 7315, European Center for Ceramics, Limoges, France.
University of Annaba, LR3MI Lab., Mechanical Engineering Department, PB 12, Annaba, Algeria.
University of Constantine I, Mechanical Engineering Department, Constantine, Algeria.
Crystal Growth Laboratory, University of Victoria, Victoria, BC, Canada, V8W 3P6.

Computer Modeling in Engineering & Sciences 2014, 97(1), 53-80. https://doi.org/10.3970/cmes.2014.097.053

Abstract

Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a static magnetic field increased the amount of silicon transported into the melt. The magnetic field also induced a change in dissolution interface shape. This change indicates a change in flow structure in the melt. Both simulation models (axisymmetric and 3-D) predicted this change in flow structure.
In the absence of magnetic field, a flat and stable interface was observed in the experiments. In the presence of an applied field, the dissolution interface remains flat in the center but curves back into the source material near the wall. The application of the magnetic field gave rise to higher dissolution of silicon near the crucible wall. This enhanced dissolution near the wall was well predicted by the present 3-D simulation model, but not by the axisymmetric model. This indicates that this effect was due to the three-dimensionality of the melt flow.

Keywords

SiGe bulk single crystal, LPD growth method, Dissolution, Convection, Diffusion, Magnetic field, Stabilized finite element techniques

Cite This Article

Mechighel, F., Armour, N., Dost, S., Kadja, M. (2014). Axisymmetric and 3-D Numerical Simulations of the Effects of a Static Magnetic Field on Dissolution of Silicon into Germanium. CMES-Computer Modeling in Engineering & Sciences, 97(1), 53–80.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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