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Journal of Crystal Growth, Vol.339, No.1, 75-85, 2012
A fixed-grid method for transient simulations of dopant segregation in VGF-RMF growth
In this work a fixed-grid, virtual-front tracking model originally developed for modeling dendritic growth has been adopted for transient simulations of dopant segregation in vertical gradient freeze (VGF) melt growth of Ga-doped germanium under the influence of a rotating magnetic field (RMF). The interfacial Stefan conditions for temperature and solute are formulated in volumetric terms in energy and solute conservation equations, which allow the interface to be tracked implicitly with no need to calculate the growth velocity. The model and the code are validated against an analytical solution for the transient solidification of a binary alloy at constant velocity. The numerical results show the strong relationship between the melt flow pattern and the dopant concentration in the crystal grown. The better melt mixing during growth under the influence of RMF is found to have a significant impact on the axial and radial macrosegregation of dopants. Simulation results are in good qualitative agreement with previous experimental observations of the dopant segregation in VGF-RMF growth, which now are seen ass a direct consequence of the mixing state of the melt. (C) 2011 Elsevier B.V. All rights reserved.