A fixed-grid method for transient simulations of dopant segregation in VGF-RMF growth

• Published in: Journal of crystal growth Vol. 339; no. 1; pp. 75 - 85
• Main Authors: Nikrityuk, Petr A., Pätzold, Olf, Stelter, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.01.2012; Elsevier
• Subjects: A1. Directional solidification; A1. Solidification; A1. Stirring; A2. Vertical gradient freeze; Computer simulation; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Crystal growth; Dopants; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; Growth from melts; zone melting and refining; Materials science; Mathematical analysis; Mathematical models; Melts; Methods of crystal growth; physics of crystal growth; Physics; Segregations; Solubility, segregation, and mixing; phase separation; Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation; Tracking; A1. Solidification; A1. Stirring; A1. Directional solidification; A2. Vertical gradient freeze; Tracking; Directional solidification; Segregation; Digital simulation; Stirring; Magnetic field effects; Theoretical study; Vertical gradient freeze method; Gallium additions; Transients; Interfaces; Binary alloys; Energy conservation; Growth mechanism; Germanium; Modelling; Growth from melt; Analytical solution; Crystal growth from melts
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/j.jcrysgro.2011.11.070

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. ► A fixed-grid method has been adopted for simulations of the dopant segregation. ► The Stefan conditions are formulated in source terms in conservation equations. ► The solid interface is tracked implicitly. ► The formation of dopant striations is well reproduced by numerical simulations. ► RMF is found to have a significant impact on the axial mixing of the melt.