Numerical simulations were carried out to study the thermosolutal and flow structures observed in the dissolution experiments of silicon into a germanium melt. The dissolution experiments utilized a material configuration similar to that used in the Liquid Phase Diffusion LPD and MeltReplenishment Czochralski Cz crystal growth systems. In the present model, the computational domain was assumed axisymmetric. Governing equations of the liquid phase SiGe mixture , namely the equations of conservation of mass, momentum balance, energy balance, and solute species transport balance were solved using the Stabilized Finite Element Methods STGLS for fluid flow, SUPG for heat and solute transport . Measured concentration profiles and dissolution height from the samples processed with and without the application of magnetic field show that the amount of silicon transported into the melt is slightly higher in the samples processed under magnetic field, and there is a difference in dissolution interface shape indicating a change in the flow structure during the dissolution process. The present mathematical model predicts this difference in the flow structure. In the absence of magnetic field, a flat stable interface is observed. In the presence of an applied field, however, the dissolution interface remains flat in the center but curves back into the source material near the edge of the wall. This indicates a far higher dissolution rate at the edge of the silicon source
Dissolution, convection, diffusion, numerical simulation, stabilized finite element techniques
Primary Language  English 

Journal Section  Research Article 
Authors 

Publication Date  December 1, 2011 
Published in Issue  Year 2011, Volume 01, Issue 2 
Bibtex  @ { twmsjaem761788, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {21461147}, eissn = {25871013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2011}, volume = {01}, number = {2}, pages = {127  149}, title = {MATHEMATICAL MODELING OF THE DISSOLUTION PROCESS OF SILICON INTO GERMANIUM MELT}, key = {cite}, author = {Mechighel, Farid and Armour, Neil and Dost, Sadik and Kadja, Mahfoud} } 