Cw. Lan et Jh. Chian, Three-dimensional simulation of Marangoni flow and interfaces in floating-zone silicon crystal growth, J CRYST GR, 230(1-2), 2001, pp. 172-180
Three-dimensional (3D) simulation is conducted for the floating-zone (FZ) g
rowth of silicon in an ellipsoid mirror furnace. for the first time, simult
aneously considering the time-dependent Marangoni flow, heat transfer, and
moving interfaces. The numerical method is based on an efficient multigrid
finite-volume method with front tracking. The growth of an 8 mm diameter si
licon crystal under microgravity is considered. A half-zone configuration i
s also used for benchmarking, and the calculated bifurcation points and flo
w structures are in good agreement with previous results. However. quasi-pe
riodic modes and angular waves are observed at higher Marangoni number. For
full zone calculations, including the feeding and growth interfaces. the b
ifurcation behavior is similar, but the primary bifurcation is found to be
subcritical and the 3D one-fold flow mode is dominant. Significant growth r
ate fluctuations and back melting are found for a typical growth condition
as well. The major fluctuation frequency ranges from 0.1 to 0.3 Hz, and the
severe back melting may be related to the angular waves. (C) 2001 Elsevier
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