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A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.

crystals

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration