We are applying a comprehensive thermal-capillary model to study the coupled phenomena of heat transfer and interfacial phenomena (solidification and capillarity) in the HRG process. This model accounts for heat transfer in the melt-crystal-crucible domains with radiative heat loss from high temperature surfaces, melt convection due to buoyancy and surface-tension forces, and the self-consistent determination of melt-crystal, melt-ambient and crystal-ambient interface shapes. This moving-boundary problem is solved numerically by the Galerkin finite element method, using elliptic mesh generation.
Extensive parametric sensitivity studies are conducted to identify the variables that impact the process. The effect of pull rate, pulling angle, melt height, crucible geometry and furnace heat transfer are investigated. Transient simulations are performed to analyze the dynamics of the growth process and to determine its stability. Preliminary results indicate that quasi-steady-states exist for this system but that most are unstable. In this light, the dynamic analysis of this system will be require to identify attainable stable states and possible strategies to stabilize unstable ones.
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