Modeling of Melt Flow and Free Surface Profiles in Floating Zone Processes with RF Excitation

"Numerical models are developed to represent complex electromagnetic, free surface deformation and fluid flow phenomena in floating zone refining processes with radio frequency inductive heating. The computational methodology is based on the coupled finite/boundary element method for the electromagnetic field distribution and the Galerkin finite element method for magnetically driven fluid flow and free surface profiles of the molten zone. With the models, the complex transport and free surface phenomena in a floating zone system can be studied as a function of various operating conditions including applied current, frequency, inductor position and shape, surface tension, floating zone diameter and height. Results show that the equilibrium shape is sensitive to the height of the molten zone and that the free surface shapes can have a significant effect on the melt flow in the molten zone. Our extensive simulations also suggest that to ensure accurate results, the same mesh should be used, whenever possible, for both the electromagnetic forces and fluid flow calculations.1. IntroductionThe floating zone processes have been widely used in the materials industry to grow ultra-pure rare earth metal or semiconductor single crystals for sensor or electronic applications that have a tough demand on purity. Developed based on the principle of magnetic melting/levitation, the processes possess a main advantage that the molten zone is supported in air by the electromagnetic forces generated by the coil (see Figure 1), and therefore is free from contamination from a container. Consequently, the final products made from the floating zone processes have higher inherent purity than those by other techniques [1-4].Complex physical phenomena occur in the floating zone processing of materials. These include free surface deformation, magnetically-driven melt flow, which may be turbulent or mildly turbulent [5] depending on the applied conditions, and solidification. Thermal stresses also develop in the single crystals, which are affected by the flow and temperature field and which can have direct implications to qualities of single crystals [6]. An understanding of the fundamentals governing these physical phenomena can be of critical value in elucidating the physics that controls the properties of the metal or semiconductor crystals being produced, thereby providing a rational basis for process improvement and quality control."