Numerical Modeling of Horizontal Wafering of Silicon Melts on a Molten Substrate

B. Erik Ydstie, Sukumar Balaji, and Sudhir Ranjan. Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213

In the current study, we model the variations in geometric topology and the interactions between two immiscible fluids using Finite Element Method. The well known technique, Level Set Method is employed to track the changes in shapes, moving boundaries and interactions between fluids. The Multiphysics modeling software COMSOL is used for this purpose. To test the predictions, the modeling work is coordinated with experimental efforts.

In order to obtain a silicon film of varying thickness at the surface of molten substrate, a drift of silicon melt in a known volume of molten substrate such as slag was modeled. Based on the slag properties, the moving boundary problem is simulated. Experiments were carried out at 1500C to melt silicon in slag, which is comprised of various metal oxides and whose melting point is around 1000-1200C. The set-up is then slowly cooled to study the stability of the melt at room temperature. Both the experimental and the simulated results confirm the formation of stabilized shapes with varying sizes based on the physical properties of both the slag and the silicon melt.

The simulated model is then used to carry out sensitivity analysis for the two phase system. The most important physical parameters that characterize the final form of the silicon film are density, surface tension, viscosity and the film thickness. The sensitivity of each parameter is studied individually by keeping other parameters constant. Based on the influence of each parameter, outstretching of silicon melts on molten slag system and ways of continuous floating of the thin layer on the slag surface are being devised.

Keywords: Level set method, two phase flow, moving boundary, sensitivity analysis, COMSOL Multiphysics.