Effect of temperature field and different walls on the wetting angle of molten silicon

A capillary model is developed for calculating the wetting angle of molten silicon on different walls by using the microfluidic two-phase flow level set method and studying the characteristics of the rising process. A mathematical model formulation rigorously accounts for the mass and momentum conservation by using the improved Navier-Stokes equation and considering the Marangoni effect. Compared with the experimental data, the change of the wetting angle on the chemical vapor deposition (CVD) diamond wall indicates the grids independence and the validity of the numerical algorithm. We also discuss the influence of surface tension, and Marangoni stress induced by the gradient of surface tension coefficient, and wall adhesion to the change of wetting angle for three different walls, which include SiC wall, graphite wall, and CVD diamond wall, at different temperatures (1683-1873 K). Result shows that at the same temperature, the thermal-capillary effects that induce the molten silicon to undulation are raised. The wetting angle is reduced after first being increased and finally stabilized. At the initial stage, the fluctuation of the liquid-air interface is volatile due to the large changes of the liquid-air and the wall-air surface tensions, and subsequently, the fluctuation tends to be stable while the wetting angle is close to a fixed value. It is also found that with the graphite wall, these changes are more likely to be stable. This research provides a theoretical guide to obtain a stable growth environment for silicon belt fabricated from the molten silicon.