Effects of thermocapillary convection and shear flow on the distribution of inclusions in half-floating zones

Abstract

The distribution of inclusions plays a critical role in the performance of crystalline silicon, which is an important raw material for solar panels and semiconductors. To describe the formation of the aggregated inclusions, a three-phase gas–liquid-solid system was designed, in which the gas and liquid phases interact directly through the free surface, and the inclusions interact with them in the liquid. It is worth noting that the inclusions and gas phase did not interact directly. In the gas and liquid phases, the finite volume method was used to solve the Naiver-Stokes equations, and the CLSVOF method was used to track the free surface deformation. The motion of the inclusions was tracked using the Lagrange method. The inclusions and fluid were coupled in two ways: energy and momentum exchange. The numerical results show that the spatial distributions of the inclusion volumetric concentration, number density, and characteristic radius have some features of the recirculation zone. The closer to the center of the liquid bridge, the lower the density of inclusions. When the direction of the shear flow is opposite to that of the thermocapillary convection, this phenomenon is more obvious. This indicates that the crystal quality in the middle region is higher when various parameters are appropriate.