Modelling of heat transfer and fluid flow in a silicon melt for the Czochralski process

Abstract

In order to get a better understanding of the heat transfer and the fluid flow of a silicon melt in the Czochralski process, the focus has been to use modelling together with theoretical analysis to gather more understanding about the process. By using the C++ based software OpenFOAM, a 2D model of the melt has been created. Two different methods were developed for the influence of the crystal interface on the melt, and it was discussed that it was more beneficial to set the crystal as a boundary condition, rather than using multiple regions. The model was validated by inducing a temperature difference on the surface, which caused the system to try to prevent this temperature difference in the melt. This also helped explain the influence instability has on the melt. There are still a lot of approximations used in this model, and adding rotation, soldification and making it 3D would be beneficial. However, the 2D model made in this thesis has shown the general trend and effects of the various parameters. This thesis has thus laid the foundation for further work in OpenFOAM.