Zone melting is an efficient purification method that is widely used in the manufacture of semiconductors. Recently, it has been used in the purification of industrial phosphorus. It is a complicated process consisting of both the melting-solidification process and the solute diffusion process. There is a great demand for a quantitative understanding of the underlying mechanism. In this thesis, we propose a variational phase-field model to simulate the zone melting process. The resulting coupled system of Allen-Cahn equation, heat equation and solute diffusion equation is solved numerically. To overcome the stiffness caused by the nonlinear term in Allen-Cahn equation, We propose a semi-implicit scheme based on a convex splitting of the free energy. By a proper splitting of the...[ Read more ]

Zone melting is an efficient purification method that is widely used in the manufacture of semiconductors. Recently, it has been used in the purification of industrial phosphorus. It is a complicated process consisting of both the melting-solidification process and the solute diffusion process. There is a great demand for a quantitative understanding of the underlying mechanism. In this thesis, we propose a variational phase-field model to simulate the zone melting process. The resulting coupled system of Allen-Cahn equation, heat equation and solute diffusion equation is solved numerically. To overcome the stiffness caused by the nonlinear term in Allen-Cahn equation, We propose a semi-implicit scheme based on a convex splitting of the free energy. By a proper splitting of the free energy functional, it can be shown that the semi-implicit scheme is unconditionally energy stable. To demonstrate its efficiency, this numerical method is also compared with the method of exponential integrators. We then give a systematic numerical study of the zone melting process. The results are also compared with the experimental results. The efficiency of the zone melting is analyzed. We expect our numerical model and results will provide some guidance for future experiments and applications.