Modeling and Simulation of Czochralski Bulk Crystal Growth Process

The main objective of this book aims at developing a new generation of software product, in order to obtain a fully automatic simulator predicting the entire Czochralski process. Firstly, new efficient, robust and high-quality mesh generation algorithms for any complex geometry were implemented. A Finite Element Navier-Stokes solver based on unstructured meshes was developed. Enhanced turbulence models, together with a generic transformation method to avoid negative k when solving the turbulent kinetic energy equation by the Newton-Raphson method were implemented. Moreover, mathematical models governing the gas convection and oxygen distribution in the silicon melt were developed, and numerical methods to solve these governing equations were implemented, while appropriate numerical approaches to capture the wall shear stress along the meniscus experienced by the silicon melt were investigated. Numerical experiments devoted to investigate the industrial Czochralski process are presented. Comparisons of the simulation results with literature and experimental observations are also presented, and conclusions are drawn based on these results and observations.