Modeling and Simulation of Czochralski Bulk Crystal Growth Process

The main objective of this book aims at developinga new generation of software product in order toobtain a fully automatic simulator predicting theentire Czochralski process.Firstly new efficient robust and high-quality meshgeneration algorithms for any complex geometry wereimplemented.A Finite Element Navier-Stokes solver based onunstructured meshes was developed. Enhancedturbulence models together with a generictransformation method to avoid negative k whensolving the turbulent kinetic energy equation by theNewton-Raphson method were implemented. Moreovermathematical models governing the gas convection andoxygen distribution in the silicon melt weredeveloped and numerical methods to solve thesegoverning equations were implemented whileappropriate numerical approaches to capture the wallshear stress along the meniscus experienced by thesilicon melt were investigated.Numerical experiments devoted to investigate theindustrial Czochralski process are presented.Comparisons of the simulation results with literatureand experimental observations are also presented andconclusions are drawn based on these results andobservations.