The goal of the research in this thesis is to extend the understanding of the physics involved in the heat exchanger method growth of bismuth germanium oxide crystals, and the silicon single crystals growth in batchwise and continuous Czochralski systems. The specific objectives focus on the investigation of heat, mass and momentum transport phenomena in crystal growth systems. These objectives have been met by constructing a comprehensive pseudo steady state and transient models describing the crystal growth process.
The transient analyses of heat exchanger method that have been presented in this thesis are meaningful because these are the first time dependent simulation of bismuth germanium oxide crystals growth in the heat exchanger growth system. In the numerical analyses of heat transfer, hydrodynamics and free boundaries in Czochralski silicon growth, the success in better understanding the physics involved in the Czochralski process is evident, and the development of mathematical model which is suitable for dynamic simulation of Czochralski process by eliminating the simplifying assumption, such as crystal height or melt volume, are some degree of success. Dynamic simulations of two dimensional dopant distribution in batchwise and continuous Czochralski silicon growth are a platform for future extensions of the model to make quantitative predictions of mass transfer process.
Robust numerical algorithms for solution of nonlinear free and moving boundary problems were constructed for quasi-steady state and transient model by systematic implementation of finite element discretization and implicit time integration method in transient models for the resulting differential algebraic set of equations. Newton/Raphson method, coupled with frontal elimination method for linear systems, was effective in solving the large set of nonlinear algebraic equations.
The growth of bismuth germanium oxide crystal (BGO) in the heat exchanger method is simulated with the heat ...