טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSheinman Roman
SubjectFeedback Control of Bridgman Crystallization
DepartmentDepartment of Chemical Engineering
Supervisors Professor Daniel Lewin
Professor Simon Brandon


Abstract

The vertical Bridgman process for growth of large crystals is based on the gradual cooling of the melt by the slow movement of the furnace from the hot to the cold zone. The main demand from the process is the highest crystal quality, as quantified on a microscopic level as uniformity in crystal structure. The problem of quality originates from morphological instability of the growing interface. It is possible to define characteristics quantitatively describing the stability limits.

Factors that can affect the stability are distributions of temperature and of solute concentration in the vicinity of the interface. Both of these are influenced by the velocity with which the ampoule with melt is pulled off the heater. A reduced-order model has been developed to predict the onset of instability, which uses a quasi steady state approximation for temperature distribution, and “Stirred Tanks in Series” model for distribution of solute. The parameters of the reduced model were been fitted to a detailed finite element model.

The availability of the reduced-order model facilitates process optimization. The targets of the optimization procedure are to maximize the crystal quality in the least amount of time.

The next step is the implementation of a model predictive control (MPC). The controller utilizes the receding horizon method by performing the previously developed optimization procedure to estimate an optimal profile of the pulling velocity and adjusts it each step. The controller is tested against FEM simulator.