Dynamics and control of the Czochralski process: I. Modelling and dynamic characterization

A nonlinear dynamic model of the Czochralski process, valid throughout the batch growth cycle is derived for use in designing an improved process controller. The model is a lumped element representation of the major system components, and simulates the dynamic system response to disturbances and system inputs. The linearized model is used to determine the system eigenstructure, revealing the system stability, transient response constants, and coupling. Significant results for control design include the identification of the basic time varying nature of the eigenstructure and the disturbances acting on the system, and identification of mechanisms that affect the transient system characteristics. In addition, the growth dynamic effects of liquid encapsulation, low thermal gradient schemes, and magnetic fields are discussed.