Nonlinear model-based control of the Czochralski process I: Motivation, modeling and feedback controller design

This paper presents a new approach for model-based control of the Czochralski process. The main idea is not to rely on a complex mathematical model of the overall process. Such a model usually suffers from many unknown parameters, boundary and initial conditions making the control system not robust. Instead, only those parts of the process are modeled the parameters of which are known with sufficient accuracy and the structure of which is sufficiently precise. From this model a nonlinear model-based controller is derived as the core of the proposed control system. It is used in combination with conventional PID controllers. Doing so, tracking of crystal diameter and growth rate trajectories is realized with a lot of model knowledge included in the control system. Thus, its performance is improved greatly. The usefulness of the approach is proven by several experimental results from growth of gallium-arsenide (GaAs) and indium-phosphide (InP) crystals.