MPC Based Feedforward Trajectory for Pulling Speed Tracking Control in the Commercial Czochralski Crystallization Process

In this work, we propose a simple but efficient method to design a target temperature trajectory for pulling speed tracking control of the crystal grower in the Czochralski crystallization process. In the suggested method, the model predictive control strategy is used to incorporate the complex dynamic effect of the heater temperature on the pulling speed into the temperature trajectory design quantitatively. The feedforward trajectories designed by the proposed method were implemented on 200 mm and 300 mm silicon crystal growers in the commercial Czochralski process. The application results have demonstrated its excellent and consistent tracking performance of pulling speed along whole bulk crystal growth.