Gray-Box Model-Based Predictive Control of Czochralski Process with Successive Model Update

Abstract

The Czochralski (CZ) process, a well-established monocrystalline silicon ingot production process, is a nonlinear, time-varying batch process. In the semiconductor industry, it is desirable to improve the control method and manufacture higher-quality 300-mm-diameter silicon ingots at a lower cost. The authors developed a nonlinear model predictive control method based on the gray-box (GB) model of the CZ process and successive linearization. This study proposes a method for updating the prediction model, to handle a plant-model mismatch. The proposed method constructs several GB models beforehand and selects a proper model based on the moving horizon estimation. This method was applied to the GB model-based predictive control, and its disturbance rejection performance was compared with that of the conventional control method without a model update. The obtained control simulation results demonstrated that the sums of the integral absolute errors of the controlled variables using the proposed method were smaller than those using the conventional method in 128/180 simulations.