Modeling and application of Czochralski silicon single crystal growth process using hybrid model of data-driven and mechanism-based methodologies

Abstract Czochralski (Cz) silicon single crystal growth process is a large delay, nonlinear dynamic time-varying system with complex physicochemical reactions, multi-field and multi-phase coupling, and its modeling and control has always been a problem in the automatic control field. In this paper, a hybrid modeling method based on the data-driven model and mechanism model is proposed, and applied to the Cz silicon crystal growth process modeling. Firstly, to simplify the model complexity and improve the model accuracy, the crystal growth process model is divided into the energy transfer model and a hydrodynamic and geometric model. Here, a Hammerstein–Wiener model based on a long short-term memory network (LSTM-Hammerstein–Wiener) is established for the energy transfer process with multiple heat transfer links and hysteresis effect. Further, a novel robust LSTM-Hammerstein–Wiener model is proposed by introducing the M-estimation method, which avoids the effect of the outliers on model robustness. Secondly, the proposed robust LSTM-Hammerstein–Wiener is combined with the hydrodynamic and geometric model to obtain the hybrid model between the heater power and the crystal diameter. Meanwhile, the crystal diameter error compensation model is established to reduce the unmodeled dynamics of the mechanism model, thereby improving the accuracy of the hybrid model. Besides, the proposed hybrid model is applied to the model-free adaptive control of silicon single crystal diameter. Finally, various data experiment results based on actual operating data verify the effectiveness of the proposed hybrid model.