An Interpretable GWO-LSTM-SA Model for Crystal Diameter Prediction in Czochralski Process

The growth process of Czochralski silicon single crystal (Cz-SSC) has problems such as high nonlinearity and time-varying working conditions, making it difficult to develop a precise crystal diameter model through first principles. To address this problem, an interpretable long short-term memory network model (LSTM-SA) based on self-attention is proposed and used to predict crystal diameter. Firstly, the maximum mutual information coefficient (MIC) for selecting the characteristic variables related to the crystal diameter is used. Secondly, the SA mechanism is integrated into the LSTM network, which helps the model automatically learn and focus on the time periods and key variable information that have a significant impact on the prediction of the crystal diameter index. Then, the network parameters of the LSTM are optimized using the gray wolf optimization (GWO) algorithm to achieve the best prediction. Finally, using SHAP algorithm to complete the interpretability of crystal diameter prediction results, to quantitatively obtain the contribution and direction of different characteristic variables to the prediction results. Based on the actual industrial data, an interpretable prediction model GWO-LSTM-SA for crystal diameter was established. The experimental results show that the proposed method provides accurate predictions and interpretable results compared to other conventional models.