This study proposes a data-driven framework with post hoc interpretability analysis for one-step-ahead crystal diameter prediction in the Czochralski (CZ) silicon single-crystal growth process. To address the strong multivariable coupling, nonlinear dynamics, variable-specific delays, and difficulty of online measurement in CZ growth, the maximal information coefficient (MIC) was first used to screen key auxiliary variables from industrial process data. The Grey Wolf Optimizer (GWO) was then employed for multi-variable delay estimation and feature alignment, and a hybrid temporal convolutional network (TCN)–long short-term memory (LSTM) model was constructed to combine local temporal feature extraction with long-term dependency learning. Four input configurations were designed according to whether lag alignment and diameter history were included, and the proposed TCN-LSTM was systematically compared with standalone TCN and LSTM models. The results show that both diameter history and delay alignment improve prediction performance. Under the current single-run evaluation protocol, the TCN-LSTM configurations yielded lower prediction errors than the corresponding TCN and LSTM models under the same input settings. Under the withlag-withY configuration, the TCN-LSTM model achieved MSE = 0.00259, RMSE = 0.05087, MAE = 0.03949, and R2 = 0.96982. After GWO-based hyperparameter optimization, the best TCN-LSTM configuration further improved to MSE = 0.00239, RMSE = 0.04894, MAE = 0.03651, and R2 = 0.97207. SHAP-based analysis was further used to provide a post hoc interpretation of the relative contributions of key process variables to diameter variation. Overall, the proposed framework provides a data-driven prediction approach and may support subsequent process analysis and optimization in industrial CZ growth.
Pan et al. (Fri,) studied this question.
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