CNN–BiLSTM–Attention-Based Hybrid-Driven Modeling for Diameter Prediction of Czochralski Silicon Single Crystals

High-precision prediction of the crystal diameter during the growth of electronic-grade silicon single crystals is a critical step for the fabrication of high-quality single crystals. However, the process features high-temperature operation, strong nonlinearities, significant time-delay dynamics, and external disturbances, which limit the accuracy of conventional mechanism-based models. In this study, mechanism-based models denote physics-informed heat-transfer and geometric models that relate heater power and pulling rate to diameter evolution. To address this challenge, this paper proposes a hybrid deep learning model combining a convolutional neural network (CNN), a bidirectional long short-term memory network (BiLSTM), and self-attention to improve diameter prediction during the shoulder-formation and constant-diameter stages. The proposed model leverages the CNN to extract localized spatial features from multi-source sensor data, employs the BiLSTM to capture temporal dependencies inherent to the crystal growth process, and utilizes the self-attention mechanism to dynamically highlight critical feature information, thereby substantially enhancing the model’s capacity to represent complex industrial operating conditions. Experiments on operational production data collected from an industrial Czochralski (Cz) furnace, model TDR-180, demonstrate improved prediction accuracy and robustness over mechanism-based and single data-driven baselines, supporting practical process control and production optimization.