Hybrid Mechanism–Data-Driven Modeling for Crystal Quality Prediction in Czochralski Process

The V/G criterion is a critical indicator for monitoring dynamic changes during Czochralski silicon single crystal (Cz-SSC) growth. However, the inability to measure it in real time forces reliance on offline feedback for process regulation, leading to imprecise control and compromised crystal quality. To overcome this limitation, this paper proposes a novel soft sensor modeling framework that integrates both mechanism-based knowledge and data-driven learning for the real-time prediction of the crystal quality parameter, specifically the V/G value (the ratio of growth rate to axial temperature gradient). The proposed approach constructs a hybrid prediction model by combining a data-driven sub-model with a physics-informed mechanism sub-model. The data-driven component is developed using an attention-based dynamic stacked enhanced autoencoder (AD-SEAE) network, where the SEAE structure introduces layer-wise reconstruction operations to mitigate information loss during hierarchical feature extraction. Furthermore, an attention mechanism is incorporated to dynamically weigh historical and current samples, thereby enhancing the temporal representation of process dynamics. In addition, a robust ensemble approach is achieved by fusing the outputs of two subsidiary models using an adaptive weighting strategy based on prediction accuracy, thereby enabling more reliable V/G predictions under varying operational conditions. Experimental validation using actual industrial Cz-SSC production data demonstrates that the proposed method achieves high-prediction accuracy and effectively supports real-time process optimization and quality monitoring.