Soft measurement of interface shape variation in Czochralski silicon crystal growth using an improved transformer model

Interface shape deviation directly influences stress distribution, oxygen concentration, and defect formation during the Czochralski silicon crystal growth process and thus serves as a critical indicator of crystal quality. However, the strong coupling among multiple physical fields, pronounced dynamic nonlinearity, and frequent process disturbances make the interface shape deviation extremely difficult to measure directly. To address this challenge, this study proposes a soft-sensing model for interface shape deviation based on a Local Sparse Attention Transformer (LSA-Transformer). The model integrates a local multi-head attention mechanism to enhance sensitivity to short-term disturbances and nonlinear dynamics, while a uniformly distributed sparse attention strategy is introduced to efficiently capture long-term dependencies and reduce redundant attention computation. Experiments were conducted using real crystal growth process data and compared with several representative data-driven models, including backpropagation neural networks, support vector machines, long short-term memory networks, TCNs, informers, and the standard transformer. The results show that the proposed model achieves the best predictive performance across all evaluation metrics, obtaining an RMSE of 0.01 308, MAE of 0.0 105, MAPE of 1.05%, and R2 of 0.93 805 on the test dataset. Compared with the standard transformer, the proposed method improves prediction accuracy by ∼18.7% while also maintaining lower computational overhead. These results demonstrate that the proposed LSA-Transformer provides an effective and robust solution for soft sensing of interface shape deviation, offering significant potential for intelligent monitoring and quality control in silicon single-crystal growth processes.