Research on V/G Value Prediction Method for Silicon Single-Crystal Growth Based on Multi-Condition Invariant Feature Extraction

In the Czochralski process of silicon single-crystal growth, the V/G value at the solid–liquid interface is a key parameter affecting intrinsic crystal defects. However, online V/G detection remains difficult because the temperature gradient G cannot be directly measured, while multi-condition distribution shifts and limited labeled data reduce the robustness of data-driven models. To address these issues, this paper proposes DWC-ISBiGNN, an adaptive multi-condition invariant feature extraction method based on the Invariant-Specific Bidirectional Graph Neural Network. The proposed method introduces dynamic sample graph construction with stage-aware global nodes to capture non-stationary process correlations, source-domain credibility weighting to suppress negative transfer, and a semi-supervised training framework combining stage-conditional alignment with teacher–student regression consistency to exploit unlabeled target-domain data. Experiments on industrial data from a 12-inch silicon single-crystal production line show that DWC-ISBiGNN achieves an RMSE of 0.0041, an MAE of 0.00285, and an $R^2$ of 0.9549. Compared with the original IS-BiGNN, the RMSE is reduced by 32.6%, and $R^2$ is increased by 5.43 percentage points. The results demonstrate that the proposed method provides an effective soft-sensing approach for V/G prediction under multiple operating conditions.