Physics-Informed Neural Network-Based Prediction of V/G Value in Czochralski Silicon Single Crystal Growth Process

To address the challenges of inadequate soft-sensing accuracy and generalization capability for the quality-related variable, the V/G value, in the growth process of traditional semiconductor-grade silicon single crystals, this study proposes a Physics-Informed Neural Network (PINN)-based prediction method that integrates the partial differential equations (PDEs) of crystal heat transfer with neural networks. This method achieves an organic integration of mechanistic and deep learning models by incorporating the crystal heat transfer equations and their boundary conditions as physical constraints into the neural network’s loss function. The experimental outcomes indicate that the PINN model achieves high-precision predictions of both crystal temperature distributions and solid-liquid interface V/G value, and significantly enhancing computational efficiency compared to traditional solution methods, thereby providing a novel technical approach for real-time monitoring of V/G value in crystal growth processes.