Modeling of Quality Factor and Process Parameter Optimization in Czochralski Silicon Single Crystal Growth

To address the increasingly stringent process requirements in Czochralski silicon single crystal growth, this paper proposes a hybrid process parameter optimization strategy integrating a DBN-RBF fusion model with an improved SPEA2 algorithm, taking the shape variable of solid-liquid interface$h$and the defect evaluation criteria$V / G$in quality factors as objective functions. The proposed strategy constructs a DBN-RBF fusion model by integrating Deep Belief Network (DBN) and Radial Basis Function Neural Network (RBFNN), establishing predictive models for the shape variable of solid-liquid interface and the defect evaluation criteria. Subsequently, an enhanced Strength Pareto Evolutionary Algorithm 2 with Cauchy distribution mutation strategy (SPEA2-C) is developed to optimize key process parameters including crucible temperature and crystal pulling rate. The experimental results show that the maximum difference between the numerical simulation and the optimization results is 2.9%, while the actual shape variable of solid-liquid interface measurement error is only 2.9%, which verifies the effectiveness and high precision of the strategy in the process parameter optimization, and can be applied to the growth process parameter optimization of high-quality silicon single crystal.