Improved Langevin Surrogate-Assisted Process-Parameter Optimization for Candidate Recipe Generation in Czochralski Silicon Single Crystal Growth

To support offline process-parameter screening for Czochralski (CZ) silicon single crystal growth, this paper proposes a surrogate-assisted optimization framework based on an improved Langevin evolutionary algorithm. First, a multi-variable constrained optimization model is established, with the LSA-Transformer-predicted solid–liquid interface deformation used as the objective evaluation and with process-smoothness and physical-feasibility constraints considered. Six key process parameters–heater power, pulling rate, argon flow rate, crystal rotation speed, crucible rotation speed, and magnetic field strength–are selected as decision variables. Second, building on the classical Langevin algorithm, an adaptive inertia weight mechanism, a diversity promoter (DP) operator, and a local escaping operator (LEO) are introduced to improve global exploration and local optima escape in complex search spaces. Verification on 23 classical benchmark functions indicates that the ILEE algorithm shows competitive overall performance and achieves better or comparable results on many functions when compared with particle swarm optimization (PSO), grey wolf optimization (GWO), the original Langevin evolutionary algorithm (LEE), and other baseline algorithms. The proposed framework is then used for offline candidate recipe generation during the crystal equal-diameter growth stage (200 mm, 400 mm, 600 mm, 800 mm, and 1000 mm). The optimized candidate parameter combinations yield lower surrogate-predicted interface deformation under the given LSA-Transformer model and physical constraints. Because these values are not independent CFD or experimental measurements, the results should be interpreted as process-parameter guidance for future physical validation. This work provides a feasible surrogate-assisted offline screening framework for CZ silicon single crystal growth.