Data-Driven Coordinated Control of Czochralski Silicon Single Crystal Growth Operation Process Based on Indirect Control Strategy

Conventional control strategies for crystal growth often focus solely on regulating the crystal diameter, while neglecting fluctuations in the thermal field temperature. This oversight leads to process instability in Czochralski silicon single crystal growth (Cz-SSCG) and hinders the consistent production of high-quality crystals. To address this issue, this paper proposes a data-driven coordinated control method based on an indirect control strategy, aimed at simultaneously regulating both the crystal diameter and the thermal field temperature by dynamically tuning the virtual set-point of the thermal field temperature in real time. Firstly, a data-driven crystal diameter prediction controller is developed, leveraging a dynamic linearization approach to facilitate real-time tuning of the virtual thermal field temperature set-point. Within this framework, an adaptive controller parameter update strategy is proposed by optimizing the objective function of the predictive control model for crystal diameter regulation. Additionally, an extended state observer is designed to estimate external disturbances and integrated into the predictive controller to mitigate their impact on both diameter control and temperature set-point tuning. Finally, a local PID controller is employed to realize the indirect regulation of the crystal diameter. The convergence of the optimal control approach for the thermal field temperature set-point adjustment is mathematically proven. The effectiveness of the proposed method is validated through a coordinated control case study for Cz-SSCG.