(617c) Predictive Modeling and Optimal Control of a Particulate Polysilicon Reactor System for Enhanced Solar Cell Manufacturing

In 2022, the global photovoltaic industry reached the terawatt era, with a cumulative installed capacity of 1.185 GW [1]. Crystal silicon cells represent over 95% of this capacity [2]. Solar-grade silicon, a high-purity polysilicon, is pivotal in the photovoltaic industry, particularly in manufacturing solar panels. It accounts for approximately 20% of the total solar cell manufacturing cost. Consequently, reducing the production cost of solar-grade silicon is a primary factor in enhancing the solar manufacturing process. Several technologies have been explored based on different intermediate Si gaseous species. However, the Siemens process remains the dominant technology for 90% of global polysilicon production. Despite being a mature technology in the photovoltaic industry, it has significant limitations, including its batch-processing nature and energy inefficiency.

Fluidized-bed reactors (FBR) emerge as a promising technology for solar-grade silicon production, representing a more energy-efficient process with more significant operational benefits than the conventional Siemens process. Their performance has been assessed by various experimental [3-4] and computational studies [5-7]. However, controlling the FBR system is challenging due to the complex gas-solid interactions. Several multiphase gas-solid modeling approaches using computational fluid dynamic tools have been developed to predict and analyze FBR system dynamics. Limited research has been conducted on model-based control strategies for enhancing silicon production in FBR systems. Prior research has primarily employed traditional control methods due to the complexity of the models. In addition, the control approaches have been solely used to regulate mass hold-up and particle size distribution, overlooking the objective of minimizing powder loss to enhance process yield. Advanced control strategies, such as model predictive control (MPC), appear promising to address these challenges.

This work presents a predictive modeling framework for silicon production in FBRs, suitable for real-time optimization and control applications. The proposed model characterizes the particle size distribution of the product and the powder loss. Two different flow regime modeling approaches are considered to describe the silane pyrolysis reaction and to represent the deposition rate contributing to particle growth. A discrete population balance equation is employed to estimate the particle size distribution as a function of the deposition rate. Subsequently, a nonlinear model predictive control is utilized to regulate the system towards the desired operating conditions. Detailed open-loop and closed-loop simulation studies demonstrate the successful integration of nonlinear MPC and the proposed predictive modeling approach.

References:

[1] Yu, Y., Bai, X., Li, S., Shi, J., Wang, L., Xi, F., Ma, W., and Deng, R. (2023). Review of silicon recovery in the photovoltaic industry. Current Opinion in Green and Sustainable Chemistry, page 100870.

[2] Ballif, C., Haug, F.-J., Boccard, M., Verlinden, P. J., and Hahn, G. (2022). Status and perspectives of crystalline silicon photovoltaics in research and industry. Nature Reviews Materials, 7(8):597-616.

[3] Cadoret, L., Reuge, N., Pannala, S., Syamlal, M., Coufort, C., and Caussat, B. (2007). Silicon CVD on powders in fluidized bed: Experimental and multifluid Eulerian modeling study. Surface and Coatings Technology, 201(22-23):8919-8923.

[4] Hashimoto, K., Miura, K., Masuda, T., Toma, M., Sawai, H., and Kawase, M. (1990). Growth kinetics of polycrystalline silicon from silane by thermal chemical vapor deposition method. Journal of the Electrochemical Society, 137(3):1000.

[5] Chanlaor, P., Limtrakul, S., Vatanatham, T., and Ramachandran, P. A. (2018). Modeling of chemical vapor deposition of silane for silicon production in a spouted bed via discrete element method coupled with Eulerian model. Industrial & Engineering Chemistry Research, 57(36):12096-12112.

[6] Du, J., Dutta, S., and Ydstie, B. E. (2014). Modeling and control of solar-grade silicon production in a fluidized bed reactor. AIChE Journal, 60(5):1740–1751.

[7] Tejero-Ezpeleta, M. P., Buchholz, S., and Mleczko, L. (2004). Optimization of reaction conditions in a fluidized bed for silane pyrolysis. The Canadian Journal of Chemical Engineering, 82(3):520–529.