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454911 Gray-Box Modeling of 300mm Czochralski Single-Crystal Si Production Process

In this research, a statistical model is embedded into the first-principle model proposed by Zheng et al. (2015) to further improve the model accuracy, since a first-principle model of .the dynamics of the meniscus height is difficult to build. The statistical model is used for estimating a key parameter in the nonlinear first-principle model, which significantly affects the meniscus height. Moving window partial least squares (MWPLS) is used to develop the statistical model since it can cope with the time-varying characteristics of CZ process, which originate from changes in the crystal length and the crucible position. The developed gray-box model was applied to a 300 mm CZ single-crystal silicon production process. It was confirmed that the accuracy of the developed model was much better than the model proposed by Zheng et al. (2015).

**References**

J. Abdollahi, M. Izadi, and S. Dubljevic. Model predictive temperature tracking in crystal growth processes. *Comput. Chem. Eng.*, 71:323–330, 2014.

M. A. Gevelber and G. Stephanopoulos. Dynamics and control of the Czochralski process I. Modelling and dynamic characterization. *J. Cryst. Growth*, 84:647–668, 1987.

R. Irizarry-Rivera and W. D. Seider. Model-predictive control of the Czochralski crystallization process part I. Conduction-dominated melt. *J. Cryst. Growth*, 178:593–611, 1997.

K. Lee, D. Lee, J. Park, and M. Lee. MPC based feedforward trajectory for pulling speed tracking control in the commercial Czochralski crystallization process. *Int. J. Cont. Autom.*, 3:252–257, 2005

J. Ng and S. Dubljevic. Optimal control of convection-diffusion process with time-varying spatial domain: Czochralski crystal growth. *J. Proc. Cont.*, 21:1361–1369, 2011.

J. Winkler, M. Neubert, and J. Rudolph. Nonlinear model-based control of the Czochralski process I: Motivation, modeling and feedback controller design. *J. Cryst. Growth*, 312:1005–1018, 2010.

Z. Zheng, T. Seto, S. Kim, M. Kano, T. Fujiwara, M. Mizuta, and S. Hasebe. Development of a first principle model of Czochralski process and its verification with real industrial data. *APCChE 2015*, Melbourne, Australia, Sep. 2015.

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