**Page description appears here**

“Empirical Modeling of Heating Element Power for the Czochralski Crystallization Process”

Authors: Magnus Komperød and Bernt Lie,
Affiliation: Østfold University College and Telemark University College
Reference: 2010, Vol 31, No 1, pp. 19-34.

     Valid XHTML 1.0 Strict

Keywords: Czochralski Crystallization Process, Empirical Modeling, Hammerstein-Wiener Model, Heating Element, Nonlinear System Identification

Abstract: The Czochralski (CZ) crystallization process is used to produce monocrystalline silicon. Monocrystalline silicon is used in solar cell wafers and in computers and electronics. The CZ process is a batch process, where multicrystalline silicon is melted in a crucible and later solidifies on a monocrystalline seed crystal. The crucible is heated using a heating element where the power is manipulated using a triode for alternating current (TRIAC). As the electric resistance of the heating element increases by increased temperature, there are significant dynamics from the TRIAC input signal (control system output) to the actual (measured) heating element power. The present paper focuses on empirical modeling of these dynamics. The modeling is based on a dataset logged from a real-life CZ process. Initially the dataset is preprocessed by detrending and handling outliers. Next, linear ARX, ARMAX, and output error (OE) models are identfied. As the linear models do not fully explain the process´ behavior, nonlinear system identification is applied. The Hammerstein-Wiener (HW) model structure is chosen. The final model identified is a Hammerstein model, i.e. a HW model with nonlinearity at the input, but not at the output. This model has only one more identified parameter than the linear OE model, but still improves the optimization criterion (mean squared ballistic simulation errors) by a factor of six. As there is no nonlinearity at the output, the dynamics from the prediction error to the model output are linear, which allows a noise model to be added. Comparison of a Hammerstein model with noise model and the linear ARMAX model, both optimized for mean squared one-step-ahead prediction errors, shows that this optimization criterion is 42% lower for the Hammerstein model. Minimizing the number of parameters to be identified has been an important consideration throughout the modeling work.

PDF PDF (366 Kb)        DOI: 10.4173/mic.2010.1.2

[1] Komperød, M., Hauge, T., Lie, B. (2008). Preprocessing of experimental data for use in model building and model validation, In The 49th Scandinavian Conference on Simulation and Modeling.SIMS 2008. Oslo, Norway.
[2] Lee, K., Lee, D., Park, J., Lee, M. (2005). URL, MPC based feedforward trajectory for pulling speed tracking control in the commercial Czochralski crystallization process. International Journal of Control, Automation, and Systems, 3:252-257.
[3] Ljung, L. (1999). System Identification - Theory for the User, 2nd Edition, Prentice-Hall, Upper Saddle River, New Jersey.
[4] Ljung, L. (2009). System Identification Toolbox 7 - User´s Guide, The MathWorks, Inc.

  title={{Empirical Modeling of Heating Element Power for the Czochralski Crystallization Process}},
  author={Komperød, Magnus and Lie, Bernt},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.