“A Sensor Fusion Algorithm for Filtering Pyrometer Measurement Noise in the Czochralski Crystallization Process”

Authors: Magnus Komperød, John A. Bones and Bernt Lie,
Affiliation: Østfold University College, SINTEF and Telemark University College
Reference: 2011, Vol 32, No 1, pp. 17-32.

Keywords: Complementary filters, Czochralski crystallization process, Measurement noise filtering, Pyrometer temperature measurement, Sensor fusion algorithm

Abstract: The Czochralski (CZ) crystallization process is used to produce monocrystalline silicon for solar cell wafers and electronics. Tight temperature control of the molten silicon is most important for achieving high crystal quality. SINTEF Materials and Chemistry operates a CZ process. During one CZ batch, two pyrometers were used for temperature measurement. The silicon pyrometer measures the temperature of the molten silicon. This pyrometer is assumed to be accurate, but has much high-frequency measurement noise. The graphite pyrometer measures the temperature of a graphite material. This pyrometer has little measurement noise. There is quite a good correlation between the two pyrometer measurements. This paper presents a sensor fusion algorithm that merges the two pyrometer signals for producing a temperature estimate with little measurement noise, while having significantly less phase lag than traditional lowpass- filtering of the silicon pyrometer. The algorithm consists of two sub-algorithms: (i) A dynamic model is used to estimate the silicon temperature based on the graphite pyrometer, and (ii) a lowpass filter and a highpass filter designed as complementary filters. The complementary filters are used to lowpass-filter the silicon pyrometer, highpass-filter the dynamic model output, and merge these filtered signals. Hence, the lowpass filter attenuates noise from the silicon pyrometer, while the graphite pyrometer and the dynamic model estimate those frequency components of the silicon temperature that are lost when lowpass-filtering the silicon pyrometer. The algorithm works well within a limited temperature range. To handle a larger temperature range, more research must be done to understand the process´ nonlinear dynamics, and build this into the dynamic model.

PDF PDF (556 Kb)        DOI: 10.4173/mic.2011.1.2

References:
[1] Brown, R. G. Hwang, P. Y. C. (1997). Introduction to random signals and applied Kalman Filtering - 3rd edition, John Wiley and& Sons Inc.
[2] Haugen, F. (2004). Dynamic Systems - Modeling, Analysis and Simulation, Tapir Academic Press, Trondheim, Norway.
[3] Irizarry-Rivera, R. Seider, W. D. (1997). Model-predictive control of the Czochralski crystallization process Part I, Conduction-dominated melt. Journal of Crystal Growth, 178:593-611 doi:10.1016/S0022-0248(97)00085-7
[4] Irizarry-Rivera, R. Seider, W. D. (1997). Model-predictive control of the Czochralski crystallization process Part II, Reduced-order convection model. Journal of Crystal Growth, 178:612-633 doi:10.1016/S0022-0248(97)00086-9
[5] Lan, C. W. (2004). Recent progress of crystal growth modeling and growth control, Chemical Engineering Science, 59:1437-1457 doi:10.1016/j.ces.2004.01.010
[6] Lee, K., Lee, D., Park, J., Lee, M. (2005). 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.
[7] Ljung, L. (1999). System Identification - Theory for the User, 2nd Edition, Prentice-Hall, Upper Saddle River, New Jersey.
[8] Ljung, L. (2009). System Identification Toolbox 7 - User´s Guide, The MathWorks, Inc.
[9] Lyons, R. G. (2011). Understanding digital signal processing - 3rd edition, Prentice Hall.


BibTeX:
@article{MIC-2011-1-2,
  title={{A Sensor Fusion Algorithm for Filtering Pyrometer Measurement Noise in the Czochralski Crystallization Process}},
  author={Komperød, Magnus and Bones, John A. and Lie, Bernt},
  journal={Modeling, Identification and Control},
  volume={32},
  number={1},
  pages={17--32},
  year={2011},
  doi={10.4173/mic.2011.1.2},
  publisher={Norwegian Society of Automatic Control}
};