Shape estimation for online diameter calibration in Czochralski silicon crystal growth

Steven L. Kimbel; Joseph A. O'Sullivan

doi:10.1117/12.417181

2 February 2001 Shape estimation for online diameter calibration in Czochralski silicon crystal growth

Steven L. Kimbel, Joseph A. O'Sullivan

Proceedings Volume 4188, Process Imaging for Automatic Control; (2001) https://doi.org/10.1117/12.417181
Event: Intelligent Systems and Smart Manufacturing, 2000, Boston, MA, United States

Abstract

The diameter setpoint of a growing crystal in the silicon Czochralski process is a key cost parameter, whose optimal choice depends in part upon the diameter calibration accuracy. Measurement of the crystal diameter during solidification is made remotely, due to high temperatures and vacuum vessel design. Vision systems for diameter control detect the diameter of the bright ring reflection from the silicon melt surface at the crystal meniscus, rather than the actual crystal diameter. Distortion due to the bright ring measurement would result in a destabilizing nonlinear diameter measurement even if the crystal diameter response were linear. Using a published model of the meniscus shape, two and three-dimensional modeling of the bright ring is performed, and simple approximations are made to predict the bright ring bias as a function of diameter slope. Tracking of a diameter maximum during vertical translation could provide a calibration measure, given accurate translation data. The use of deformable templates or snakes is suggested for tracking the diameter maximum, and is bench-tested to provide estimates of on-line calibration accuracy, a key parameter for selection of the optimum diameter setpoint. Implementation of the modified calibration strategy requires corrections for camera distortion, crystal thermal expansion and window diffraction.

Citation Download Citation

Steven L. Kimbel and Joseph A. O'Sullivan "Shape estimation for online diameter calibration in Czochralski silicon crystal growth", Proc. SPIE 4188, Process Imaging for Automatic Control, (2 February 2001); https://doi.org/10.1117/12.417181

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