What is Self-Calibration?

A problem arises because modern manufacturing and measuring instruments are so precise, with reproducibility in nanometers, that there are no standard measurement grids of comparable accuracy with which to calibrate them.  A mathematically rigorous approach for calibrating high-precision stages uses the stage to calibrate itself.   This approach called self-calibration offers many advantages, including the possibility of standardizing measurements of accuracy.

Self-calibration, or more specifically positional or dimensional self-calibration, refers to the use of an imperfectly calibrated measuring instrument and one or more imperfectly calibrated measurement grid artifacts to improve the calibration of the instrument and the artifact(s). To impart a standard scale, one artifact must include an accurately calibrated one-dimensional scale gauge, or an additional measurement of an artifact must be made on a standardized line-scale measuring instrument.

Typically, as a convenient mathematical idealization, a measuring instrument is modeled by assuming that measurements are continuous, one-to-one and reproducible to within a small random error. An artifact is modeled by assuming that its grid points are rigidly fixed in relationship to one another, or that the artifact flexes or is strained slightly in a predictable manner in each measurement position.

Self-calibration requires an understanding of how to place an artifact, or multiple artifacts, in various positions within the workspace of the measuring instrument, so that the measurements result in a well-conditioned system of equations for determining accurate corrections for the artifact measurements, subject to the model constraints. The correction factors for the instrument’s coordinate system and for the artifact’s grid-point measurements may be solved simultaneously. Or the problem may be so formulated that improved artifact measurements are deduced first, then these are used to improve the coordinate system of the measuring instrument. The net effect of self-calibration is that the grid pattern of the artifact in any one of its measured positions is congruent (to within measurement random error) to the grid pattern in any other of its measured positions.

In 1984 Dr. Michael Raugh patented the first algorithm for self-calibrating e-beam lithography stages that was based on an in-depth mathematical analysis. In 1985 Raugh published the first statement of necessary and sufficient conditions for stage self-calibration. Dr. Raugh is a retired professor of mathematics and applied mathematician who consults through Interconnect Technologies, LLC.

NIST awarded 2 contracts to Interconnect Technologies Corporation to research and develop algorithms and procedures for self-calibration of high-precision two-dimensional stages, with Dr. Raugh serving as Principal Investigator.

US4583298  1984 Auto calibration method suitable for use in electron beam lithography, Inventor:  Raugh; Michael R., Palo Alto, CA

US05798947   1998 Methods, apparatus and computer program products for self-calibrating two-dimensional metrology stages .  Inventors:  Ye; Jun, Palo Alto, CA.   Pease; Roger Fabian Wedgwood, Arlington, VA. Takac; Michael T., San Jose, CA

Raugh, Michael R., "Error estimation for lattice methods of stage self-calibration," SPIE Proceedings: Microlithography ‘97: SPIE’s 22nd Annual International Symposium on Microlithography, 9-14 March, 1997, Santa Clara, CA.

Jun Ye, Errors in High-Precision Mask Making and Metrology, Solid State Electronics Laboratory, Semiconductor Research Corporation Contract No. MC-515, Mar. 1996, pp. 1-167.

Takac, M. T., J. Ye, M. R. Raugh, R. F. Pease, C. N. Berglund, G. Owen, "Self-calibration in two dimensions: the experiment," SPIE Proceedings: Metrology, Inspection, and Process Control for Microlithography X, Bellingham: SPIE, vol 2725, Pp130-146, 11-13 March 1996.

Takac et al., Self-Calibration In Two Dimensions: The Experiment, SPIE Proceedings on "Metrology, Inspection and Process Control for Microlithography X", Santa Clara, California, vol. 2725, Mar. 11-13, 1996, pp. 130-146.

Raugh, M. R. and J. M. Minor, "Statistical Perspectives of Self-Calibration," SPIE Proceedings: Metrology, Inspection, and Process Control for Microlithography X, Bellingham: SPIE, vol 2725, 11-13 March 1996.

Evans, Chris J., Hocken, Robert J., and W. Tyler Estler, "Self-Calibration: reversal, redundancy, error separation, and ‘absolute testing," CIRP Annals, Vol 45/2, 1996, pp 617-634.

Raugh, M. R. and S. A. Rizvi, "Overlay can be improved by self-calibrated XY measuring Instrument: a lattice perspective," SPIE Proceedings: 16th Annual Symposium on Photomask Technology and Management, Volume 2884, Redwood City, CA, 18-20 September 1996.

Takac, M. T., "Self-Calibration in Two-Dimensions," BACUS Photomask News, Bellingham: SPIE, March 1994.

Takac, M. T., "Self-Calibration in One Dimension," 13th annual BACUS Symposium on Photomask Technology and Management, Bellingham: SPIE, 1993.

Kuniyoshi et al., Stepper Stability Improvement By A Perfect Self-Calibration System, SPIE vol. 2197, pp. 990-996.

Rizvi, Syed A., "A Problem in Position Metrology," SRC Newsletter, 1992.

Raugh, Michael. R., "Self-Consistency and Transitivity in Self-Calibration Procedures," Stanford University Computer Systems Laboratory Technical Report CSL-TR-91-484, July 1991.

Rizvi, Syed A., "Let’s Begin to Standardize Registration Metrology," Semiconductor International, Oct. 1989.

Raugh, M. R., "Absolute two-dimensional sub-micron metrology for electron beam lithography: A theory of calibration with applications," Precision Engineering, 7(1), pp. 3-13 Jan 1985.

Raugh, M. R., "Absolute 2-D sub-micron metrology for E-beam lithography," SPIE Proceedings Volume 480, Paper No. 21, 1984.

Lawson et al., Calibration Algorithms For An Electron Beam Metrology System, Microelectronic Engineering 1, 1983, pp. 41-50.

Questions?       Email michael.raugh ATSIGN gmail.com

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