Relative merits of using maximum error versus 3(sigma) in describing the performance of laser-exposure reticle writing systems

Henry Chris Hamaker

doi:10.1117/12.209285

26 May 1995 Relative merits of using maximum error versus 3(sigma) in describing the performance of laser-exposure reticle writing systems

Henry Chris Hamaker

Author Affiliations +

Proceedings Volume 2440, Optical/Laser Microlithography VIII; (1995) https://doi.org/10.1117/12.209285
Event: SPIE's 1995 Symposium on Microlithography, 1995, Santa Clara, CA, United States

Abstract

Various techniques for estimating the performance of laser reticle writing systems are examined and compared. The criterion used to measure performance is based on finding the effective maximum error E_m, which is defined as the value for which 99.73% of the error population falls within the limits +/- E_m. The commonly used technique of using 3(sigma) , where (sigma) is the standard deviation, is shown to be a poor estimate when statistical analyses based on the normal distribution do not describe the data well. Improved accuracy is obtained when corrections based on the skewness (gamma) ₁ and the coefficient of excess flatness (gamma) ₂ are included. For system qualification, direct observation of the maximum error among a set of approximately 256 samples of the error is the preferred technique. When the sample size differs significantly from this value, the use of corrections based on (gamma) ₁ and (gamma) ₂ to determine the maximum error is preferred over alternative methods due to its emphasis on the behavior in the tails of the distribution.

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Henry Chris Hamaker "Relative merits of using maximum error versus 3(sigma) in describing the performance of laser-exposure reticle writing systems", Proc. SPIE 2440, Optical/Laser Microlithography VIII, (26 May 1995); https://doi.org/10.1117/12.209285

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