Improved estimates of the range of errors on photomasks using measured values of skewness and kurtosis

Henry Chris Hamaker

doi:10.1117/12.228171

8 December 1995 Improved estimates of the range of errors on photomasks using measured values of skewness and kurtosis

Henry Chris Hamaker

Proceedings Volume 2621, 15th Annual BACUS Symposium on Photomask Technology and Management; (1995) https://doi.org/10.1117/12.228171
Event: 15th Annual BACUS Symposium on Photomask Technology and Management '95, 1995, Santa Clara, CA, United States

Abstract

Statistical process control (SPC) techniques often use six times the standard deviation sigma to estimate the range of errors within a process. Two assumptions are inherent in this choice of metric for the range: (1) the normal distribution adequately describes the errors, and (2) the fraction of errors falling within plus or minus 3 sigma, about 99.73%, is sufficiently large that we may consider the fraction occurring outside this range to be negligible. In state-of-the-art photomasks, however, the assumption of normality frequently breaks down, and consequently plus or minus 3 sigma is not a good estimate of the range of errors. In this study, we show that improved estimates for the effective maximum error E_m, which is defined as the value for which 99.73% of all errors fall within plus or minus E_m of the mean mu, may be obtained by quantifying the deviation from normality of the error distributions using the skewness and kurtosis of the error sampling. Data are presented indicating that in laser reticle- writing tools, E_m less than or equal to 3 sigma. We also extend this technique for estimating the range of errors to specifications that are usually described by mu plus 3 sigma. The implications for SPC are examined.

Citation Download Citation

Henry Chris Hamaker "Improved estimates of the range of errors on photomasks using measured values of skewness and kurtosis", Proc. SPIE 2621, 15th Annual BACUS Symposium on Photomask Technology and Management, (8 December 1995); https://doi.org/10.1117/12.228171

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