Specific Process Knowledge/Characterization/Profiler: Difference between revisions
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[[File:Error probability distributions sep 2020 update big.png|upright=2|alt=Four different probability distributions that contribute to the total error on the Dektak measurement for the 6.5 micron range. By far the widest distribution is the one from the error on the calibration standard, which is a Gaussian. The others are the non-Gaussian spread of the average measurement of the calibration standard height, which cuts off at the QC limits, the resolution, which is a very narrow uniform distribution, and the spread of measurement values for a given step being measured, which is a Gaussian whose width depends on the step in question.|right|thumb|The probability distributions of the main sources of error that are convoluted to create the total error on a Dektak measurement.]] | [[File:Error probability distributions sep 2020 update big.png|upright=2|alt=Four different probability distributions that contribute to the total error on the Dektak measurement for the 6.5 micron range. By far the widest distribution is the one from the error on the calibration standard, which is a Gaussian. The others are the non-Gaussian spread of the average measurement of the calibration standard height, which cuts off at the QC limits, the resolution, which is a very narrow uniform distribution, and the spread of measurement values for a given step being measured, which is a Gaussian whose width depends on the step in question.|right|thumb|The probability distributions of the main sources of error that are convoluted to create the total error on a Dektak measurement.]] | ||
To estimate the accuracy of the Dektak's measurements we have to combine the error of the calibration with the error from the limit on the resolution and the scatter of repeated measurements. This is shown graphically on the right. You can see an uncertainty budget for the Dektak measurements here (made by Rebecca Ettlinger in 2020): [[Media:uncertainty budget DektakXT Oct2020.xlsx]]. It is based on the assumption that all the error sources are independent and can therefore be added by the sum of squares method. Or as expressed by the international bureau of standards and measures, the "combined standard uncertainty [..] is the positive square root of the combined variances[..]". See [[JCGM_100_2008_E.pdf this document]]. | To estimate the accuracy of the Dektak's measurements we have to combine the error of the calibration with the error from the limit on the resolution and the scatter of repeated measurements. This is shown graphically on the right. You can see an uncertainty budget for the Dektak measurements here (made by Rebecca Ettlinger in 2020): [[Media:uncertainty budget DektakXT Oct2020.xlsx]]. It is based on the assumption that all the error sources are independent and can therefore be added by the sum of squares method. Or as expressed by the international bureau of standards and measures, the "combined standard uncertainty [..] is the positive square root of the combined variances[..]". See [[File:JCGM_100_2008_E.pdf this document]]. | ||
The error stemming from the uncertainty on the calibration standard dominates for all ranges except the 1 mm range, where the resolution also plays a role. This leads to the 95 % confidence intervals listed above in the table: just over 18 nm for the smallest range, just over 0.2 µm for the medium ranges, and about 0.6 µm for the 1 mm range. As noted above, be aware that if you have a step height that is difficult to measure, the scatter of repeated measurements could easily lead to larger confidence intervals. | The error stemming from the uncertainty on the calibration standard dominates for all ranges except the 1 mm range, where the resolution also plays a role. This leads to the 95 % confidence intervals listed above in the table: just over 18 nm for the smallest range, just over 0.2 µm for the medium ranges, and about 0.6 µm for the 1 mm range. As noted above, be aware that if you have a step height that is difficult to measure, the scatter of repeated measurements could easily lead to larger confidence intervals. | ||