Specific Process Knowledge/Characterization/Stylus Profiler Measurement Uncertainty: Difference between revisions

[[File:Error probability distributions rev.png|upright=2|400px|alt=Four different probability distributions that contribute to the total error on measurements with the Dektak XTA 6.5 micron range. By far the widest distribution is the one from the error on the standard step, which is a Gaussian. The others are the non-Gaussian spread of the average measurement of the 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. Note this figure was made when the best estimate of the true standard size was 917 +/- 17 nm; it is recalibrated every 5 years and has been 916-923 nm over the years, with a 95 % CI of approx. 18 nm|right|thumb|Figure 2: The probability distributions of the main sources of error are convoluted to create the total error on a profiler measurement.]]

Apart from the error due to the standard step height's intrinsic uncertainty, there is a contribution to the overall uncertainty from the deviation of the value that the profiler measures from the theoretical height of the standard step. This can be called "QC error" since we accept some variation in our quality control routine. In practice for the 917 nm standard this range is about ± 4 nm for the Dektak XTA and ± 8 nm for the P17, while for the large standard it ranges from about 0.06 µm on the Dektak XTA to about 0.15 µm on the P17. You can see this deviation in the QC data in LabManager for a given instrument.

There is also a tiny contribution to the total error from the instrument's limited resolution and finally of course there is random noise in any measurement. For many repeated measurements of the same line on the standard step height (a rigid, well defined vertical step) we have found the random error from the Dektak XTA is on the order of ± 5 nm for the 917 nm standard and 0.05 µm for a 24.925 µm standard. The random error with the P17 profiler is even smaller (about 0.001 µm).  

To estimate the overall accuracy of the profiler's measurements you can convolute these various sources of error. The error sources are shown graphically in Figure 2 for measuring the small standard step with the Dektak XTA's smallest range. You can see an uncertainty budget for the Dektak XTA measurements here (''made by Rebecca Ettlinger in 2020''): [[Media:Uncertainty budget Dektak rev.xlsx |Uncertainty budget Dektak rev.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.