Specific Process Knowledge/Characterization/Profiler: Difference between revisions
→Total uncertainty budget: added image |
|||
| Line 92: | Line 92: | ||
The size of the calibration standard confidence intervals mean that the measurement uncertainty is much more significant for very shallow steps below 500-1000 nm than for steps in the micron range: The 95 % confidence interval in the 65 kÅ range is obviously at least ± 30nm, so measuring a 100-200 nm step will have a large error percentage-wise. Note that this error (from the calibration standard) is systematic. The random error associated with repeated measurements is usually smaller (perhaps ± 5 nm). One can therefore measure shallow steps to compare samples even if the absolute numbers are not very reliable. | The size of the calibration standard confidence intervals mean that the measurement uncertainty is much more significant for very shallow steps below 500-1000 nm than for steps in the micron range: The 95 % confidence interval in the 65 kÅ range is obviously at least ± 30nm, so measuring a 100-200 nm step will have a large error percentage-wise. Note that this error (from the calibration standard) is systematic. The random error associated with repeated measurements is usually smaller (perhaps ± 5 nm). One can therefore measure shallow steps to compare samples even if the absolute numbers are not very reliable. | ||
====Total uncertainty | ====Total uncertainty==== | ||
We can numerically estimate the accuracy of | We can numerically estimate the accuracy of the Dektak's measurements based on the error of the calibration combined with the error from the limit on the resolution and the scatter of repeated measurements. This is shown graphically in the Figure on the right. You can see an uncertainty budget for the Dektak measurements here (made by Rebecca Ettlinger in 2020): [[Media:uncertainty budget dektaks.xlsx]]. It is based on the procedure described [https://www.nde-ed.org/GeneralResources/Uncertainty/Combined.htm here]. | ||
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 30 nm for the smallest range, about 0.17 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 30 nm for the smallest range, about 0.17 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. | ||
[[File:Error probability distributions.png|Upright|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.]] | |||
==Dektak 8 stylus profiler== | ==Dektak 8 stylus profiler== | ||