Specific Process Knowledge/Characterization/Stylus Profiler Measurement Uncertainty

Stylus Profiler Measurement Accuracy

The accuracy of a height measurement with the profiler depends on the measurement settings, the sample, the instrument calibration and the resolution.

Optimal Measurement Settings

Both the force setting and the scan speed are important: Too high force may compress a soft material like Al, Au or some polymers, while too low force may lead to the stylus "jumping" over features, especially if the scan speed is high. Too low scan speed may result in drift of the measurement and noise from vibrations while too high scan speed may mean that the stylus tip does not have time to reach the bottom of the features you are measuring and can also give rise to increased noise levels (see the Dektak XTA manual on LabManager, Figure 3 for details).

A sharp vertical step is easiest to measure. If the step is gradual or the surface is rough, it can be difficult to determine where to measure and how the scan should be leveled. Underlying sample curvature can also make it hard to level the scan. See further below under Total Uncertainty for steps < 1 µm.

Calibration Standard Uncertainty

Figure 1: Measurement uncertainty from uncertainty in the calibration standard (Not to scale). The linearity of the sensor means that the measurement error increases approximately linearly with the size of the feature being measured. The percentage-wise error on the smallest standard step is larger than on the bigger standard step, meaning the lines are not completely straight.

Nanolab staff periodically check most of the the stylus profilers' measurement accuracy with a standard step height of 923 nm for the smaller ranges and 23.058 µm (previously almost 25 µm) for the larger ranges, so that the middle ranges are checked with both standards. The 95 % confidence intervals for the standards are 18 nm for the 917 nm standard and 0.068 µm for the 23.058 µm standard. If the control measurement is beyond the limit set in our Quality Control procedure, the instrument is calibrated and the users informed (see LabManager for details, for instance the Dektak XTA control instruction and control measurement data)

This means the 95 % confidence interval of a 1 µm step measured with the smallest measurement range is at least the 1.8 % error of the standard step while the 95 % confidence interval of a 25 µm step measured with a larger range is at least the 0.3 % error of the standard step. Steps between 1 and 25 µm measured with the intermediate ranges will presumably have an intermediate error just due to the intrinsic uncertainty on the standard step height. See Figure 1.

Total Uncertainty for steps > 1 µm

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): 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.

The resulting error calculation for the Dektak XTA of a 1 µm very well defined standard step is about 2 % (as the uncertainty on the calibration standard dominates), while for a very well defined step of 25 µm the cumulative error is about 0.7-1 %. However, in real devices the random error will often be much larger than for our standard samples and so the real confidence interval will be larger.

To calculate the accuracy of your particular measurement, you should repeat the measurement several times and estimate the standard deviation. If the scatter is quite small you can try to calculate the total error on your measurement using the sum of squares method to combine the intrinsic step height error, the QC error and the random scatter error. If the scatter of your measurements is large that will be the dominant source of error in your measurement and you can safely ignore the other contributions.