AFM Calibration for 2D Materials

 

Purpose

This technical note explains the procedure required to calibrate an AFMWorkshop AFM in order to get accurate measurements of 2D materials. 2D materials, which are layered materials with thicknesses on the nanometer scale, are an example of an AFM sample with particular calibration requirements. AFM is very useful tool for studies of 2D materials, because it can make accurate measurements with sub-nanometer accuracy, and with high contrast on any sample. However standard calibration procedures may lead to inaccurate values when measuring the height of 2D materials. Following the procedures described here will allow the AFM to produce accurate measurements of 2D materials.

 

Why AFMs need to be calibrated

All microscopes need to be calibrated in order to produce accurate results. One of the advantages of AFM is that unlike an optical microscope, that usually has a fixed set of magnifications that can be used, the AFM can produce images at a very wide range of scales. The user chooses the X-T scale to be imaged base d on what information they wish to extract from their sample. Since it's a three-dimensional microscope, the AFM also measures the sample dimension I the z-scale, using the feedback mechanism and the z piezo to measure the height of the features in the sample. In order to do this, the AFM software uses a set of calibration values, that relate the voltage applied to the piezoelectrics in the scanner, to real distances. In the AFM workshop software, there are either three or four of these values, depending on the scanner used. The software allows the user to update these values in order to allow re-calibration of the scanner movement. When the instrument is installed, the scanner comes pre-calibrated based against internal standards, so the instrument will be making accurate measurements from the first scan, but there are two reasons when the user would want to re-calibrate the instrument.

The first reason that re-calibration of AFM instruments is necessary to carry out, is that the piezoelectric actuator in AFM scanners often change their response over time. In general, this is a slow response, especially once the instrument has been in use a few months. However, it is, in general, a good idea to recalibrate an AFM on an annual basis. The second reason for calibration is that piezo-electric response to voltage is non-linear. In other words, the number of nanometers that a piezoelectric actuator moves per applied volt will not be the same when measuring very large samples, compared to when measuring very small samples. This is important for AFM in particular, because AFM instruments are capable of measuring on a very wide range of scales. The non-linearity of the piezo extension is illustrated schematically below.

 

 

As can be seen in the image shown above, calibration accuracy depends on the specific height at which calibration has been carried out. In fact, the response of piezo stacks such as used in AFM scanner sis considerably more linear than is shown in figure 1. However, the point still remains. For superior accuracy in measurements made with an AFM, it is useful ensure the scanner calibration is accurately calibrated at a scale similar to that at which the measurements will be made.

 

How AFMs are calibrated

Calibration of an AFM scanner can be carried out in X, Y, and Z axes. X and y axis calibration is usually measured by measuring the repeat distances, known as pitch, of regular repeating patterns in X and XY. It is usually made at the micron, to 10s of microns scale. For example, for a scanner with 100 x100 scan range in X and Y, features with a 10 micron pitch would usually be used. For a 15 micron scanner features with pitch between 1 and 3 microns would normally y be used. In general, the accuracy of calibration in the Z axis is considered more important than accuracy of X-Y calibration. This is because X’Y measurements are typically subject to errors related to the probe size. On the other hand, z axis measurements can be expected to be absolutely accurate in an AFM. For this reason, if possible, critical dimensional measurements are made in the Z axis. Measurements of large features in the X- Y axis can also be made much more accurate by using the position sensors of the AFM and operating in closed-loop mode. Position sensors can also be used in the Z axis. AFMWorkshop scanners with 50 and 100 microns ranges have Z axis sensors incorporated, which improves the accuracy of Z measurements. However, this method is not appropriate for 2 dimensional materials, as the noise in the position sensors is greater than the noise in the standard height measurement, and thus it’s necessary to make a calibration on the nanometer scale for the z axis.

 

Samples for calibration

A wide variety of samples can be used for dimensional calibration. For x-y dimensions, the most commonly used are purpose-designed semiconductor grid samples. These samples typically have a square grid of repeating patterns, such as holes or pillars, although sometimes they have patterns in lines. These samples are easy to use, especially since there is usually a large area that can be used, which all shows the desired features. They can be found with a range of repeat pitch, most commonly between 1 and 10 pm. Other possible samples for X-Y calibration include TEM grids, or replicas thereof, and self-assembled nanospheres.

For z-calibration, it is also common to sue semiconductor devices as standards. There are a very wide range of such standards available. Typically, they show well-defined step heights, most commonly in the range of 100 to 1000 nm. Other possibilities include measuring the height of monodisperse colloid particles, but these have some disadvantages, including the fact that the accuracy of AFM is greater than the dispersion of sizes in nearly all samples.

For z-calibration at a scale relevant to two dimensional materials, probably the best option is to use a well-characterized layered material displaying steps of known height. There are a few of these available from different suppliers, made from different materials. One useful example of a layered material particularly useful for this procedure is the 6H polymorph of silicon carbide (SiC), which can be prepared in order to display either half or one monolayer steps across its surface, which correspond to heights of 0.75 or 1.5 nm, respectively.

 

Procedure for calibration

 

Requirements

• Any AFM Workshop AFM
• Version 4.X AFMWorkshop Control software
• Vibrating mode probe (new)
• SiC sample — either 0.75 or 1.5 (optionally both, but it’s not necessary)
• 100 nm calibration sample (optional)
• AFMWorkshop calibration applet (optional)

 

Procedure

1. Place the sample in the instrument, and insert the probe.
2. Align the laser and perform the Tune Frequency procedure as normal.
3. If using version 4.X software and a 50 or 100 pm scanner, select the “Highest” resolution mode, and perform a range check.
4. Choose a clean area of the sample, go into feedback.
5. For lowest noise, if using a 50 or 100 km scanner, disengage position sensors using the context setting menu in the TopoScan tab (In the Topo Scan, in the Scan Parameters frame, click the gear icon, and then set XGPID Gain and YGPID to 0).
6. Measure a 4 x 4 pm image, with 256 pixel resolution.
7. Choose a smaller area in that region with clear steps, no dirt, and wide terraces. A 1.5 1.5 pm area is recommended.
8. Perform a scan at 256 or 512 pixel resolution and save the file. The image you get should look something like the one shown below. The terraces in the height value are clearly visible, but are tilted due to the flattening routine in the software. When the image is saved, this flattening is not included.

 


Figure 2. AFM image of small area as shown in the AFMWorkshop control software.

 

NOTE: Correct processing of the data you obtain is very important to ensure correct measurement of your data, impacting the calibration. It is very important to ensure the data is levelled properly as described here before making step height measurements.

9. Processing: Open the height image in Gwyddion. Firstly, perform a “level data by mean plane subtraction” procedure. Then go into the “Align Rows” menu, and select “Median”. Click OK. These two procedures will perform an overall levelling of the image, but will not result in flat terraces, rather, the image will look something like the image shown below. At this stage, the whole image is flat, from left to right, but the terraces are tilted to achieve this. A line profile is also shown in the image below to highlight this

 


Figure 3. Preprocessed image of steps on SiC sample. The image is flat overall, but he terraces are tilted.

 

10. Now select the “Three Point Level” option in Gwyddion. The icon looks like a triangle. This allows you to define a plane using three points on the same terrace. Choose three points as shown below. It is a good idea to increase the Averaging radius to a value around 10 (or less if the terraces are very narrow). Once the image looks well leveled, with each terrace as flat as possible, click the “Shift minimum data value to zero” button.

 


Figure 4. Levelling the terraces using the Three Point Level method. All three points must be placed on the same terrace, preferably far apart, as shown here. Having done, this, the terraces are flattened. Compare to Figure 3.

 

11. At this stage, it can be useful to check a height profile to see how the levelling worked. However, we will not be using the height profile to measure the step height, as it’s not the most accurate method. Use the “Extract Profiles” tool to see the height profile perpendicular to the step edges. You should get a profile similar to the one shown below.

 


Figure 5. A line profile through a well-levelled image, showing flat terraces.

 

12. Now that we have a flat image, we can analyze the step height. This is done best by using a height histogram. In Gwyddion, obtain the histogram, by clicking the Tool “Calculate 1D Statistical Functions”, Ensure that Quantity is set to “Height Distribution”, and click apply. You should find a new graph showing the height histogram, similar to that shown below.

 


Figure 6. Histogram of the image shown in figure 4, showing the height difference between the steps in the image was 0.99nm

 

13. The histogram you have obtained can be analyzed in terms of the step height manually by using the “Measure distances in graph” option. In the case above, we can see that the step height was 0.99, whereas the sample was SiC 1.5, so it should be 1.5 nm. In order to correct this, we can make a change to the “Z Drive Calibration” parameter, which is found on the PRE’SCAN tab, in the settings menu (Gear icon) of the system panel.
14. Open the scanner calibration setting menu, and take a note of the current Z Drive Calibration value. You can insert a new value depending on what value you got. If you are in doubt how to do this, consult the user’s manual, or use the AFMWorkshop Calibration applet. In the example above, to change from 0.99 to 1.50, I multiplied the old Z Drive Calibration value by 1.5. Insert your new Z Drive calibration in to the panel, click Save, and then make a new scan, just the same as before. After doing this, here is the new scan (after flattening), with accompanying histogram:

 


Figure 7. Image of SiC 1.5 Sample and height histogram after recalibration

 

15. In order to show that with this calibration, the system can give accurate results on 2D materials, even if they differ from the calibration sample, we can now scan the 0.75 SiC sample, using the same calibration values.

 

The result found is shown below.

 

 

The average step height found on the SiC0.75 sample, using the calibration from the 1.5 sample was 0.758 nm. Therefore, we can say that this system is now suitable to give measurements to within a 2% accuracy at <2nm size scales.

In order to determine how calibration at the 1nm size scale affects the determination of dimension at larger scale, we can use these calibration values to measure a 100 nm calibration sample. This gives as idea of the level of non-linearity in the piezo response. Upon doing this, we found that the measure values were 13% off the actual values at around 100 nm. The error of 13 % can be considered small, given that we are increasing in scale by two orders of magnitude. Thus, there is a small, but significant error. When using calibration values determined using distances far from the values measured.

 

Conclusions

Overall, considering the agreement found between the two SiC samples measured here, we can say that the AFM calibrated using this calibration method is suitable to give accurate measurements in the sub-nanometer to few-nanometer range, and thus highly suitable for measuring 2D materials. Furthermore, although non-linear, the agreement between calibrations at 1nm and 100 nm is not too far off. However, it is always to recommended to calibrate Z axis measurements at a spatial scale relevant to the those of critical measurements.

 

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