TSD01 consists of large variety of densely packed particles with average diameter around 60 nm. Particles’ shape is not ideally round. Some of them are rather cylindrical. Others have vertical walls and sharp corners (see REM photo to the left). These features are necessary to collect enough statistics for further “blind” tip estimation using Deconvolution algorithm.
(Figure 1 REM image of TS01 surface)
TSD01 could be used for both qualitative or quantitative estimation of tip’s shape and curvature radius.
Qualitative tip’s shape estimation with TSD01
Qualitative tip’s shape estimation could be done by comparison of AFM images of TSD01 surface of different AFM probes. Below you may find AFM images of TSD01, performed by two different silicon cantilevers.
(Figure 2 AFM image of TSD01 by AFM tip #1)
(Figure 3 AFM image of TSD01 by AFM tip #2)
Looking at images’ scales, one may notice that particles’ height on the left image is higher than on the right. That means that tip #1 penetrates deeper into gaps between particles during the scan. And tip #1 is the sharpest one between them both.
This conclusion was further approved by “blind” tips’ estimation. But before to present the results, obtained by this method, we should say a couple of words about Deconvolution method itself.
“Blind” reconstruction of AFM tip’s shape
When we get topography image from AFM, the result is not the “real” shape of the surface, but rather a convolution of tip’s and sample’s outlines in each point of the scan.
Deconvolution algorithm for AFM surface reconstruction was suggested by J.S. Villarrubia in 1997 and now it is implemented in many different AFM-image-processing programs.
Before using this method, one should solve another tricky task: to define exact tip’s shape. In his publication J.S. Villarrubia presents (together with Deconvolution) the method of “blind” estimation of tip’s shape. For better understanding of this method let’s imagine an ideal vertical bulk (the left image) which width is equal to “0”. It’s not difficult to calculate that when a probe passes such an object, its image on AFM topography scan will be just the inverted probe’s shape (a dotted line).
(Figure 4 Probe moves accross an ideal vertical bulk)
Thus, every particle of topography imaged, which size is comparable to a tip, should hold some information about its real shape. The algorithm of “blind reconstruction” compares shapes of all particles (local maximums) of the topography scan and finds common features between them (this procedure is described in detail in ). On the basis of such comparison it outputs approximated tip’s shape. Reliability of the result depends on particles amount (it should be enough to collect statistics) and their shape (then closer to an “ideal bulk” – than better, as we have seen previously).
Quantitative tip’s shape estimation with TSD01
Which are the criteria of the test structure for tip’s shape “blind” estimation?
1) It should be rigid.
2) It should have many particles of 20-100nm approximate diameter, so that their size should be comparable to tip’s one.
3) All the particles should densely sit on the surface. For detailed tip’s shape estimation each particle should contain, say 10×10 points. From the other hand, there should be 50, 100 or more particles in range of one scan so that we had enough statistics for further intersections. Knowing that standard AFM scans contain 512×512 or 1024×1024 points, one unambiguously comes to this conclusion.
4) It’s often stated that round particles of well-defined radius are ideal for tip’s “blind” reconstruction. But this is the mistake which just goes intuitively from the 2nd criterion. As we discussed above, speaking about “ideal bulk approximation”, only AFM images of vertical objects of “zero” width hold the most exact information about tip’s shape. If even they don’t exist in nature, every vertical wall and sharp corner of our particle holds exact information about tip’s shape at least in plane, which tip moves along passing this wall or corner. Thus, the test structure for tip’s shape “blind” estimation should have got irregular shape with many vertical walls and corners.
TSD01 manufacture process determines its physical properties: all particles are grown chaotically around small cores of several nanometers. Thus, they have similar, but very irregular shapes. Some of them may have sections, close to cylindrical. Others appear to be rounder. They have many sharp corners as well.
Writing several dozens of such particles during the same AFM image a tip leaves much information about its true shape from each side. This statistic is usually enough to get reasonable tip images after tip’s “blind” estimation by standard deconvolution procedure.
Below you may find the results of “blind” tip’s shape reconstruction from the AFM scans of TSD01 test structure, shown at the beginning of these notes.
(Figure 5 AFM image of TSD01, taken by the probe #1, and tip’s “blind” estimation’s result)
(Figure 6 AFM image of TSD01, taken by the probe #1, and tip’s “blind” estimation’s result)
Tip’s images were obtained by variations of Threshold parameters according to recommendations, listed in .
As you may notice, the results of tip’s shape estimation correspond to our previously-made suggestion that the probe #1 is sharper than the probe #2.
Literature J.S. Villarrubia, J. Res. Natl. Inst. Stand. Technol. 102, 425 (1997)
 L.S. Dongmo, J.S. Villarrubia, S.N. Jones, T.B. Renegar, M.T. Postek, J.F. Song., Ultramicroscopy 85 (2000), 141 – 153