RESOLUTION

Suppose there are three AFM probes available for imaging: a hardened AFM probe with R <30nm, a standard tapping mode AFM probe with R <10nm and a high resolution AFM probe with R ~1nm. Which of the three AFM probes should be chosen to get enough resolution?

One way of describing resolution is to consider whether two adjacent objects can be resolved by a particular AFM probe. If we have two rigid spikes and a 0.1nm detector sensitivity in the z-direction, then the minimum diameter between these spikes for the AFM probe to distinguish between them is d=(0.8R)^1/2, where d is the distance between the spikes and R is the radius of the AFM tip.

The amount of lateral resolution required should also be considered. Is it necessary only to know that there are two objects present? Or is it important to have the accurate lateral dimensions of these objects? The larger the radius of the AFM tip and the larger the opening angle of the AFM tip, the greater convolution will be present in the lateral dimensions. This effect has a greater impact on the accuracy of the dimensions of smaller objects than larger ones. For two spheres, the distance separating them must be d=4(Rr)^1/2, where r is the radius of the spheres, in order for the AFM tip to fully probe between them. δr=(d-r) is also the lateral distance that will be "added" by the size of the tip to the sphere's topography.

Step size, which is the ratio of the scan size and the number of sampling points, should be also taken into account.

Let's consider the case of imaging the topography of very small spheres 4nm in diameter. The choice of the AFM tip and the scan size will determine if the spheres can be resolved. There are different possibilities:

Yes: the spheres will be resolved even by a hardened R<30nm AFM probe because they are far apart from each other. However, the width of the spheres will appear to be 31nm, because of convolution due to the AFM tip radius.	No: the spheres will not be resolved by a hardened R<30nm AFM probe, because the AFM probe tip can not penetrate even 0.1nm between them. A smaller scan size will not help.
Yes: the spheres will be resolved, and the AFM tip will fully probe between them if they are at least 15nm apart. The spheres will appear to have a width of 18nm.	Yes: the spheres will be resolved as individual objects, but the scan height will be 0.17nm only. The spheres may not be resolved if they are made of soft material or if the AFM probe tip is not a perfect sphere. Scan size should be smaller than 1micron at 512 sampling points.
Yes: the spheres will be resolved by a High-Resolution AFM probe. The sphere width will appear to be 5nm. But: the measurement process will be more complicated. Scan size should be small enough and very low forces should be used.	Yes: the spheres will be resolved as individual objects, and the AFM tip will be able to penetrate more than 0.7nm between them. As the tip-sample forces are minimized, this will also work for spheres of soft materials.

Standard AFM probes with R<10nm provide additional resolution in the lateral dimension and are good for getting good quality everyday images of large and small features.

Because the Hi'Res-C AFM tips have a very sharp AFM tip and a high aspect ratio geometry, the convolution in the lateral dimension is minimized. Hi'Res-C AFM probes should be used when the best lateral resolution is necessary or when the feature size is exceptionally small.

AFM Tip Size	Scan Size
Rc <30nm HARDENED	Scan size 3µm. Diameter of spherical molecules 150nm. Click to enlarge. Height image of polystyrene latex spheres. /Courtesy of S. Magonov/
Rc <10nm STANDARD	Scan size 800nm. Diameter of spherical molecules about 40nm. Click to enlarge. Composite film of poly(p-xylylene) matrix and nanoparticles of MoO3 and TiO2. /Courtesy of R. Gaynutdinov/
Rc <1nm HIGH RESOLUTION	Scan size 250nm. Diameter of spherical molecules 9nm. Click to enlarge. Carbosilane dendrimers in a dense film. /Courtesy of D. Ivanov/