Guide to Resolution

Options

Suppose there are three probes available for imaging: Long Scanning (R~30 nm), General Purpose (R~10 nm) and High Resolution (R~1 nm). Which of the three 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 probe. If we have two rigid spikes and a 0.1 nm detector sensitivity in the z-direction, then the minimum diameter between these spikes for the 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 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 tip and the larger the opening angle of the 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 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 4 nm in diameter. The choice of the 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 Long Scanning probe because they are far apart from each other. However, the width of the spheres will appear to be 31 nm, because of convolution due to the tip radius. No: the spheres will not be resolved by a Long Scanning probe, because the probe tip can not penetrate even 0.1 nm between them. A smaller scan size will not help.  
Yes: the spheres will be resolved, and the tip will fully probe between them if they are at least 15 nm apart. The spheres will appear to have a width of 18 nm. Yes: the spheres will be resolved as individual objects, but the scan height will be 0.17 nm only. The spheres may not be resolved if they are made of soft material or of the probe tip is not a perfect sphere. Scan size should be smaller than 1 micron at 512 sampling points.  
Yes: the spheres will be resolved by a High-Resolution probe. The sphere width will appear to be 5 nm. 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 tip will be able to penetrate more than 0.7 nm between them. As the tip-sample forces are minimized, this will also work for spheres of soft materials.  

It is important to remember that resolution is slightly lower for softer samples, as the tip-sample interactions can cause deformation.

LS probes are good for accurate measurement of vertical dimensions of rigid samples, lateral information for large features, or for when accurate lateral measurements are not important. These probes are especially durable, allowing many more scans to be taken without a loss of resolution or damage to the tip.

GP probes provide additional resolution in the lateral dimension and are good for getting good quality everyday images of large and small features. The smaller opening angle of the GP probes provides better lateral resolution for features larger than 10 nm than their NSC/CSC equivalents.

Because the HI'RES tips have a very sharp tip and a high aspect ratio geometry, the convolution in the lateral dimension is minimized. HI'RES probes are for when the best lateral resolution is necessary or when the feature sizes are exceptionally small.

Tip Size Scan Size



Rc < 30nm


Scan size 3µm. Diameter of spherical
molecules
150nm. Click to enlarge. Height
image of polystyrene latex spheres.
/Courtesy of S. Magonov/


Rc < 10nm



Scan size 800 nm. 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


Scan size 250 nm. Diameter of
spherical molecules is 9nm. Click to enlarge.
Carbosilane dendrimers in a dense film.
/Courtesy of D. Ivanov/

high resolution

Lateral resolution below 1 nm. For scanning small areas below 250 nm at 512 points.

1 nm radius
multiple diamond-like tips
hi'res-C

1 nm radius Tungsten spike
hi'res-w

general purpose

Lateral resolution down to 5 nm for scan size below 1 μm.

10 nm radius tetrahedral tip
GP

10 nm radius conical tip
NSC/CSC

Long Scanning

Accurate resolution of surface features larger than 10 nm in diameter. Good for scan sizes above 3 μm at 512 points.

30 nm radius
LS

20 nm radius
Si3N4 - coated Si probes
NSC/CSC

 
 

 

 

 

 
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