Guide to Resolution
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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:
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| 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. |
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| 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. |
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| 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. |
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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.
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