Biomedical Engineering Reference
In-Depth Information
data for blind reconstruction. Also, the accuracy of the estimate was shown to depend
strongly on the image size used. Specifically, small images will tend to overestimate the
sharpness of the tip, due to lower signal-to-noise ratio at small scan sizes and this noise at
high resolutions can also introduce distortions in the estimated tip shape versus the real
shape [56]. On the other hand, large images or images with a low pixel density will tend to
give results suggesting a much 'blunter' profile of the tip due to undersampling of the
surface topography [57]. Overall, blind reconstruction is a technique which is relatively
simple to apply, and can considerably improve the quality of AFM data, by removing large
part of the dilation effect of the tip, as long as care is taken in the application of the
technique. It is always worth remembering, however, that in the case of a blunt tip or sharp
sample features, there will exist some parts of the sample that are never probed by the tip
[58] (see for example, Figure 2.28, where the corners of the depressions, or corners of the
protrusions could not be imaged), and deconvolution cannot help here.
2.5.5 Cantilever force constants
Cantilevered AFM probes fabricated with MEMS processing technologies are subject to
fairly dramatic distributions of specifications. For example, a wafer of probes could have
only 85% of the probes less than 10 nm in diameter. The other 15% could have any
diameter. This distribution can dramatically affect the quality and resolution of AFM
images. Besides the probe geometry, the cantilevers can have a substantial variation in
specifications, especially the thickness of the cantilevers. Because the force constant of the
cantilever varies as the inverse cube of the thickness, the force constants of MEMS
fabricated cantilevers can vary dramatically. Table 2.1 shows an example of the variability
of cantilever geometries and the calculated impact on critical specifications. It can be seen
that in relative terms, the thickness has a very high variability compared to the width or
length, and that this greatly affects the force constant variability.
Calibration of cantilever force constants
As illustrated in Table 2.1, there is considerable variability in the force constant of an
AFM cantilever, mainly because of variations in the thickness of the cantilevers. Thus,
when knowledge of the exact force applied is required, the force constant of the cantilever
used for the tests must be calculated [59]. This is particularly important for force
spectroscopy applications (discussed further in Chapter 3), but knowledge of the applied
force is also very important for reproducibility in imaging studies. A large amount of work has
been done to determine optimum techniques to measure the force constants of AFM
Table 2.1. Example of the variability in manufactured
AFM cantilever properties.
Cantilever Data
Value
Range
Thickness
2
m
1.5-2.5
Mean width
50
m
45-55
Length
450
m
445-455
Force constant
0.2 N/m
0.07-0.4
Resonance frequency
13 kHz
9-17
