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80 Chapter 2
Equations (2.41), (2.43) and (2.45) can be solved for the unknown amounts
and by also employing Eqs. (2.42), (2.44) and (2.46).
2.2.2.2 Three Dimensional Force Detection in Atomic Force Microscopy
Applications
In atomic force microscopy (AFM) reading applications, a
microcantilever such as the one sketched in Fig. 2.10 is designed to
determine the amounts of force that are applied on its tip about the x-, y- and
z-directions, and thus describe (read) a three-dimensional variable geometry.
The experimental setup pictured in Fig. 2.8 can again be utilized to evaluate
the tip rotations and
Figure 2.10 Tip forces detected by a microcantilever in atomic force microscopy
Example 2.5
Evaluate the forces and that act on the tip of the constant
rectangular cross-section microcantilever of Fig. 2.10 by using the available
experimental data.
Solution:
It can simply be shown that the tip slope which is produced through
bending by the combined action of and as well as the slope which
is generated by torsion due to can be calculated as:
If the only experimental information consisted of the tip slopes and
the bending-produced deformation can globally be interpreted as generated
by an apparent tip force, such that:
