Thesis-PDF - IAP/TU Wien

crystal and the cantilever tip (phase imaging) additional information about the
viscoelastic properties of the sample can be gained (see Figs. 3.4, 3.5) .
Figure 3.4: The phase shift is calculated from the horizontal displacement
of the cantilever oszillation (solid line) relative to the oszillation of the driving
piezo crystal (dashed line) in time. The shift depends on different surface
properties (e.g. elasticity, stickiness) and parameters of the AFM operation.
The phase offset is caused by interaction with the surface and changes for
different materials as it depends on various parameters such as adhesion, friction
or viscoelasticity. Therefore phase imaging can help distinguish different areas of
interest on the sample not distinguishable by their topologies.
Choosing a cantilever with a high frequency lets the surfaces seem stiff, and
the tip-sample adhesion forces are greatly reduced. Unlike contact and non-contact
modes, when the tip contacts the surface, it has sufficient oscillation amplitude to
overcome the tip-sample adhesion forces. ([41], [38])
Resolution Limits
In order to obtain atomic resolution with the AFM, the spring constant of the
cantilever should be weaker than the equivalent spring constant between atoms.
For example, the vibration frequencies of atoms bound in a molecule or in a crystalline
solid are typically on the order of 10 13 Hz or higher. Combining this with
the mass of the atoms m, on the order of 10 −25 kg, gives an interatomic spring
constant k(ω 2 m), on the order of 10 N/m. Therefore, a cantilever beam should
have a spring constant of around 1 N/m or lower. To compare with a macroscopic
object, the spring constant of a piece of household aluminum foil that is 4mm long
and 1 mm wide is also about 1 N/m.
Second, tips as sharp as possible are desirable when imaging solids. The tip
diameter naturally sets a resolution limit as features smaller than this diameter
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