W. Richard Bowen and Nidal Hilal 4

9.2 dyNAMIC AFM METHOdS 251
be compressed by a distance �z 3 such that �z 1 � �z 2 � �z 3. Therefore
the deflection of the cantilever �z 2 is less on softer materials, and the term
�z 2/�z 1 is deemed to be indicative of surface compliance (Figure 9.2).
This method can be implemented using the advanced capabilities
of modern AFMs, one approach is similar to that described by Scott and
Bushan (2003) [2]. In this example, the modulating amplitude is obtained
by inducing vibration of the cantilever, the sample remaining fixed in position.
Using an interleaved scanning approach, the sample height is first
determined using tapping mode. The probe height is then adjusted such
that (i) the probe is kept in constant contact with the surface and (ii) a constant
scan height is maintained by compensating for the known sample
height variation, i.e. the distance between the fixed end of the cantilever
and the surface is held constant. The surface is then rescanned with the
oscillating probe driven, in this case, at the resonant frequency (Figure 9.3).
Clearly, the method by which the sample–tip interaction is spatially
modulated can be achieved in several ways. The probe may be caused
1
1 2
FIguRE 9.2 FMM: discrimination between areas of varying stiffness. (1) Hard substrate
and (2) soft substrate; cantilever deflection signal �z 2 is reduced due to deformation of the
sample.
2