W. Richard Bowen and Nidal Hilal 4

2 1. BAsIC PRINCIPLEs OF ATOMIC FORCE MICROsCOPy
.4.5 force modulation mode
Force modulation mode combines some of the aspects of both contact
and dynamic modes of imaging. During the operation of the force
modulation mode of AFM, either the cantilever or the sample is oscillated
sinusoidally in the z-direction, while raster-scanning the probe
across the sample surface whilst in constant contact [66–70]. The amplitude
and phase of these oscillations is monitored simultaneously with
the creation of a topographic image of the surface. This allows changes in
the mechanical compliance of the surface to be monitored and compared
with changes in the topography. From the knowledge of the stiffness of
the cantilever, the geometry of the probe apex and its area of contact with
the sample and the utilisation of an appropriate contact mechanics model
such as the Hertz or the Johnson, Kendall and Roberts (JKR) models, it
is possible to extract useful quantitative information about the material
properties of the surface, such as the elastic modulus. The ability of this
technique to monitor differences in the surface mechanical properties
between different domains of surfaces to the high resolution obtainable
with the AFM is of much use in the characterisation of materials engineered
on the nano-scale.
.4.6 lateral/frictional force mode
In lateral force mode, the forces exerted upon the probe tip in the lateral
(x) direction as it is scanned across a surface are recorded simultaneously
with topography. This is of particular interest for obtaining
quantitative measurements of the frictional forces felt between the probe
and the sample [29, 30, 71–74] and of much interest in the field of nanotribology,
where the frictional and wearing properties of materials used to
construct micro-machines is of great importance due to their high surface
area to volume ratio. To extract quantitative data from the measurements,
a number of variables need to be accounted for, such as the normal force
applied by the probe tip, the lateral spring constant of the cantilever (see
Section 1.4.2), the geometry of the tip apex (particularly its area of contact
with the surface) and the sensitivity of the optical lever to the torsional
bending of the lever arm.
.5 The afm as a forCe sensor
One of the major applications of the AFM is in the quantitative measurement
of interaction forces between either the probe tip, or an attached
particle replacing the tip, and a sample surface. This technique has been
employed to examine a wide variety of systems including the mechanical