W. Richard Bowen and Nidal Hilal 4

1.5 THE AFM As A FORCE sENsOR 3
properties of materials on the micro- and nano-scales [75–80] of interest
for characterising nano-engineered materials; adhesion between surfaces
[80–85]; attractive and repulsive surface forces, such as van der Waals and
electrostatic double layer forces [86–89] both of interest when studying
the properties of colloidal particles; and to probe the mechanical properties
and kinetics of bond strength of biomolecules [90–93].
As the tip of the cantilever is brought into and out of contact with a
surface, a force curve is generated, describing the cantilever deflection
(or force) as a function of distance. A typical force curve is illustrated in
Figure 1.4. Raw data are plotted as displacement of the z-piezo on the
abscissa, whilst cantilever deflection is plotted as the signal on the photodetector
(commonly either as voltage V or sometimes as current A)
on the ordinate. As the cantilever begins its approach (described by the
red trace), it is away from the surface and hence there is no detection of
change in force (point 1 in the figure) – the cantilever is said to be at its
‘free level’, i.e. at this point there are no net forces acting on it (assuming
that the probe is not travelling fast enough for hydrodynamic drag
forces to have a significant effect). As the probe comes into close proximity
with the cantilever, long-range forces may cause interaction between
the probe and the objective surface. Repulsive forces will cause the lever
to deflect upwards and away from the surface, whereas attractive forces
will deflect the lever downwards, towards the surface. If the gradient of
attractive forces is less than the stiffness of the lever, then the probe will
momentarily be deflected downwards, before re-equilibrating at its free
level due to the restoring force stored in the lever. If the probe reaches
a point where the gradient of attractive forces exceeds the stiffness of
the cantilever, then the cantilever will be rapidly deflected downwards
allowing the probe to touch the surface in a ‘snap-in’ or ‘jump-to-
contact’. In the absence of attractive surface forces, this jump-to-contact
will not be seen. When the cantilever makes hard contact with the surface,
it is deflected upwards due to repulsion between electron shells of
atoms in the opposing material surfaces, and a positive force is observed
(point 2). The cantilever is then retracted and initially follows the path
of the approach trace in the contact region. The cantilever often remains
attached to the surface by adhesive forces which results in a downwards
deflection of the cantilever as the probe retracts away from the surface,
causing a hysteresis between the trace and the retrace. Eventually the
separation force becomes sufficient to overcome the adhesion between
the probe tip and the surface, and the cantilever snaps back to its initial
free level position (point 3).
This behaviour results in a curve of deflection (measured as raw signal)
versus displacement of the piezo in the z-direction. When the surface
being pressed against is hard and does not undergo significant deformation,
the z-movement will be equal to the deflection of the cantilever. As a