Imaging and Manipulation of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 109

Force

contact between tip and sample

repulsive

intermittent contact

Tip-sample distance

0

non-contact between
tip and sample

attractive

Fig. 3.1 AFM modes of operation as a function of the tip-sample separation

In the FM mode, the interaction force between the tip and the sample modifies
slightly the resonant cantilever frequency f 0 , such that its shift f is proportional to
the gradient of this force. The shift in frequency is then measured and the interacting
force is calculated by integration. A two-dimensional distribution of this force is
obtained by scanning the whole surface of the sample.
In the AM mode, the gradient of the force between the tip and the sample
is proportional to the phase of the deflected signal and the cantilever amplitude,
both parameters being controlled by a lock-in amplifier. Irrespective of the AFM
dynamical modulation mode, a feedback signal preserves constant the frequency,
amplitude, or phase of the oscillating cantilever.
In the static mode , termed as contact mode or repulsive mode, the cantilever
makes direct contact with the sample, and the deflection of cantilever z .x;y/ is
induced by the weak repulsive force acting between the surface atoms and the atoms
on the tip. In the contact operation mode, a feedback system maintains constant
the force on the surface, and thus the deflection of the cantilever is preserved at
a constant value of, generally, less than 0.1 nm. The surface topography z .x;y/
is determined, with vertical and horizontal resolutions as small as 0.1 nm, by
measuring the cantilever deflection. In this operating mode, the AFM responds
to forces in the 10 nN-10 pN range, which is located between the hydrogen
bonding force, of 10 pN, and chemical ionic bonding forces, of around 100 nN
( Bhushan 2004 ).
In the contact mode, the surface topography is exposed at the atomic scale, such
that individual atoms or clusters of few atoms can be discerned. Distinctive V-shaped
cantilevers, as that displayed in Fig. 3.2 , which reduce the lateral forces that could
destroy the cantilever, must be used to achieve atomic resolution. These V-shaped
cantilevers have a lower spring constant than an equivalent atomic spring constant
of only 0:04-1 Nm 1 . The equivalent atomic spring constant is determined from
! 2 m 10Nm 1 , corresponding to atoms bound to molecules or solid crystals that
oscillate at 10 THz and have a mass of 10 25 kg. The AFM contact mode has some
drawbacks, for example, some surfaces (e.g., biological surfaces) are destroyed as a
result of direct contact with the cantilever tip, and strong lateral forces are produced
by the capillarity of the thin water layer that is adsorbed at ambient temperature on
any surface.