Chemistry Reference
In-Depth Information
circuit that can automatically produce a transfer function that is approximately the
same as the inverse transfer function of a given transfer function [9, 17]. This
approximation becomes better with the use of operational ampli
ers having higher
bandwidths. This method works not only for reducing the quality factor but also for
extending the apparent resonant frequency, so long as thedriver for thepiezoactuators
has enough gain at high frequencies. Using this method and holding a piezoactuator
(resonant frequency, 370 kHz) at its corners, we achieved a bandwidthof 500 kHz for a
z-scanner which can be maximally displaced by 1
m
m (unpublished data).
12.5.3
Dynamic PID Control
Various efforts have been made to increase the AFM scan speed. However, not much
attention has been directed towards reducing the tip-sample interaction force. This
reduction is quite important for biological AFMimaging. Themost ideal scheme is the
use of non-contact AFM (nc-AFM) but, to date, high-speed nc-AFM has not been
exploited. It isunknownif thehigh-speedandnon-contactconditionscanreconcilewith
eachother.Wediscuss thismatter later. Thereareseveralmethods toreduce the force in
tapping mode: (a) using softer cantilevers, (b) enhancing the quality factor of small
cantilevers, (c) using a shallower amplitude set point (i.e. r is close to 1) . However,
none of these methods appear compatible with high-speed scanning. Softer
cantilevers can be obtained only by sacri
cing the resonant frequency. The most
advanced small cantilevers developed seem to have reached their limit in balancing
high resonant frequency with a small spring constant. Although the tapping force
decreases with increasing Q in the cantilever so too does its response speed.
The last possibility, a shallower amplitude set point, promotes parachuting
during which the error signal is saturated at 2A
0
(1
r), and therefore, the parachut-
ing time is prolonged with increasing r, resulting in decrease in the feedback
bandwidth. This dif
cult issue was resolved by the invention of a new PID controller
known as a dynamic PID controller whose gains were automatically changed
depending on the cantilevers oscillation amplitude [6]. Brie
y, a threshold level is set
between the peak-to-peak free oscillation amplitude, 2A
0
, and the set point amplitude,
2A
0
r. When the cantilever oscillation amplitude exceeds this threshold level, the
feedback gain is increased, which either shortens the parachuting time or avoids it
entirely. The dynamic PID controller can avoid parachuting in fact even when r is
increased to
0.9. Therefore, the feedback bandwidth becomes almost independent
of r so long as r is set at less than
0.9 (Figure 12.3). Thus, high-speed scanning and
gentle handling of the sample do not necessarily con
ict.
12.6
Bioimaging
Various attempts to capture biological processes have been made in order to test
high-speed AFM. Imaging studies have also been undertaken to establish
