Biomedical Engineering Reference
In-Depth Information
Kawakatsu et al., 2002). This detection scheme is very often used in low-temperature,
ultrahigh vacuum (UHV) systems. It is also possible to use cantilevers with inte-
grated deflection sensors based on piezoresistive films (Tortonese et al., 1993; Yuan
et al., 1994; Linnemann et al., 1996). Since no optical parts are needed in the experi-
mental setup of an AFM with self-sensing cantilevers, their design can be very com-
pact (Stahl et al., 1994). However, since it is very difficult to produce piezoresistive
cantilevers with a high, consistent quality, they are rarely used today.
During scanning of the surface, the deflection of the cantilever is kept constant by
a feedback system, which controls the vertical movement of the scanner. A schematic
of the feedback system is drawn in Figure 2.3. It works as follows: The current signal
of the photodiode is compared with a preset value. The feedback system including a
proportional, integral, and differential (PID) controller varies the z-movement of the
scanner to minimize the difference. As a consequence, the tip-sample force is kept
practically constant for an optimal setup of the PID parameters.
While the cantilever is moving relative to the sample in the x-y-plane of the sur-
face by a piezoelectric scanner, the current z-position of the scanner is recorded as
a function of the lateral x-y-position with (ideally) sub- Angstrom precision. The
(a)
(b)
8
8
Soft sample
Hard sample
Soft sample
Hard sample
4
4
0
0
-4
-1.5
-4
-1.0
-0.5 0.0 0.5
Tip-sample distance z (nm)
1.0
1.5
-1.5
-1.0
-0.5 0.0 0.5
Tip-sample distance z (nm)
1.0
1.5
(c)
(d)
8
8
Soft sample
Hard sample
Soft sample
Hard sample
4
4
0
0
-4
-4
-1.5
-1.0
-0.5 0.0 0.5
Cantilever position d (nm)
1.0
1.5
-1.5
-1.0
-0.5 0.0 0.5
Cantilever position d (nm)
1.0
1.5
FIGURE 2.3
(
See color insert.
) Tip-sample forces using the (a) Hertz and (b) DMT-M
model for a hard (
E
hard
=
100 GPa) and soft (
E
soft
=
1 GPa) sample assuming a tip radius
of 10 nm. The other parameters are
z
0
=
2aJ.
(c) If these forces are measured with an atomic force microscope using a cantilever with a
spring constant of 5 N/m, the resulting force versus curves show significantly reduced slope
due to the elasticity of the cantilever. Without the presence of adhesion forces (Hertz model),
the curves are continuous. (d) Adhesion results in a hysteresis between forward and backward
movement of the cantilever as marked by the arrows. (See Section. 2.2 for more details on this
effect.)
0
.
3nm,μ
t
=
μ
s
=
0
.
3,
E
t
=
130 GPa,
A
H
=
0
.
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