Biomedical Engineering Reference
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(a)
(c)
10
8
F
ts
Reconstructed
9
8
7
6
5
4
0
-4
-0.5
6
8
Cantilever position (nm)
10
12
0.0
0.5
1.0
1.5
2.0
Tip-sample distance (nm)
(b)
-40
(d)
40
-50
-60
-70
-80
-90
-100
-110
-120
30
20
Δ
E
Reconstructed
10
0
-0.5
6
8
Cantilever position (nm)
10
12
0.0
0.5
1.0
1.5
2.0
Tip-sample distance (nm)
(e)
40
20
0
-20
-40
-0.5
0.0
0.5
1.0
1.5
2.0
Tip-sample distance (nm)
FIGURE 2.12
A numerical verification of the proposed algorithm. On the basis of the equa-
tion of motion Equation 2.12, the amplitude (a) and phase (b) versus distance curves during
the approach toward the sample surface have been numerically calculated. Both curves show
the instability that is typical for AM-DFM operation in ambient conditions. As described in
the text, the data is used for the reconstruction of the tip-sample force (c) and the energy dissi-
pation (d). The assumed tip-sample model interactions according to Equations 2.9c and 2.30d
are plotted by solid lines. Finally, (e) reflects the κ
(
D
)
values that can be computed from the
amplitude and phase values given in (a) and (b).
component to our original model interaction force
F
DMT
−
M
Equation 2.9. Instead
of exploring elaborate energy dissipation mechanisms, it is sufficient for princi-
ple demonstration to simply add an additional dissipative force term
F
diss
,thatis,
F
ts
F
diss
. To characterize
F
diss
, we chose viscous damping with an exponen-
tial distance-dependence:
F
diss
=
F
air
+
z
. The energy dissipation caused by
this type of dissipation is given by (Gotsmann et al., 1999)
=
F
0
exp
(
−
z
/
ζ
0
)
4π
2
f
d
AF
0
ζ
0
exp
I
1
A
ζ
0
D
+
A
Δ
E
=
−
(2.30)
ζ
0
where
I
1
is the modified Bessel function of the first kind.
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