Force Imaging
Force Calibration (Contact Mode AFM)
Rev. D
Dimension 3100 Manual
225
Ramp size
or offset the scan to a different area of the sample. However, keep in mind that if the
force is minimized in a smooth area of the sample, the cantilever may pull off when it translates to a
rougher part of the sample.
Calculating Contact Force
The force curve clearly shows the relationship between the setpoint and the deflection of the
cantilever. Because the setpoint defines the value of the deflection signal maintained by the
feedback loop, the force curve can be used to calculate the contact force of the tip on the sample if
the spring-constant,
, of the cantilever is known. The contact force is defined by the equation:
where “ ” is the deflection measured from the setpoint to V
CSmin
in nanometers. An example of
how to compute the contact force from the
Force Plot
graph is shown in
.
Figure 13.4e
Computing Contact Force
Recalling that contact force F = kd, we can calculate the contact force from the sample plot above.
Let us assume, for example, that the spring constant of the cantilever is
and that
. The plot above may be measured at the points where the retract
portion of the curve intersects the setpoint to the pull-off (point). The distance is then multiplied
times the deflection sensitivity to obtain
. In this example:
Therefore, the contact force is calculated as:
k
F
k
d
×
=
d
Setpoint
Tip
Deflection
1.0 V / div
Z Position (10.0 V / div)
VCSmin
k
0.6N
m
------------
=
deflection sensitivity
70nm
V
--------------
=
d
d = (4.5 div) (1V/div) (70nm/v) = 315nm
F = (0.6N/m) (315nm)
= 189nN
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