Force Imaging
Force Calibration (Contact Mode AFM)
196
MultiMode SPM Instruction Manual
Rev. B
Calculating Contact Force
The force curve clearly shows the relationship between the setpoint and the de
fl
ection of the
cantilever. Because the setpoint de
fi
nes the value of the de
fl
ection 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 de
fi
ned by the equation:
where “ ” is the de
fl
ection 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 11.4d
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 de
fl
ection sensitivity to obtain
. In this example:
Therefore, the contact force is calculated as:*
When the
Data type
is set to
Height
with the feedback gains set high, the tip tracks the sample
surface with nearly constant de
fl
ection of the cantilever. When the cantilever de
fl
ection is constant,
the force is constant and the force calculation above determines the contact force between the tip
and the surface over the entire scan area.
k
F
k
d
×
=
d
Setpoint
Tip
Deflection
1.0 V / div
Z Position (10.0 V / div)
VCSmin
k
0.6
N
m
-----------
=
deflection sensitivity
70
nm
V
--------------
=
d
d
= (4.5 div) (1V/div) (70
nm
/
v
) = 315nm
F
= (0.6N/
m
) (315nm)
= 189nN
