Instruction manual

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 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 11.4d.
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 deflection 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 deflection of the cantilever. When the cantilever deflection 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
Fkd×=
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