and a sample when an AFM is operated. In contact mode the deflection of the cantilever is measured, and in vibrating mode the changes in frequency and amplitude are used to measure the force interaction. As a rule of thumb, the forces between the probe and surface are greater with contact modes than with vibrating modes.

In contact mode, the cantilever is scanned over a surface at a fixed deflection, Figure 4-5. Provided that the PID feedback loop is optimized, a constant force is applied to the surface while scanning. If the PID feedback parameters are not optimized, a variable force is exerted on the surface by a probe during a scan.

FIGURE 4-5 Left: Potential diagram showing the region of the probe while scanning in contact mode. Right: In contact mode the probe glides over the surface.

The forces applied to the surface by the probe in contact mode are given by Hook's law:

The force constant may be calculated if the dimensions and material of the cantilever are known. Most commercially available cantilevers for the AFM are supplied with the approximate values for the force constant. However, there is typically a very large error in the force constant because of the uncertainties in the thickness of the cantilever. If it is important to know the exact force between the probe and surface, it is recommended to use the Sader⁵ method. In this method the length and width of the cantilever are measured with an optical microscope. The Q of the cantilever is measured and then the force constant can be calculated.