Measuring forces in the tip-sample space
In addition to imaging the surface of samples, another major application of AFM is force spectroscopy. Force spectroscopy involves the direct measurement of forces between the tip and the sample surface as a function of the distance between the two. The result is called a force-distance curve.
The deflection of the cantilever is monitored as it is moved towards and away from the surface, and the deflection plotted as a function of piezoelectric displacement gives the force-distance curve. The horizontal axis in such a curve is typically the vertical distance moved by the sample stage. The vertical axis is the deflection of the cantilever as the tip is moved towards the sample surface, contacts and pushes against the surface and then away from the surface. The vertical axis can then be converted to force by multiplying the deflection of the cantilever by the spring constant of the cantilever (Hooke’s law).
An example of a force distance curve is displayed in Figure 3. The blue curve is the approach cycle and the orange curve is the retract cycle. The different sections of the curve are defined as follows.
- The probe is moving towards the sample surface and does not experience any force and therefore no change in deflection. Therefore the curve is flat. When the tip contacts the surface there is often observed a small “snap-on” section.
- The probe is then pushed against the surface. This is known as the compliance regime and can be used to determine the mechanical properties of surfaces.
- The approach cycle is completed and the retract cycle begins
- The snap-off section of the retract curve. This can yield information on tip-sample adhesion and has been used to determine bond strengths.
- The tip has completely disengaged from the surface and the probe is now moving away from the surface. It now experiences no surface forces and therefore the deflection of the cantilever is zero and the curve is flat.
Figure 3. showing a typical force distance curve acquired on silicon in air
In order to determine the force experienced by an AFM probe important calibrations must be performed. The first is converting the photodiode output from mV or nA (depending on the instrument manufacturer) to nm. This is usually done by performing force-distance curves against a surface much stiffer than the cantilever. The slope of the force curve in the compliance regime will then give the conversion factor or sensitivity. This is also sometimes referred to as the inverse optical lever sensitivity or INVOLS. Surfaces that can be used for such a calibration are typically mica, glass or silicon. For very stiff cantilevers sapphire is a good choice. The calibration surfaces should also be flat and clean and an average of at least 10 force curves on at least 3 separate locations on the sample surface should be acquired.
The next calibration that must be performed is determining the AFM cantilever spring constant. A large number of techniques now exist to calibrate this value. Methods are based on:
- Beam theory: These require knowledge of the cantilever dimensions and material properties
- Resonance methods: Require knowledge of the resonance frequency of the cantilever and/or the thermal noise response of the cantilever
Loading the cantilever with a known force
The appropriate method needs to be chosen and will depend on the type of cantilever used. All AFM users endeavouring to calibrate AFM cantilevers must make sure they use all appropriate corrections as many techniques require corrections due to, for example, the tip-offset distance, cantilever angle to the surface, or tip-height.
The forces that can be measured include atomic bonding, van der Waals forces, single moecule stretching and rupture forces. Force spectroscopy can be used to measure the dispersion force due to a polymer adsorbed on the surface of a substrate, or in biophysics, the mechanical properties of biological materials.