# The Principles of Operation of Scanning Force Microscopes (SFM)

Scanning Force Microscopy (SFM) can be used not only as tool for topography acquisition but also can be used to produce spatially resolved maps of the surface or material properties of a sample; these include charge density, adhesion and stiffness, as well as the force required to break specific igand-receptor bonds. SFM can also be used as a tool for force spectroscopy - measuring forces as a function of distance. For oscillating cantilever tip-sample force can affect some other characteristics of cantilever oscillation - amplitude, frequency, phase, dissipation etc. Correspondingly dependence of these characteristics upon tip-sample distance can also be regarded as spectroscopic data.

## Force-Distance Curves

Force is measured in an SFM  by collecting a force curve, which is a plot of cantilever deflection, dc, as a function of sample position along the z-axis (i.e. towards or away from the probe tip; the z-piezo position). It assumes a simple relationship (i.e. Hooke's Law) between the force, F, and the cantilever deflection:

F = - k dc

where k is the spring constant of the cantilever.

## Interpretation of SFM Force Curves

The interpretation of SFM force curves relies almost entirely on established force laws, particularly those determined using the SFA. These force laws describe force as a function of the probe-sample separation distance (D) rather than as a function of the z-piezo position. Thus, to be useful, the force curves must be transformed into descriptions of force as a function of distance, F(D). However, current SFMs do not have an independent measure of D. Instead, the transformation to D is achieved by subtracting the cantilever deflection from the z-piezo movement.

For a very hard surface, zero separation is defined as the region in the force curve in which the cantilever deflection is coupled 1:1 with the sample movement; this appears in the force curve as a straight line of unit slope. A corrected curve is called a force-distance curve. Notice that determining D by this approach requires that the tip make contact with the sample. In practice, there are two factors (long-range forces and sample elasticity) that can make determining the point of contact very difficult. A complete force curve includes the forces measured as the probe approaches the sample and is retracted to its starting position.

Under ambient conditions, the main source of adhesion is the formation of a capillary bridge between the tip and the sample. In air, most samples have several nanometers of water adsorbed to the surface; this water layer wicks up the tip and forms a 'bridge' between the tip and the sample. Pulling the tip out of that bridge requires a large force to overcome the surface tension. In fluid, the adhesive force depends on the interfacial energies between the tip and sample surfaces, and the solution; varying the solution can thus change the force of adhesion.

A different form of 'adhesion' occurs when a polymer is captured between the AFM tip and the substrate. In this case, there is a very distinctive 'adhesive' force as the tip is pulled away. Typically, these curves initially retrace the approach curve near the surface but, away from the surface, exhibit a smooth negative deflection as the polymer is stretched until it breaks or detaches from the tip or the substrate, and the cantilever returns to the zero-deflection line. If multiple polymer molecules attach to the tip and substrate, a saw-tooth pattern can be observed as individual polymers detach.

## Amplitude-Distance Curves

Amplitude-modulation (intermittent-contact, semicontact) mode is widely spreaded oscillating mode and generally speaking can be interpreted and described by the amplitude, phase, frequency and dissipation on one another or on the cantilever-sample distance dependences.

The study of such dependences is necessary according to following circumstances. First of all it relates to obtaining high-grade images (without noise and with high resolution). Then the study of suitable dependences can help in determining the nature of tip-sample interaction, defining forces included in this interaction and formation SPM images. At last the study of suitable curves can help in obtaining more contrastive images and quantitative parameters of sample under investigation.

Obtained in Amplitude-modulation mode images are determined by the row of factors related to the sample as well as to conditions of measurement and values of scanning parameters.

For interpreting results of amplitude-modulation mode usage one can to study dependence of oscillation amplitude the tip-sample distance. Suitable amplitude-distance (a-d) curves (their typical view one can see on the animated picture) can be monotonic or can to have areas of bistability and hysteresis. The presence of the bistability (as is shown on the same picture) leads to arising of the artifacts on the images obtained in Amplitude-modulation mode.

Origin of bistability lies in possibility of simultaneously co-existence oscillations predominantly in attractive or predominantly in repulsive potentials.

The bistability also can arise in complicated shape of tip-sample potential when in initial area cantilever stiffness is greater than potential derivative and the potential derivative becames greater tha cantilever stiffness. With suitable choise of set-point amplitude of cantilever oscillation, its stiffness, sharpness of the tip one can reach conditions when over all sample surface under investigation areas with bistability are absent.

## Frequency-Distance Curves

Analyzing the measured frequency shift versus distance curves one can determine the distance dependence of the tip-sample force. The results of such analyzing demonstrate that not only non-contact, but also elastic contact forces can be quantitatively measured by dynamic force spectroscopy opening a new and direct way to the verification of contact mechanical models of nanoasperities.

This information has been sourced, reviewed and adapted from materials provided by NT-MDT Spectrum Instruments.

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