A method is presented to measure the energy dissipated by the tip–sample interaction in tapping-mode atomic force microscopy (AFM). The results show that if the amplitude of the cantilever is held constant, the sine of the phase angle of the driven vibration is then proportional to changes in the tip–sample energy dissipation. This means that images of the cantilever phase in tapping-mode AFM are closely related to maps of dissipation. The maximum dissipation observed for a 4 N/m cantilever with an initial amplitude of 25 nm tapping on a hard substrate at 74 kHz is about 0.3 pW.

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The conservative and dissipative forces between tip and sample of a dynamic atomic force microscopy ͑AFM͒ were investigated using a combination of computer simulations and experimental AFM data obtained by the frequency modulation technique. In this way it became possible to reconstruct complete force versus distance curves and damping coefficient versus distance curves from experimental data without using fit parameters for the interaction force and without using analytical interaction models. A comparison with analytical approaches is given and a way to determine a damping coefficient curve from experimental data is proposed. The results include the determination of the first point of repulsive contact of a vibrating tip when approaching a sample. The capability of quantifying the tip-sample interaction is demonstrated using experimental data obtained with a silicon tip and a mica sample in UHV. ͓S0163-1829͑99͒01839-1͔

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The performance of a scanning force microscope (SFM) operated in the dynamic mode at high oscillation amplitudes is determined by the response of the system to a given set of interaction forces between the probing tip and the sample surface. To clarify the details of the cantilever/tip dynamics two different aspects were investigated in experiment and computer simulation. First, the interaction forces dominating the oscillatory motion of the probe were varied by applying an additional electrostatic force field. It is shown that such variations in the attractive part of the interaction potential can cause a switching between two different oscillation states and thereby significantly contribute to the contrast obtained from phase imaging. Secondly, the interaction forces were kept constant but the system response itself was varied by modifying the effective quality factor of the oscillating cantilever with an active feedback circuit. This provides a means to influence the transition from the attractive to the partly repulsive interaction regime, i.e. the onset of the intermittent contact or tapping mode.Operating an SFM in the dynamic mode at high amplitudes (> 10 nm) offers the possibility of minimizing the contact time of the probing tip with the sample surface and thereby reduce lateral or friction forces involved in the scanning process. It also allows the collection of additional data related to different sample properties by recording the phase shift between the force driving the cantilever and its oscillation. In the last few years these features of operating the SFM in the dynamic mode [1, 2] were shown to be very useful to characterize several different kinds of sample surfaces, e.g. thin organic films, polymers, biological samples or even liquid droplets [3]. Although this has led to a steady increase in the number of possible applications, there are still several details of the interaction process between the tip and the sample that need further clarification. The overall goal must be to relate the experimentally accessible data, such as the amplitude and * Corresponding author phase signal, more or less directly to specific sample properties, such as topography, elasticity and viscoelasticity.Because highly nonlinear interaction forces are involved when the oscillating tip is in close proximity to a solid surface, the analysis of the dynamic system becomes quite complex. Therefore supplementary computer simulations based on proper mathematical models are useful to investigate the details of the interaction process. Basically, the equation of motion describing the dynamic properties of the probing tip has to be solved in such a way that the influence of different parameters characterizing the probe as well as the sample surface can be examined. There have been several reports recently on different approaches to this problem, providing analytical [4] as well as numerical [5][6][7][8][9][10][11] solutions. Most of them are based on the point-mass model, but there are also approaches which describe the comp...