Theory of Energy Dissipation into Surface Vibrations
A new avenue in the development and application of the NC-AFM has been opened after the realisation that the amount of excitation needed to keep the oscillation amplitude constant also provides atomic-scale information [1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ]
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19.1
Introduction
A new avenue in the development and application of the NC-AFM has been opened after the realisation that the amount of excitation needed to keep the oscillation amplitude constant also provides atomic-scale information [1-9]. While the frequency shift of the cantilever is thought to be relatively well understood, the nature and magnitude of the change in the excitation signal (damping) has eluded most theorists. The damping signal can be straightforwardly interpreted as dissipation if the electronics system completely linearises the cantilever dynamics and if the response of the whole system is sufficiently fast compared to the scanning speed, so that no transient effects affect the damping signal. Whether this is indeed the case is still the subject of discussion [10,11]. On the other hand, because the tip-surface system is an open one, there is always energy transfer. It is the subject of this chapter to discuss the dissipation mechanisms in NC-AFM. Thus, we shall make no distinction between damping and dissipation in the following discussion. We shall start by briefly describing the dissipation mechanisms that have been proposed so far in NC-AFM. In the remaining part of the chapter, the focus will be on atomic-scale stochastic dissipation. In order to obtain insights into the nature of the dissipation mechanisms in NC-AFM, it is essential to extract those features common to all NCAFM experiments that the theory should consistently account for. Figure 19.1 shows typical experimental topological and damping images of a Cu(100)
Fig. 19.1. Topological (left) and damping signal (right) images of Cu(lOO). (Courtesy of C. Loppacher)
S. Morita et al. (eds.), Noncontact Atomic Force Microscopy © Springer-Verlag Berlin Heidelberg 2002
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Michel Gauthier et al.
surface in ultrahigh vacuum and at room temperature. Large scanning areas can be seen with constant corrugation amplitude. Only for a small number of events does the corrugation suddenly change in both images. At the edge of two constant corrugation regions, there is a small shift in the position of the spots. An irreversible modification in the tip structure is compatible with these rare changes in corrugation and relative position because the interaction between the tip and surface is remarkably sensitive to details of the tip apex structure. Two minimal statements can be made concerning the nature of the damping signal on the constant corrugation portions of the surface. First, the damping signal varies on the atomic scale. This suggests that the underlying mechanism is also sensitive to atomic details, although any dissipation mechanism that depends uniquely on the separation would appear to have an atomic dependency when the scan is performed at constant frequency shift, because the separation is continuously adjusted. Here we assume that this possibility is systematically ruled out in all experiments, for example, by using the damping signal itself to regulate the separation. Second, the scanning is structurally nondestructive, the
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