No abstract

Numerical simulations of the frequency modulation atomic force microscope, including the whole dynamical regulation by the electronics, show that the cantilever dynamics is conditionally stable and that there is a direct link between the frequency shift and the conservative tip-sample interaction. However, a soft coupling between the electronics and the nonlinearity of the interaction may significantly affect the damping. A resonance between the scan speed and the response time of the system can provide a simple explanation for the spatial shift and contrast inversion between topographical and damping images, and for the extreme sensitivity of the damping to a tip change. DOI: 10.1103/PhysRevLett.89.146104 PACS numbers: 68.37.Ef, 07.79.Lh, 87.64.Dz The rapid advance in nanoscale physics has constantly triggered innovative refinement of tools for detecting novel atomic scale phenomena. Scanning tunneling microscopy (STM) [1] exploits the exponential distance decay of the tip-sample tunneling current, and its confinement to the foremost atoms of the tip can provide atomically resolved images of conducting surfaces. Atomic force microscopy (AFM) [2] was devised to extend these capabilities to more general surfaces but the tip-sample contact area is often too large to permit atomic resolution. To remedy the situation, the amplitude modulation (AM) technique [3] (also known as tapping mode), where the change in amplitude of a vibrating cantilever due to the interaction is used for imaging the sample, has been adapted for AFM. However, the nonlinearity of the tipsample force can lead to a complicated dynamical behavior [4] because two stable oscillation states coexist in many situations of interest.Frequency modulation (FM) AFM [5] (also called noncontact AFM) has achieved the long-standing goal of true atomic resolution with AFM in UHV [6,7], as well as the direct measurement of the covalent bonding between the tip apex and sample atoms [8]. In FM-AFM, the dynamical system is more complicated because the oscillation amplitude of the cantilever is kept constant and the separation is regulated by measuring the change in the resonance frequency of the cantilever caused by the interaction force. Because the cantilever motion is highly sinusoidal, the measured frequency shift can be related to the interaction using perturbation theory [9][10][11].In FM-AFM, the amount of excitation necessary to keep the oscillation amplitude constant (damping signal) can also be used as an imaging signal [12 -17], but its magnitude and characteristics have been more difficult to quantify and interpret than the frequency shift. In principle, the damping signal could unleash important information about the surface such as that related to the phonon local density of states in complete analogy with STM [18,19], although preliminary studies indicate that its magnitude is small compared to those reported in experiments. A number of mechanisms such as adhesion hysteresis [10,20 -22] or Joule dissipation have been proposed to account for the...

A general theory is presented which describes the damping in dynamic force microscopy due to the proximity of the surface, consistently with resonant frequency shift effects. Orders of magnitude for the experimentally measured "dissipation" and image corrugation are reproduced. It is suggested that the damping does not mainly result from energy dissipation, but arises because not all solutions of the microlever equation of motion are accessible. The damping is related to the multivalued nature of the analytical resonance curve, which appears at some critical tip-surface separation.