Effect of Microscopic Nonconservative Process on Noncontact Atomic Force Microscopy

Abstract

Effects of the tip-induced nonconservative processes of the tip or surface atom on the cantilever dynamics of noncontact atomic force microscopy (nc-AFM) are theoretically analyzed based on the time-averaging perturbation theory. The typical order of the magnitude of the Q value due to such nonconservative processes is estimated to be on the order of 104, which is comparable to the intrinsic dissipation of the cantilever free oscillation. The additional frequency shift due to the hysteresis loop of the force curve is estimated to be on the order of 10 Hz. This part of the frequency shift sets in like a step function when the tip turning point approaches the surface within a certain threshold height. This feature explains the experimental observation of the discontinuous frequency shift at chemical reactive sites.

Site-specific force-distance characteristics on NaCl(001): Measurements versus atomistic simulations

“…Indeed, the resulting force hysteresis between approach and retraction would manifest itself as a drop in the frequency shift at the distance where the jump occurs upon approach. [37][38][39][40] It is important to note that in the experiments the tip is oscillated with a large amplitude and high frequency relative to the time scale of the frequency versus distance measurement. Each data point is actually the average of many oscillation cycles.…”

“…This does not imply that the system evolves continuously; indeed the underlying force hysteresis causes dissipation. [37][38][39][40] Stable imaging appears impossible at distances below the maximum one for which a force hysteresis appears. One possible exception arises if the underlying instability leads to a more stable tip configuration which is preserved in subsequent approach-retraction cycles.…”

Interplay between Nonlinearity, Scan Speed, Damping, and Electronics in Frequency Modulation Atomic-Force Microscopy

“…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.…”

“…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].…”

“…This clearly requires a nonperturbative approach to the dynamical problem including the whole FM-AFM system; as we shall see, many effects found here are beyond the reach of perturbation theory [9,10,23]. To accomplish this, we perform numerical simulations of FM-AFM which are depicted in Fig.…”