Linearity of amplitude and phase in tapping-mode atomic force microscopy

Abstract

In this article tapping-mode atomic force microscope dynamics is studied. The existence of a periodic orbit at the forcing frequency is shown under unrestrictive conditions. The dynamics is further analyzed using the impact model for the tip-sample interaction and a spring-mass-damper model of the cantilever. Stability of the periodic orbit is established. Closed-form expressions for various variables important in tapping-mode imaging are obtained. The linear relationship of the amplitude and the sine of the phase of the first harmonic of the periodic orbit with respect to cantilever-sample offset is shown. The study reinforces gentleness of the tapping-mode on the sample. Experimental results are in excellent qualitative agreement with the theoretical predictions. The linear relationship of the sine of the phase and the amplitude can be used to infer sample properties. The comparison between the theory and the experiments indicates essential features that are needed in a more refined model. Disciplines Electrical and Computer Engineering | Engineering Physics CommentsThis article is from Physical Review B 61 (2000) In this article tapping-mode atomic force microscope dynamics is studied. The existence of a periodic orbit at the forcing frequency is shown under unrestrictive conditions. The dynamics is further analyzed using the impact model for the tip-sample interaction and a spring-mass-damper model of the cantilever. Stability of the periodic orbit is established. Closed-form expressions for various variables important in tapping-mode imaging are obtained. The linear relationship of the amplitude and the sine of the phase of the first harmonic of the periodic orbit with respect to cantilever-sample offset is shown. The study reinforces gentleness of the tappingmode on the sample. Experimental results are in excellent qualitative agreement with the theoretical predictions. The linear relationship of the sine of the phase and the amplitude can be used to infer sample properties. The comparison between the theory and the experiments indicates essential features that are needed in a more refined model.

Transient force atomic force microscopy: systems approaches to emerging applications

“…This is satisfied in most typical operations because in the dynamic mode, the time spent by the tip under the sample's influence is negligible compared to the time it spends outside the sample's influence [16]. The assumption is also corroborated by experimental results provided later.…”

Channel modeling and detector design for dynamic mode high density probe storage

“…This is satisfied in most typical operations because in the dynamic mode, the time spent by the tip under the media's influence is negligible compared to the time it spends outside the media's influence [10]. Indeed typically the oscillation amplitudes range from 10-80 nm whereas the tip-media interaction is effective from 2-5 nm separations and lower separations.…”

A Review of the Systems Approach to the Analysis of Dynamic-Mode Atomic Force Microscopy

“…The forcing signal is assumed to be periodic, with period . It is shown in [21] that under unrestrictive assumptions, a cantilever-sample system admits a periodic solution with the same period as that of the forcing signal . Such a periodic solution is denoted by…”