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2015 | OriginalPaper | Chapter

15. Intermittent Contact Mode/Tapping Mode

Author : Bert Voigtländer

Published in: Scanning Probe Microscopy

Publisher: Springer Berlin Heidelberg

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Abstract

While the previous chapter was aimed at providing a basic understanding of dynamic atomic force microscopy, we turn now to the intermittent contact mode (or tapping mode) which the mode that is used most frequently under ambient conditions.

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previous chapter Amplitude Modulation (AM) Mode in Dynamic Atomic Force Microscopy

next chapter Mapping of Mechanical Properties Using Force-Distance Curves

The phase \(\phi (A/A_\mathrm {free})\) can be obtained numerically from (2.25) and (2.28). If this result is plotted in Fig. 15.3 it is indistinguishable on top of the curve obtained from (15.4). Alternatively (2.25) and (2.28) can be rearranged analytically leading to (15.4) in a very good approximation.

If we approximate the tip-sample force by \(F_\mathrm {ts} = k' z\) (harmonic oscillator), \(\left\langle F_\mathrm {ts} \cdot z \right\rangle = - 1/2\,k' A^2\) results (cf. (17.10)). Inserting this into (15.11) and remembering that according to (15.4) \(A/A_\mathrm {free} = - \sin {\phi }\), the following expression for the phase is obtained \(\tan {\phi } = k/(k' Q_\mathrm {cant})\), which corresponds to expression (14.14) obtained for the harmonic oscillator.

Correspondingly, the left “ear” also occurs on the high-frequency side of the resonance curve.

Here we used the dependence \(\phi (A/A_\mathrm {free})\) while in an experiment the \(\phi (d)\) is obtained. However, the two dependences can be converted into each other using the (measured) \(A(d)\) dependence.

There are also other reasons for the switch between different oscillation sates. For instance, the presence of a valley in the surface topography can enhance the attractive forces and thus change the force-distance behavior locally, resulting in a switch to another branch of the oscillation state.

Since \(\phi <0\), \(\left\langle P_\mathrm {drive} \right\rangle \) is positive.

While we used here the principle of energy conservation to derive (15.17), this equation can be obtained alternatively by multiplying (15.9) with \(\omega _0 A \sin (\omega t + \phi )\) and integrating over one period.

Title: Intermittent Contact Mode/Tapping Mode
Author: Bert Voigtländer
Publisher: Springer Berlin Heidelberg
Book: Scanning Probe Microscopy
Print ISBN: 978-3-662-45239-4

Electronic ISBN: 978-3-662-45240-0

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-662-45240-0_15

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