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Erschienen in:

2015 | OriginalPaper | Buchkapitel

14. Amplitude Modulation (AM) Mode in Dynamic Atomic Force Microscopy

verfasst von : Bert Voigtländer

Erschienen in: Scanning Probe Microscopy

Verlag: Springer Berlin Heidelberg

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Abstract

In dynamic atomic force microscopy the cantilever is excited using a piezo actuator which oscillates the cantilever base. The driving frequency is usually close to the resonance frequency of the cantilever. Due to the interaction between tip and the surface, the resonance frequency of the cantilever changes.As shown in this chapter, an attractive force between tip and sample leads to a lower resonance frequency of the cantilever, while for repulsive tip-sample forces the resonance frequency increases.

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Vorheriges Kapitel Static Atomic Force Microscopy

Nächstes Kapitel Intermittent Contact Mode/Tapping Mode

Actually, this is not strictly true: As shown later it is not the sign of the force, but rather the sign of the force gradient that determines the direction of the resonance frequency shift.

Since the two springs attach to the tip from above and below one might think that this should lead to a subtraction of the spring constants. Here we show that the spring constants indeed add up. As indicated in Fig. 14.2 the cantilever spring under the influence of a tip-sample force can be replaced by a cantilever effective mass held by two springs. In static equilibrium, \(z=0\), the forces of both springs compensate as \(F_{k} + F_{k'} = 0\). If the cantilever is moved by \(\Delta z\) during the oscillation, Fig. 14.2b shows that the force components relative to the forces in static equilibrium point in the same direction for both springs and \(\Delta F = \Delta F_k + \Delta F_{k'} = - (k + k') \Delta z\) results. Thus the spring constants \(k\) and \(k'\) combine to \(k_\mathrm {eff} = k + k'\).

The tip length is set to zero in order to avoid an additional offset length.

Technically the driving signal can be considered as a carrier signal which is modulated by a low-frequency (quasi-DC) amplitude signal (deviations from the desired amplitude setpoint). Then the task of the lock-in amplifier is the demodulation of the low frequency amplitude signal. The term demodulation is traditionally used in connection with signal detection in AM radio receivers. This is the reason why the term AM detection is used for this detection scheme.

This value for the frequency shift was chosen as it leads to half of the original amplitude in the steady-state.

The curves in Fig. 14.9 are plotted using (14.12) and (14.13). The resonance curves for two different resonance frequencies do not exactly correspond to a shift of the resonance curve. However, Fig. 14.9a shows that these curves correspond to a very good approximation to a shift.

Titel: Amplitude Modulation (AM) Mode in Dynamic Atomic Force Microscopy
verfasst von: Bert Voigtländer
Verlag: Springer Berlin Heidelberg
Buch: Scanning Probe Microscopy
Print ISBN: 978-3-662-45239-4

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

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-662-45240-0_14

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