Abstract
In Chap. 15 we introduced the intermittent contact mode (tapping mode), which is a very successful operation mode in dynamic atomic force microscopy.
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Notes
- 1.
Under the influence of the tip-sample force the resonance frequency of the free cantilever, \(\omega _0\), shifts to \(\omega '_0\).
- 2.
For the case of AM detection, we have seen in Sect. 14.5 that after a change of the resonance frequency of the cantilever the new steady-state amplitude and phase are reached only after a large time constant \(\tau _\mathrm {cant} = 2Q/\omega _0\), corresponding to about \(Q\) oscillations.
- 3.
This transition from the free state to the state with tip-sample interaction present (working point) gives an upper limit for energy changes occurring during scanning. Deviations from the setpoint values (amplitude/frequency shift) under feedback operation are much smaller than the deviations in amplitude/frequency shift between the free cantilever and the situation with tip-sample interaction present.
- 4.
While the PLL provides a frequency match \(\omega _\mathrm vco =\omega _\mathrm cant \), a phase \(\phi _0\ne 0\) remains. The relation
$$\begin{aligned} \omega _\mathrm {cant} = \omega _\mathrm {work} + \Delta \omega \overset{!}{=} \omega _\mathrm {vco} = \omega _\mathrm {work} + K_\mathrm {pd} K_\mathrm {vco} \cos \left( \delta \omega t + \phi _0\right) , \end{aligned}$$(17.34)results for the condition \(\delta \omega = 0\) in
$$\begin{aligned} \Delta \omega = K_\mathrm {pd} K_\mathrm {vco} \cos \phi _0. \end{aligned}$$(17.35)Thus a static phase difference \(\phi _0\) different from \(\phi _0 = 90^{\circ }\) evolves in order to adapt the VCO frequency to the changed cantilever frequency.
- 5.
This is the case for a PLL with a fast time constant. If the PLL has a time constant longer than \(\tau _\mathrm {cant}\), the PLL time constant will limit the overall time constant.
- 6.
In the PLL circuits used for example in communications, the PI controller is often not included.
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Voigtländer, B. (2015). Frequency Modulation (FM) Mode in Dynamic Atomic Force Microscopy—Non-contact Atomic Force Microscopy . In: Scanning Probe Microscopy. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45240-0_17
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DOI: https://doi.org/10.1007/978-3-662-45240-0_17
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