Noncontact Atomic Force Microscopy - Yale School of Engineering ...

Static cantilever deflection in dynamic force microscopy
S. Kawai, Th. Glatzel, S. Koch, B. Such, A. Baratoff, and E. Meyer
Department of Physics, University of Basel, Klingelbergstr. 82, 4056 Basel Switzerland
P.I-05
So far, the influence of the time-averaged cantilever deflection in dynamic force
microscopy (DFM) and spectroscopy [1] has been assumed negligibly small or constant,
or else regarded as the source of jump-to-contact instabilities. But in fact, for a given tipsample
distance of closest approach, the static deflection increases with decreasing
oscillation amplitude. As a consequence, small-amplitude DFM is able to simultaneously
detect the influence of atomic-scale interaction forces on time-averaged, as well as
dynamic measured quantities. The use of higher resonances [2,3] is well-suited for this
comparison because a typical static stiffness kc ~ 30 N/m can cause a measurable timeaveraged
deflection. Nevertheless kc is still high enough to avoid cantilever jump-tocontact
instabilities when a surface with a low reactivity is scanned with a sharp Si tip [4]
We theoretically and experimentally studied the effects of the time-averaged
deflection in DFM. Figure 1(a) and 1(b) shows a series of frequency shift and static
deflection vs. distance curves measured using different amplitudes A2nd of the second
flexural mode above a maximum of the topographic image of KBr(001). Figure 1(c)
shows force vs. distance curves with and without compensation of the static deflection. It
is found that the static deflection affects not only the Z-distance scale,
but also the
converted force. Force curves extracted from Δf2nd(Z) measured with different A2nd
coincide if shifted along Z and exhibit a wiggle which is likely due to a sideways
displacement of the tip apex towards a nearby counterion on the sample surface [1].
Figure 1: A series of (a) frequency shift and (b) static deflection vs. distance curves. (c) Force vs.
distance curves with (Zc) and without (Z’c) compensation of the static deflection.
[1] A. Schirmeisen et al., Phys. Rev. Lett. 97, 136001 (2007).
[2] S. Kawai et al., Appl. Phys. Lett. 86, 193107 (2005).
[3] S. Kawai and H. Kawakatsu, Appl. Phys. Lett. 88, 133103 (2006)
[4] S. Kawai and H. Kawakatsu, Phys. Rev. B 79, 115440 (2009).
96