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

Th-1000
Analysis of bimodal and higher mode small-amplitude near-contact
AFM and energy dissipation
S. Kawai, A. Baratoff, Th. Glatzel, S. Koch, B. Such, and E. Meyer
Department of Physics, University of Basel, Klingelbergstr. 82, 4056 Basel Switzerland
Recently enhanced atomic-scale contrast was achieved on KBr(001) in UHV using
resonant self-excitation of the lowest two cantilever flexural modes with constant tip
oscillation amplitudes A1 >> A2 by monitoring the interaction induced frequency shift Δf2
while controlling the closest approach distance z via Δf1 [1]. Optimum sensitivity and
contrast in non-contact AFM using the 2 nd mode alone can in principle be achieved for z
below the interatomic separation and A2 close to the range of the tip-sample interaction [2
3]. Stable operation under such conditions can, however, be jeopardized by atomic jumps
even if macroscopic jump-to-contact is prevented by using a sufficiently stiff deflection
sensor. Simultaneous excitation of the fundamental mode with a large A1 alleviates this
problem for reasons to be discussed.
Under the stated conditions, Δf2 is to a good approximation proportional to the time
average of the interaction force gradient over one cycle of the fundamental oscillation, as
demonstrated and verified by simulations and measurements [1]. An application of the
same argument to atomic-scale Kelvin Force Microscopy using voltage modulation at f2
shows that the resulting deflection signal at f2 is proportional to the time average of the
electrostatic force [4].
Measurements to be reported separately using the 2 nd mode alone with amplitudes as
small as 0.5 nm show smooth force vs. distance curves extracted from Δf2, as well as a
small time-averaged deflection proportional to the time-average of the force.
In all three cases, the site-dependent distance dependence of the time-averaged force
gradient, electrostatic or total force can be extracted from the measured frequency shift,
deflection signal at f = f2 or f = 0 using slightly modified versions of inversion algorithms
proposed for single-mode non-contact AFM [5, 6]
The magnitude, distance and amplitude dependences of the interaction-induced energy
dissipation per oscillation cycle simultaneously measured using the 2 nd mode suggest that
the dominant cause of dissipation is a force hysteresis loop narrower than twice A, but
significantly smeared by thermal activation. However, some velocity-dependent
damping with a coefficient decaying with increasing distance must also be present.
Possible mechanisms and a hitherto ignored difficulty in extracting meaningful
"dissipative forces" in the presence of both mechanisms will be discussed.
[1] S. Kawai et al., submitted.
[2] F. J. Giessibl et al., Appl. Surf. Sci.140, 352 (1999).
[3] S. Kawai et al., Appl. Phys. Lett. 89, 023113 (2006).
[4] S. Kawai et al., unpublished
[5] O. Pfeiffer et al., Phys. Rev. B 65, 161403R (2002)
[6].J. E. Sader and S. P. Jarvis, Appl. Phys. Lett. 84, 1801 (2004)
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