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Phase imaging and the lever-sample tilt angle in dynamic atomic force microscopy

Appl. Phys. Lett. 85, 4738 (2004); doi:10.1063/1.1812839

Issue Date: 15 November 2004

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Matthew J. D'Amato
Materials Science Program, University of Wisconsin, Madison, Wisconsin 53706

Matthew S. Marcus and Mark A. Eriksson
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706

Robert W. Carpick
Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706
The phase shift in amplitude-controlled dynamic atomic force microscopy (AFM) is shown to depend on the cantilever-sample tilt angle. For a silicon sample and tip the phase shift changes by nearly 15° for a change in tilt angle of 15°. This contribution to the phase results from the oscillating tip's motion parallel to the surface, which contributes to the overall energy dissipation. It occurs even when the measurements are carried out in the attractive regime. An off-axis dynamic AFM model incorporating van der Waals attraction and a thin viscous damping layer near the surface successfully describes the observed phase shifts. This effect must be considered to interpret phase images quantitatively. ©2004 American Institute of Physics
History: Received 5 January 2004; accepted 2 September 2004
Permalink: http://link.aip.org/link/?APPLAB/85/4738/1
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KEYWORDS and PACS

Keywords
PACS
  • 07.79.Lh
    Atomic force microscopes
  • 46.40.Ff
    Resonance, damping, and dynamic stability
  • YEAR: 2004

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ISSN:
0003-6951 (print)   1077-3118 (online)
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REFERENCES (20)
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  14. The reported phase shifts are true phase shifts with respect to the drive signal. Phase shifts reported by the instrument are not properly scaled and are shifted by 90°.
  15. All phase images are acquired with a Digital Instruments MultiMode SPM and Nanoscope IIIa controller, using Si cantilevers in ambient laboratory conditions. The free amplitude A0 = 10.5  nm, cantilever quality factor Qcant = 400, resonance frequency omega0 = 2pi×265  kHz, and damped (set point) amplitude A = 5.25  nm are all measurable with or controlled by the AFM controller. For all experiments, the cantilever is driven at the resonance frequency measured far from the sample, which is slightly higher than the resonance frequency during imaging due to the tip's interaction with the surface. An average value for the cantilever spring constant of 25  N/m is measured using the method of Sader and co-workers (Ref. 16).
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  20. Measured values for the pull-off force (40–60  nN) are obtained from force-distance curves. Substituting these values into the DMT model, we obtain a range for the values of gamma  (150–180  J/m2) using a tip radius of 30  nm.

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