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Normal and torsional spring constants of atomic force microscope cantilevers

Rev. Sci. Instrum. 75, 1988 (2004); doi:10.1063/1.1753100

Published 21 May 2004

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Christopher P. Green
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

Hadi Lioe
School of Chemistry, University of Melbourne, Victoria 3010, Australia

Jason P. Cleveland and Roger Proksch
Asylum Research, Santa Barbara, California 93117

Paul Mulvaney
School of Chemistry, University of Melbourne, Victoria 3010, Australia

John E. Sader
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
Two methods commonly used to measure the normal spring constants of atomic force microscope cantilevers are the added mass method of Cleveland et al. [J. P. Cleveland et al., Rev. Sci. Instrum. 64, 403 (1993)], and the unloaded resonance technique of Sader et al. [J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999)]. The added mass method involves measuring the change in resonant frequency of the fundamental mode of vibration upon the addition of known masses to the free end of the cantilever. In contrast, the unloaded resonance technique requires measurement of the unloaded resonant frequency and quality factor of the fundamental mode of vibration, as well as knowledge of the plan view dimensions of the cantilever and properties of the fluid. In many applications, such as frictional force microscopy, the torsional spring constant is often required. Consequently, in this article, we extend both of these techniques to allow simultaneous calibration of both the normal and torsional spring constants. We also investigate the validity and applicability of the unloaded resonance method when a mass is attached to the free end of the cantilever due to its importance in practice. ©2004 American Institute of Physics.
History: Received 24 June 2003; accepted 8 March 2004; published 21 May 2004
Permalink: http://link.aip.org/link/?RSINAK/75/1988/1
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KEYWORDS and PACS

Keywords
PACS
  • 07.79.Lh
    Atomic force microscopes
  • 46.80.+j
    Measurement methods and techniques in continuum mechanics of solids
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
0034-6748 (print)   1089-7623 (online)
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REFERENCES (34)
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  14. Using finite element analysis, (Ref. 20) it is found that the distance between the center of the mass and the neutral axis of the cantilever, when the mass is aligned with the major axis of the cantilever, has an insignificant effect on the torsional mode of deformation, i.e., coupling into other modes is negligible.
  15. This condition is typically satisfied in practice.
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  27. The signal was collected and digitized using a data acquisition board (Ref. 28). Multiple measurements were taken. These were then windowed together using a Hanning function, fast Fourier transformed, and finally averaged together to obtain the required thermal noise spectra (Ref. 29).
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