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Calibration of rectangular atomic force microscope cantilevers

Rev. Sci. Instrum. 70, 3967 (1999); doi:10.1063/1.1150021

Issue Date: October 1999

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John E. Sader
Department of Mathematics and Statistics, University of Melbourne, Parkville, 3052 Victoria, Australia

James W. M. Chon and Paul Mulvaney
School of Chemistry, University of Melbourne, Parkville, 3052 Victoria, Australia
A method to determine the spring constant of a rectangular atomic force microscope cantilever is proposed that relies solely on the measurement of the resonant frequency and quality factor of the cantilever in fluid (typically air), and knowledge of its plan view dimensions. This method gives very good accuracy and improves upon the previous formulation by Sader et al. [Rev. Sci. Instrum. 66, 3789 (1995)] which, unlike the present method, requires knowledge of both the cantilever density and thickness. ©1999 American Institute of Physics.
History: Received 20 April 1999; accepted 1 July 1999
Permalink: http://link.aip.org/link/?RSINAK/70/3967/1
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KEYWORDS and PACS

Keywords
PACS
  • 07.79.Lh
    Instruments, apparatus, components, and techniques common to several branches of physics and astronomy Scanning probe microscopes, components, and techniques Atomic force microscopes
  • 06.20.Fn
    Metrology, measurements, and laboratory procedures Metrology Units and standards
  • 07.10.Cm
    Instruments, apparatus, components, and techniques common to several branches of physics and astronomy Mechanical instruments, equipment, and techniques Micromechanical devices and systems
  • YEAR: 1999

PUBLICATION DATA

ISSN:
0034-6748 (print)   1089-7623 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (21)
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  1. T. J. Senden and W. A. Ducker, Langmuir 10, 1003 (1994).
  2. Y. Q. Li, N. J. Tao, J. Pan, A. A. Garcia, and S. M. Lindsay, Langmuir 9, 637 (1993).
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  5. J. E. Sader, I. Larson, P. Mulvaney, and L. R. White, Rev. Sci. Instrum. 66, 3789 (1995).
  6. J. E. Sader, J. Appl. Phys. 84, 64 (1998).
  7. J. W. M. Chon, P. Mulvaney, and J. E. Sader, J. Appl. Phys. (submitted).
  8. D. A. Walters, J. P. Cleveland, N. H. Thomson, P. K. Hansma, M. A. Wendman, G. Gurley, and V. Elings, Rev. Sci. Instrum. 67, 3583 (1996).
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  10. M. Tortonese and M. Kirk, Proc. SPIE 3009, 53 (1997).
  11. Digital Instruments, 112 Robin Hill Road, Santa Barbara, CA 93117.
  12. AT-MIO-16E-1 board, available from National Instruments, 6504 Bridge Point Parkway, Austin, TX 78730-5039.
  13. LabVIEW is a registered trademark of, and is available from, National Instruments (see Ref. 12).
  14. The resonant frequency omegaf and quality factor Qf were obtained by fitting the power spectra to the functional P(omega) = Awhite + Bomega<sub>f</sub><sup>4</sup>/[(omega2–omega<sub>f</sub><sup>2</sup>)2 + omega2omega<sub>f</sub><sup>2</sup>/Q<sub>f</sub><sup>2</sup>]. The fitting parameters are Awhite, B, omegaf, and Qf.
  15. Mathematica is a registered trademark of, and is available from, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237.
  16. The cantilevers were vibrating at their base using the Tapping Mode cantilever tune software in the Nanoscope III atomic force microscope (Digital Instruments, USA).
  17. To establish the ultimate lower limit for L/b, for which the method is applicable, measurements need to be performed on cantilevers with aspect ratios smaller than those used in this study.
  18. J. E. Sader and L. White, J. Appl. Phys. 74, 1 (1993).
  19. J. E. Sader, Rev. Sci. Instrum. 66, 4583 (1995).
  20. J. M. Neumeister and W. A. Ducker, Rev. Sci. Instrum. 65, 2527 (1994).
  21. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw–Hill, New York, 1959).

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