Journal of Applied Physics
Feedback | Help | Exit
Journal of Applied Physics
   
 
 
 
Previous Article
Optimized cleaning method for producing device quality InP(100) surfaces
A very effective, two-step chemical etching method to produce clean InP(100) surfaces when combined with thermal annealing has been developed. The hydrogen peroxide/sulfuric acid-based solutions, whic...
Next Article
Measurements of energy dependence of properties of polycapillary x-ray lens by using organic glass as a scatterer
In order to reduce dead time in the detector system, an organic glass is used as a scatterer. By using the backscattered spectra from the organic glass, the energy dependence of the focal spot size, t...

General scaling law for stiffness measurement of small bodies with applications to the atomic force microscope

J. Appl. Phys. 97, 124903 (2005); doi:10.1063/1.1935133

Published 20 June 2005

You are not logged in to this journal. Log in

John E. Sader
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

Jessica Pacifico
School of Chemistry, University of Melbourne, Victoria 3010, Australia

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

Paul Mulvaney
School of Chemistry, University of Melbourne, Victoria 3010, Australia
A general scaling law connecting the stiffness and dissipative properties of a linear mechanical oscillator immersed in a viscous fluid is derived. This enables the noninvasive experimental determination of the stiffness of small elastic bodies of arbitrary shape by measuring their resonant frequency and quality factor in fluid (typically air). In so doing, we elucidate the physical basis of the method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for determining the stiffness of rectangular atomic force microscope cantilevers, and discuss its applicability. The validity of the derived general technique is demonstrated by calibrating atomic force microscope cantilevers with complex geometries, and its implications to small bodies in general are discussed. ©2005 American Institute of Physics
History: Received 8 February 2005; accepted 21 April 2005; published 20 June 2005
Permalink: http://link.aip.org/link/?JAPIAU/97/124903/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (77 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 07.10.Pz
    Instruments for strain, force, and torque
  • 46.25.-y
    Static elasticity
  • YEAR: 2005

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-8979 (print)   1089-7550 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (25)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1996).
  2. J. N. Israelachvili and G. E. Adams, J. Chem. Soc., Faraday Trans. 1 74, 975 (1978).
  3. G. Binnig, C. F. Quate, and Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986).
  4. B. Cappella and G. Dietler, Surf. Sci. Rep. 34, 1 (1999).
  5. M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez, and H. E. Gaub, Science 276, 1109 (1997).
  6. J. E. Sader, I. Larson, P. Mulvaney, and L. R. White, Rev. Sci. Instrum. 66, 3789 (1995).
  7. H.-J. Butt et al., J. Microsc. 169, 75 (1993).
  8. T. J. Senden and W. A. Ducker, Langmuir 10, 1003 (1994).
  9. A. Torii, M. Sasaki, K. Hane, and S. Okuma, Meas. Sci. Technol. 7, 179 (1996).
  10. J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma, Rev. Sci. Instrum. 64, 403 (1993).
  11. J. L. Hutter and J. Bechhoefer, Rev. Sci. Instrum. 64, 1868 (1993).
  12. J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999);
    13. online implementation of this method can be found at http://www.ampc.ms.unimelb.edu.au/afm
  13. J. E. Sader, J. Appl. Phys. 84, 64 (1998).
  14. T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate, J. Vac. Sci. Technol. A 8, 3386 (1990).
  15. J. E. Sader, Rev. Sci. Instrum. 74, 2438 (2003).
  16. J. E. Sader and R. C. Sader, Appl. Phys. Lett. 83, 3195 (2003).
  17. P.W. Bridgman, Dimensional Analysis (Yale University Press, New Haven, 1931).
  18. The radial resonant frequency omegaR and the quality factor Q are obtained by fitting the power spectrum in fluid to the function Bomega<sub>R</sub><sup>4</sup>/[(omega2–omega<sub>R</sub><sup>2</sup>)2+omega2omega<sub>R</sub><sup>2</sup>/Q2], where omega is the radial frequency. The fitting parameters are B, omegaR, and Q.
  19. This dependence is weak and varies approximately as the square root of the oscillation frequency at most (Ref. 13)
  20. C. P. Green, H. Lioe, J. P. Cleveland, R. Proksch, P. Mulvaney, and J. E. Sader, Rev. Sci. Instrum. 75, 1988 (2004).
  21. For an added point mass that greatly exceeds the cantilever mass, the deflection function of the fundamental mode of vibration is identical to that of a statically loaded cantilever.
  22. AT-MIO-16E-1 board, available from National Instruments, 6504 Bridge Point Parkway, Austin, TX 78730-5039.
  23. LABVIEW is a registered trademark of, and is available from, National Instruments, see Ref. 22.
  24. MATHEMATICA is a registered trademark of, and is available from, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237.
  25. The dimensionless function Omega(Re) was scaled by the arm width ratio L/d, as for the rectangular cantilever.

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics