Journal of Applied Physics
   
 
 
 
Previous Article
Low temperature annealing of 4H–SiC Schottky diode edge terminations formed by 30 keV Ar + implantation
Edge termination of Schottky barrier diodes has been achieved using 30 keV Ar + ions implanted at a dose of 1×1015 cm–2. The reverse-bias leakage current is reduced by 2 orders of magnitud...
Next Article
Magnetic trapping of neutral particles: Classical and quantum-mechanical study of a Ioffe–Pritchard type trap
Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum mechanics of magn...

Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids

J. Appl. Phys. 87, 3978 (2000); doi:10.1063/1.372455

Issue Date: 15 April 2000

You are not logged in to this journal. Log in

James W. M. Chon and Paul Mulvaney
School of Chemistry, University of Melbourne, Parkville, 3052, Victoria, Australia

John E. Sader
Department of Mathematics and Statistics, University of Melbourne, Parkville, 3052, Victoria, Australia
Detailed measurements of the frequency responses of a series of rectangular atomic force microscope (AFM) cantilever beams, immersed in a range of fluids, have been performed to test the validity and accuracy of the recent theoretical model of Sader [J. Appl. Phys. 84, 64 (1998)]. This theoretical model gives the frequency response of a cantilever beam, that is immersed in a viscous fluid and excited by an arbitrary driving force. Very good agreement between experimental measurements and theoretical calculations is found for all fluids considered. Furthermore, a critical assessment of the well-known inviscid model is presented, which demonstrates that this model is not applicable to AFM cantilever beams in general. ©2000 American Institute of Physics.
History: Received 30 August 1999; accepted 22 December 1999
Permalink: http://link.aip.org/link/?JAPIAU/87/3978/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (178 kB) View Cart

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
  • YEAR: 2000

PUBLICATION DATA

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

REFERENCES (34)

For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate, J. Vac. Sci. Technol. A 8, 3386 (1990).
  2. H.-J. Butt, P. Siedle, K. Seifert, K. Fendler, T. Seeger, E. Bamberg, A. L. Weisenhorn, K. Goldie, and A. Engel, J. Microsc. 169, 75 (1993).
  3. G. Y. Chen, R. J. Warmack, T. Thundat, and D. P. Allison, Rev. Sci. Instrum. 65, 2532 (1994).
  4. J. E. Sader, I. Larson, P. Mulvaney, and L. R. White, Rev. Sci. Instrum. 66, 3789 (1995).
  5. 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).
  6. T. E. Schaffer, J. P. Cleveland, F. Ohnesorge, D. A. Walters, and P. K. Hansma, J. Appl. Phys. 80, 3622 (1996).
  7. H. Muramatsu, N. Chiba, K. Homma, K. Nakajima, T. Ataka, S. Ohta, A. Kusumi, and M. Fujihira, Thin Solid Films 273, 335 (1996).
  8. A. Roters and D. Johannsmann, J. Phys.: Condens. Matter 8, 7561 (1996).
  9. T. E. Schaffer, M. Viani, D. A. Walters, B. Drake, E. K. Runge, J. P. Cleveland, M. A. Wendman, and P. K. Hansma, Proc. SPIE 3009, 48 (1997).
  10. F.-J. Elmer and M. Dreier, J. Appl. Phys. 81, 7709 (1997).
  11. M. Tortonese and M. Kirk, Proc. SPIE 3009, 53 (1997).
  12. W.-H. Chu, Tech. Rep. No. 2, DTMB, Contract NObs-86396(X), Southwest Research Institute, San Antonio, TX (1963).
  13. U. S. Lindholm, D. D. Kana, W.-H. Chu, and H. N. Abramson, J. Ship Res. 9, 11 (1965).
  14. D. G. Stephens and M. A. Scavullo, NASA TN D-1865 (April 1965).
  15. L. Landweber, J. Ship Res. 15, 97 (1971).
  16. G. Muthuveerappan, N. Ganesan, and M. A. Veluswami, J. Sound Vib. 61, 467 (1978).
  17. D. G. Crighton, J. Sound Vib. 87, 429 (1983).
  18. Y. Fu and W. G. Price, J. Sound Vib. 118, 495 (1987).
  19. M. K. Kwak, Trans. ASME, J. Appl. Mech. 63, 110 (1996).
  20. R. E. Hetrick, Sens. Actuators 18, 131 (1989).
  21. J. E. Sader, J. Appl. Phys. 84, 64 (1998).
  22. For a composite beam, i.e., a beam composed of two or more layers, rhoc is the average density of the beam.
  23. Park Scientific Instruments, 1171 Borregas Ave., Sunnyvale, CA 94089-1304.
  24. The theoretical models are also applicable to cantilever beams composed of crystalline materials, provided the crystal orientation is fixed over the length of the beam. The calibrated cantilevers satisfy this condition.
  25. Digital Instruments, 112 Robin Hill Road, Santa Barbara, CA 93117.
  26. Mathematica is a registered trademark of, and is available from Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820–7237.
  27. The resonant frequency in vacuum of mode n can always be calculated from a knowledge of the fundamental resonant frequency omegavac,1 using the well-known formula omegavac,n = C<sub>n</sub><sup>2</sup>/C<sub>1</sub><sup>2</sup>omegavac,1, where Cn is the nth positive root of 1 + cos Cn cosh Cn = 0.
  28. The shift in resonant frequency from vacuum to fluid is primarily accounted for in omegaR,n, which neglects all dissipative effects in the fluid. Such dissipative effects are accounted for in the quality factor Qn, which introduces a comparatively small correction to the resonant frequency in fluid omegafluid.
  29. To establish the ultimate lower limit for L/b, for which the models are applicable, measurements need to be performed on cantilevers with aspect ratios smaller than those used in this study.
  30. These measurements were obtained by directing the AFM laser beam, which is normally used to measure the deflection of the cantilever, onto the cantilever substrate. The reflected signal was then processed in an identical manner to that described in the Appendix.
  31. AT-MIO-16E-1 board available from National Instruments, 6504 Bridge Point Parkway, Austin, TX 78730-5039.
  32. LabVIEW is a registered trademark of, and is available from National Instruments (see Ref. 31).
  33. R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 1985).
  34. J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma, Rev. Sci. Instrum. 64, 403 (1993).

CITING ARTICLES

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