Accurate formulas for interaction force and energy in frequency modulation force spectroscopy
Appl. Phys. Lett. 84, 1801 (2004); doi:10.1063/1.1667267
Issue Date: 8 March 2004
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Frequency modulation atomic force microscopy utilizes the change in resonant frequency of a cantilever to detect variations in the interaction force between cantilever tip and sample. While a simple relation exists enabling the frequency shift to be determined for a given force law, the required complementary inverse relation does not exist for arbitrary oscillation amplitudes of the cantilever. In this letter we address this problem and present simple yet accurate formulas that enable the interaction force and energy to be determined directly from the measured frequency shift. These formulas are valid for any oscillation amplitude and interaction force, and are therefore of widespread applicability in frequency modulation dynamic force spectroscopy. ©2004 American Institute of Physics.
| History: | Received 31 October 2003; accepted 15 January 2004 |
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REFERENCES (12)
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- S. P. Jarvis, H. Yamada, S.-I. Yamamoto, H. Tokumoto, and J. B. Pethica,
Nature (London) 384, 247 (1996) . - P. M. Hoffmann, A. Oral, R. A. Grimble, H. O. Ozer, S. Jeffery, and J. B. Pethica,
Proc. R. Soc. London, Ser. A 457, 1161 (2001) . - N. A. Burnham and R. J. Colton,
J. Vac. Sci. Technol. A 7, 2906 (1989) . - T. R. Albrecht, P. Grutter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668 (1991).
- F. J. Giessibl,
Science 267, 68 (1995) . - M. A. Lantz, H. J. Hug, R. Hoffmann, P. J. A. van Schendel, P. Kappenberger, S. Martin, A. Baratoff, and H.-J. Guntherodt,
Science 291, 2580 (2001) . - F. J. Giessibl, Phys. Rev. B 56, 160 10 (1997). Equation (1) is derived under the assumption that the frequency shift

is much smaller than the unperturbed resonant frequency
res. - U. Durig, Appl. Phys. Lett. 75, 433 (1999).
- U. Durig, Appl. Phys. Lett. 76, 1203 (2000).
- F. J. Giessibl, Appl. Phys. Lett. 78, 123 (2001).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1975).
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, (Taylor & Francis, London, 2002). These correspond to the so-called right-sided forms of the fractional derivatives and integrals.







