ibration Analysis of an AFM microcantilever with sidewall and top surface probes based on the couple stress theory

Document Type : Research Article

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Abstract

In this paper, the resonant frequency and sensitivity of vibration modes of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) are analyzed utilizing the modified couple stress theory. The proposed ACP comprises a horizontal microcantilever, a vertical extension and two tips located at the free ends of the cantilever and the extension, which make AFM capable of scanning the top surface and the sidewall of the sample, simultaneously. To derive the exact solution of the proposed ACP vibration behaviour, the horizontal cantilever is modeled as two beam. Having obtained the equation of motion, boundary and continuity conditions, the resonant frequency and sensitivity are studied. The results predicted by the current theory are compared to those obtained by the numerical methods presented by Kahrobaiyan et al. and the comparison shows that there is some errors in the numerical method results. The results of the couple stress theory are also compare with those of the classical beam theory. The evaluation indicates that the vibration behaviour of the proposed ACP is completely size-dependent.

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References

[1] Mazeran, P.E. and J.L. Loubet, 1999. “Normal and lateral modulation with a scanning force microscope,
an analysis: implication in quantitative elastic and friction imaging”, Tribology Lett. , 7, pp. 199-212.
[2] Shen, K., D.C. Hurley, and J.A. Turner, 2004.“Dynamic behaviour of dagger-shaped cantilevers for atomic force microscopy”, Nanotechnology, 11,pp. 1582-1589.
[3] Abbasi, M. and A.Karami mohammadi, 2009. “Effect of contact position and tip properties on the flexural
vibration responses of atomic force microscope cantilevers”, IREME, 3, pp. 196-202.
[4] Mahdavi, M.H., et al., 2008. “A more comprehensive modeling of atomic force microscope cantilever”,
Ultramicroscopy, 109, no. 1, pp. 54-60.
[5] Yazdani S., Bigham S., and Y. J., 2009. “Investigation of forced torsional vibration modes of an atomic force
microscopy and effects of geometrical parameters on the resonant frequency”, Digest Journal of Nanomaterials and Biostructures, 4, no. 1, pp. 11- 18.
[6] Turner, J.A., et al., 1997. “High-frequency response of atomic-force microscope cantilevers”. J. Appl. Phys. , 82, no. 3, pp. 966-979.
[7] Yaralioglu, G.G., et al., 2000. “Contact stiffness of layered materials for ultrasonic atomic force microscopy”, J. Appl. Phys. , 87, no. 10.
[8] Chang, W.-J., T.-H. Fang, and H.-M. Chou, 2003.“Effect of interactive damping on sensitivity of vibration modes of rectangular AFM cantilevers”,Physics Letters A, 312, no. 3-4, pp. 158-165.
[9] Abbasi, M. and A.Karami mohammadi, 2010. “A new model for investigating the flexural vibration of an atomic force microscope cantilever”,Ultramicroscopy, 110, pp. 1374-1379.
[10] Dai, G., et al., 2006. “Atomic force probe for sidewall scanning of nano- and microstructures”, Applied
Physics Letters, 88, no. 17, pp. 171-908.
[11] Dai, G., et al., 2007. “Nanoscale surface measurements at sidewalls of nano- and microstructures”,
Measurement Science and Technology,18, no. 2, pp. 334-341.
[12] Chang, W.J., H.L. Lee, and T.Y. Chen, 2008.“Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe”,Ultramicroscopy, 7, no. 108, pp. 619-24.
[13] Kahrobaiyan, M.H., et al., 2010. “Sensitivity and resonant frequency of an AFM with sidewall and topsurface
probes for both flexural and torsional modes”,International Journal of Mechanical Sciences, 52,no. 10, p. 1357-1365.
[14] Ma, Q. and D.R. Clarke, 1995. “Size dependent hardness of silver single crystals”, Journal of Materials Research, 10, no. 4, pp. 853–863.
[15] McFarland, A.W. and J.S. Colton, 2005. “Role of material microstructure in plate stiffness with relevance to microcantilever sensors”, Journal of Micromechanics and Microengineering, 15, no. 5,pp. 1060–1067.
[16] Eringen, A.C., 1972. “Nonlocal polar elastic continua”, Int. J. Eng. Sci. , 10, pp. 1-16.
[17] Mindlin, R.D. and H.F. Tiersten, 1962. “Effects of couple-stresses in linear elasticity”, Arch. Rational
Mech. Anal., 11, pp. 415–448.
[18] Kahrobaiyan, M.H., et al., 2010. “Investigation of the size-dependent dynamic characteristics of atomic
force microscope microcantilevers based on the modified couple stress theory”, International Journal of Engineering Science, 48, no. 12, pp. 1985-1994.
[19] Yang, F., et al., 2002. “Couple stress based strain gradient theory for elasticity”, International Journal
of Solids and Structures, 39, pp. 2731–2743.
[20] Kong, S., et al., 2008. “The size-dependent natural frequency of Bernoulli–Euler micro beams”,International Journal of Engineering Science, 46, no.5, pp. 427-437.
[21] Lee, H.L. and W.J. Chang, 2011. “Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory”, Microelectronic Engineering, 88, no. 11, pp. 3214-3218.
[22] Turner, J.A. and J.S. Wiehn, 2001. “Sensitivity of Flexural and Torsional Vibration Modes of Atomic
Force Microscope Cantilevers to Surface Stiffness Variation”, Nanotechnology, 12, pp. 322-330.
Amirkabir Journal of Mechanical Engineering
Volume 48, Issue 2
September 2016
Pages 137-146

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