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Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscopy measurements

Published online by Cambridge University Press:  03 March 2011

F.J. Espinoza Beltrán ,
J. Muñoz-Saldaña ,
D. Torres-Torres ,
R. Torres-Martínez  and
G.A. Schneider
F.J. Espinoza Beltrán
Affiliation:
Centro de Investigación y Estudios Avanzados del IPN. Unidad Querétaro, 76001 Querétaro, Qro., México; and Hamburg University of Technology, Advanced Ceramics Group, 21073 Hamburg, Germany
J. Muñoz-Saldaña*
Affiliation:
Centro de Investigación y Estudios Avanzados del IPN. Unidad Querétaro, 76001 Querétaro, Qro., México
D. Torres-Torres
Affiliation:
Centro de Investigación y Estudios Avanzados del IPN. Unidad Querétaro, 76001 Querétaro, Qro., México
R. Torres-Martínez
Affiliation:
Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del IPN. Unidad Querétaro, 76040, Querétaro, Qro., México
G.A. Schneider
Affiliation:
Hamburg University of Technology, Advanced Ceramics Group, 21073 Hamburg, Germany
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

Measurements of vibrational spectra of atomic force microscopy (AFM) microprobes in contact with a sample allow a good correlation between resonance frequencies shifts and the effective elastic modulus of the tip-sample system. In this work we use finite element methods for modeling the AFM microprobe vibration considering actual features of the cantilever geometry. This allowed us to predict the behavior of the cantilevers in contact with any sample for a wide range of effective tip-sample stiffness. Experimental spectra for glass and chromium were well reproduced for the numerical model, and stiffness values were obtained. We present a method to correlate the experimental resonance spectrum to the effective stiffness using realistic geometry of the cantilever to numerically model the vibration of the cantilever in contact with a sample surface. Thus, supported in a reliable finite element method (FEM) model, atomic force acoustic microscopy can be a quantitative technique for elastic-modulus measurements. Considering the possibility of tip-apex wear during atomic force acoustic microscopy measurements, it is necessary to perform a calibration procedure to obtain the tip-sample contact areas before and after each measurement.

Keywords

Elastic propertiesScanning probe microscopySimulation
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 12 , December 2006 , pp. 3072 - 3079
Copyright
Copyright © Materials Research Society 2006

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References

REFERENCES

1.Binnig, G., Rohrer, H., Gerber, Ch., Weibel, E.: Surface studies by scanning tunneling microscopy. Phys. Rev. Lett. 49, 57 (1992).CrossRefGoogle Scholar
2.Binnig, G., Quate, C.F., Gerber, Ch.: Atomic force microscope. Phys. Rev. Lett. 56, 930 (1986).CrossRefGoogle ScholarPubMed
3.Binnig, G., Gerber, C., Stoll, E., Albrecht, T.R., Quate, C.F.: Atomic resolution with the atomic force microscopy. Europhys. Lett. 3, 1281 (1987).CrossRefGoogle Scholar
4.Yamamoto, S., Ishida, T., Mizutani, W., Tokumoto, H., Yamada, H.: Identifications of materials using direct force modulation technique with magnetic AFM cantilever. Jpn. J. Appl. Phys. 36, 3868 (1997).CrossRefGoogle Scholar
5.Rabe, U., Janser, K., Arnold, W.: Vibrations of free and surface-coupled atomic force microscope cantilevers. Rev. Sci. Instrum. 67, 3281 (1996).CrossRefGoogle Scholar
6.Dupas, E., Gremaud, G., Kulik, A., Loubet, J.L.: High-frequency mechanical spectroscopy with an atomic force microscope. Rev. Sci. Instrum. 72, 3891 (2001).CrossRefGoogle Scholar
7.Burnham, N.A., Gremaud, G., Kulik, A.J., Gallo, P-J., Oulevey, F.: Material’s properties measurements: Choosing the optimal scanning probe microscope configuration. J. Vac. Sci. Technol., B 14, 1308 (1996).CrossRefGoogle Scholar
8.Rabe, U., Turner, J., Arnold, W.: Analysis of the high-frequency response of atomic force microscope cantilevers. Appl. Phys. A 66, S277 (1998).CrossRefGoogle Scholar
9.Turner, J.A., Hirsekorn, S., Rabe, U., Arnold, W.: High-frequency response of atomic-force microscope cantilevers. J. Appl. Phys. 82, 966 (1997).CrossRefGoogle Scholar
10.Rabe, U., Amelio, S., Kopycinska, M., Hirsekorn, S., Kempf, M., Göken, M., Arnold, W.: Imaging and measurement of local mechanical material properties by atomic force acoustic microscopy. Surf. Interface Anal. 33, 65 (2002).CrossRefGoogle Scholar
11.Reinstaedtler, M., Rabe, U., Scherer, V., Turner, J.A., Arnold, W.: Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry. Surf. Sci. 532, 1152 (2003).CrossRefGoogle Scholar
12.Arinero, R., Lévêque, G.: Vibration of the cantilever in force modulation microscopy analysis by a finite element model. Rev. Sci. Instrum. 74, 104 (2003).CrossRefGoogle Scholar
13.Drobek, T., Stark, R.W., Gräber, M., Heckl, W.M.Overtone atomic force microscopy studies of decagonal quasicrystal surfaces. New Journal of Physics 1, 1.1 (1999).CrossRefGoogle Scholar
14.Drobek, T., Stark, R.W., Gräber, M., Heckl, W.M.: Tapping-mode atomic force microscopy and phase-imaging in higher eigenmodes. Appl. Phys. Lett. 74, 3296 (1999).Google Scholar
15.Yamanaka, K., Takano, H., Tomita, E., Fujihira, M.: Lateral force modulation atomic force microscopy of Langmuir-Blodgett film in water. Jpn. J. Appl. Phys. 35, 5421 (1996).CrossRefGoogle Scholar
16.Kopycinska-Müller, M., Geiss, R.H., Rice, P., Hurley, D.C. Influence of tip wear on atomic force acoustic microscopy experiments, in Scanning-Probe and Other Novel Microscopies of Local Phenomena in Nanostructured Materials edited by Kalinin, S.V., Goldberg, B., Eng, L.M., and Huey, D. (Mater. Res. Soc. Symp. Proc. 838E, Warrendale, PA, 2005), p. O10.16.1.Google Scholar
17.Metrology Digital Instruments Veeco Force Modulation Manual, Santa Barbara, CA, 93117(805), 957 (1999).Google Scholar
18.Rasband, W. Research Services Branch, National Institute of Mental Health, Bethesda, MD.Google Scholar
19.ANSYS ANSYS Theory Reference Manual, 9th ed., Version 5.5, (SAS IP, Inc., Canonsburg, PA, 1998).Google Scholar
20.Johnson, K.: Contact Mechanics (Cambridge University Press, England, 1987).Google Scholar
21.Rabe, U., Amelio, S., Kopycinska, M., Hirsekorn, S., Kempf, M., Göken, M., Arnold, W.: Imaging and measurement of local mechanical material properties by atomic force acoustic microscopy. Surf. Interface Anal. 33, 65 (2002).CrossRefGoogle Scholar
22.Muraoka, M.: Sensitivity-enhanced atomic force acoustic microscopy with concentrated-mass cantilevers. Nanotechnology 16, 542 (2005).CrossRefGoogle Scholar
23.Passeri, D., Bettucci, A., Germano, M., Rossi, M., Alippi, A., Orlanducci, S., and Ciavarella, M.L. Terranova M.: Effect of tip geometry on local indentation modulus measurement via atomic force acoustic microscopy technique. Rev. Sci. Instrum. 76, 093904 (2005).CrossRefGoogle Scholar
24.Kalinin, S.V., Rodriguez, B.J., Shin, J., Jesse, S., Grichko, V., Thundat, T., Baddorf, A.P., Gruverman, A.: Bioelectromechanical imaging by scanning-probe microscopy: Galvani’s experiment at the nanoscale. Ultramicroscopy 106, 334 (2006).CrossRefGoogle ScholarPubMed
25.Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and contact of elastic solids. Proc. R. Soc. London A 324, 301 (1971).Google Scholar
26.Derjaguin, B.V., Muller, V.M., Toporov, Yu.P.: Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53(2), 314 (1975).CrossRefGoogle Scholar