access icon free Sensitivity of higher mode of rectangular atomic force microscope to surface stiffness in air environment

© The Institution of Engineering and Technology
Received 11/09/2013, Accepted 25/10/2013, Revised 23/10/2013, Published

The sensitivity of the resonance frequencies and the amplitudes of the first four flexural vibration modes of atomic force microscopy with a rectangular cross-section cantilever in an air environment to variation of a sample's stiffness have been analysed. The cantilever has been modelled using Timoshenko beam theory, and the vertical and tangential forces between the tip and the sample in this simulation have been considered. The effect of tip position and the angle of the tip relative to the sample in changes of these sensitivities have been studied. Results indicate that for soft materials, the first mode compared with other modes is more sensitive to changes in the sample's elasticity, so the first mode is the best mode for supplying high-contrast images but by increasing the sample's stiffness, the higher mode will be sensitive, respectively. In addition, by increasing the angle between the cantilever and the sample's surface, the first mode is less sensitive and higher modes will be sensitive faster because of changes in material stiffness but in contrast, by increasing the distance between the tip's position and the free end of the cantilever, the sensitivity of the first mode increases and the higher mode will be sensitive for more stiff material.

Inspec keywords: surface phonons; atomic force microscopy; cantilevers; elasticity

Other keywords: flexural vibration modes; tip angle; sample elasticity; material stiffness; rectangular cross-section cantilever; sample stiffness; high-contrast images; rectangular atomic force microscopy; soft materials; Timoshenko beam theory; vertical force; surface stiffness; air environment; tip position; tangential force; resonance frequency

Subjects: Dynamics of solid surfaces and interface vibrations; Elasticity and anelasticity; Scanning probe microscopy and related techniques; Mechanical and acoustical properties of solid surfaces and interfaces; Elasticity, elastic constants; Solid surface structure

References

    1. 1)
      • 14. Johnson, K.L.: ‘Contact mechanics’ (Cambridge University Press, UK, 1985).
    2. 2)
      • 4. Dinelli, F., Biswas, S.K., Briggs, G.A.D., Kolosov, O.V.: ‘Measurements of stiff-material compliance on the nanoscale using ultrasonic force microscopy’, Phys. Rev. B, Condens. Matter Mater. Phys., 2000, 61, (20), pp. 13995–14006 (doi: 10.1103/PhysRevB.61.13995).
    3. 3)
      • 12. Timoshenko, S.P., Goodier, J.N.: ‘Theory of elasticity’ (McGraw-Hill, New York, 1951).
    4. 4)
      • 10. Lee, H.-L., Chang, W.-J., Yang, Y.-C.: ‘Flexural sensitivity of a V-shaped cantilever of an atomic force microscope’, Mater. Chem. Phys., 2005, 92, (2–3), pp. 438–442 (doi: 10.1016/j.matchemphys.2005.01.046).
    5. 5)
      • 1. Durig, U.: ‘Relations between interaction force and frequency shift in large-amplitude dynamic force microscopy’, Appl. Phys. Lett., 1999, 75, (3), pp. 433–435 (doi: 10.1063/1.124399).
    6. 6)
      • 5. Yamanaka, K., Tsuji, T., Noguchi, A., Koike, T., Mihara, T.: ‘Nanoscale elasticity measurement with in situ tip shape estimation in atomic force microscopy’, Rev. Sci. Instrum., 2000, 71, (6), pp. 2403–2408 (doi: 10.1063/1.1150627).
    7. 7)
      • 3. Rabe, U., Amelio, S., Kester, E., Scherer, V., Hirsekorn, S., Arnold, W.: ‘Quantitative determination of contact stiffness using atomic force acoustic microscopy’, Ultrasonics, 2000, 38, (1), pp. 430–437 (doi: 10.1016/S0041-624X(99)00207-3).
    8. 8)
      • 11. Farrokhpayam, A.: ‘Sensitivity of flexural vibration mode of the rectangular atomic force microscope micro cantilevers in liquid to the surface stiffness variations’, Ultramicroscopy, 135, 2013.
    9. 9)
      • 15. Song, Y., Bhushan, B.: ‘Finite-element vibration analysis of tapping-mode atomic force microscopy in Liquid’, Ultramicroscopy, 2007, 53, pp. 1095–1104 (doi: 10.1016/j.ultramic.2007.01.022).
    10. 10)
      • 8. Turner, J.A., Wiehn, J.S.: ‘Sensitivity of flexural and torsional vibration modes of atomic force microscope cantilevers to surface stiffness variations’, Nanotechnology, 2001, 12, (3), pp. 322–330 (doi: 10.1088/0957-4484/12/3/321).
    11. 11)
      • 6. Yaralioglu, G.G., Degertekin, F.L., Crozier, K.B., Quate, C.F.: ‘Contact stiffness of layered materials for ultrasonic atomic force microscopy’, J. Appl. Phys., 2000, 87, (10), pp. 7491–7496 (doi: 10.1063/1.373014).
    12. 12)
      • 2. Holscher, H., Allers, W., Schwarz, U.D., Schwarz, A., Wiesendanger, R.: ‘Determination of tip-sample interaction potentials by dynamic force spectroscopy’, Phys. Rev. Lett., 1999, 83, (23), pp. 4780–4783 (doi: 10.1103/PhysRevLett.83.4780).
    13. 13)
      • 7. Burnham, N.A., Kulik, A.J., Gremaud, G., Briggs, G.A.D.: ‘Nanosubharmonics: the dynamics of small nonlinear contacts’, Phys. Rev. Lett., 1995, 74, (25), pp. 5092–5095 (doi: 10.1103/PhysRevLett.74.5092).
    14. 14)
      • 9. Shen, K., Hurley, D.C., Turner, J.A.: ‘Dynamic behaviour of dagger-shaped cantilevers for atomic force microscopy’, Nanotechnology, 2004, 15, (11), pp. 1582–1589 (doi: 10.1088/0957-4484/15/11/036).
    15. 15)
      • 13. Derjaguin, B.V., Muller, V.M., Toporov, Y.P.: ‘Effect of contact deformations on the adhesion of particles’, Colloid Interface Sci., 1975, 53, pp. 314–326 (doi: 10.1016/0021-9797(75)90018-1).
http://iet.metastore.ingenta.com/content/journals/10.1049/mnl.2013.0533
Loading

Related content

content/journals/10.1049/mnl.2013.0533
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading