Sensitivity Analysis of Frequency Response of Atomic Force Microscopy in Liquid Environment on Cantilever's Geometrical Parameters
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
مهرنوش دمیرچلی
1
(استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد شهر قدس)
Keywords: Timoshenko beam, Sensitive analysis, Geometrical parameters, Liquid Environment, Sobol method,
Abstract :
In this paper, the non-linear dynamic response of rectangular atomic force microscopy in tapping mode is considered. The effect of cantilever’s geometrical parameters (e.g., cantilever length, width, thickness, tip length and the angle between the cantilever and the sample's surface in liquid environment has been studied by taking into account the interaction forces. Results indicate that the resonant frequency, amplitude and phase are very sensitive to changes of geometrical parameters. In order to improve and optimize the system's behavior, the sensitive analysis (SA) of geometrical parameters on the first resonant frequency and amplitude of cantilever's vertical displacement has been conducted using Sobol's method. Results show that the influence of each geometrical variable on frequency response of the system can play a crucial role in designing the optimum cantilever in liquid medium for soft and sensitive biological samples. Also, one way to speed up the imaging process is to use short cantilevers. For short beams, the Timoshenko model seems to be more accurate compared to other models such as the Euler-Bernoulli. By using the Timoshenko beam model, the effects of rotational inertia and shear deformation are taken into consideration. In this paper, this model has been used to obtain more accurate results
[Giessibl, #7][1] Giessibl F.J., Forces and frequency shifts in atomic-resolution dynamic-force microscopy, Physical Review B, vol. 56, No. 24, 1997, pp. 16010.
[2] San Paulo A., García R., Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy, Physical Review B, vol. 64, No. 19, 2001, pp. 193411.
[3] Rabe U., Janser K., Arnold W., Vibrations of free and surface‐coupled atomic force microscope cantilevers: theory and experiment, Review of Scientific Instruments, vol. 67, No. 9, 1996, pp. 3281-3293.
[4] Turner J.A., Hirsekorn S., Rabe U., Arnold W., High-frequency response of atomic-force microscope cantilevers, Journal of Applied Physics, vol. 82, No. 3, 1997, pp. 966-979.
[5] Stark R.W., Schitter G., Stark M., Guckenberger R., Stemmer A., State-space model of freely vibrating and surface-coupled cantilever dynamics in atomic force microscopy, Physical Review B, vol. 69, No. 8, 2004, pp. 085412.
[6] Butt H.J., Jaschke M., Calculation of thermal noise in atomic force microscopy, Nanotechnology, vol. 6, No. 1, 1995, pp. 1.
[7] Rabe U., Turner J., Arnold W., Analysis of the high-frequency response of atomic force microscope cantilevers, Applied Physics A: Materials Science & Processing, vol. 66, 1998, pp. S277-S282.
[8] Lee S., Howell S., Raman A., Reifenberger R., Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment, Physical Review B, vol. 66, No. 11, 2002, pp. 115409.
[9] Arinero R., Lévêque G., Vibration of the cantilever in force modulation microscopy analysis by a finite element model, Review of scientific instruments, vol. 74, No. 1, 2003, pp. 104-111.
[10] Sadeghi A., Zohoor H., Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory, Canadian Journal of Physics, vol. 88, No. 5, 2010, pp. 333-348.
[11] Hansma P., Cleveland J., Radmacher M., Walters D., Hillner P., Bezanilla M., Fritz M., Vie D., Hansma H., Prater C., Tapping mode atomic force microscopy in liquids, Applied Physics Letters, vol. 64, No. 13, 1994, pp. 1738-1740.
[12] Putman C. A., Van der Werf K.O., De-Grooth B.G., N. F. Van Hulst, J. Greve, Tapping mode atomic force microscopy in liquid, Applied Physics Letters, vol. 64, No. 18, 1994, pp. 2454-2456.
[13] Chen G., Warmack R., Huang A., Thundat T., Harmonic response of near‐contact scanning force microscopy, Journal of applied physics, vol. 78, No. 3, 1995, pp. 1465-1469.
[14] Chen G., Warmack R., Oden P., Thundat T., Transient response of tapping scanning force microscopy in liquids, Journal of Vacuum Science & Technology B, vol. 14, No. 2, 1996, pp. 1313-1317.
[15] Burnham N., Behrend O., Oulevey F., Gremaud G., Gallo P., Gourdon D., Dupas E., Kulik A., Pollock H., Briggs G., How does a tip tap?, Nanotechnology, vol. 8, No. 2, 1997, pp. 67.
[16] Sader J.E., Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope, Journal of applied physics, Vol. 84, No. 1, 1998, pp. 64-76.
[17] Y. Song, B. Bhushan, Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid, Ultramicroscopy, vol. 107, No. 10, 2007, pp. 1095-1104.
[18] Korayem M., Ebrahimi N., Nonlinear dynamics of tapping-mode atomic force microscopy in liquid, Journal of Applied Physics, vol. 109, No. 8, 2011, pp. 084301.
[19] Lee H.L., Chang W.J., Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory, Microelectronic Engineering, vol. 88, No. 11, 2011, pp. 3214-3218.
[20] Moosapour M., Hajabasi M.A., Ehteshami H., Frequency and sensitivity analysis of atomic force microscope (afm) cantilever considering coupled flexural-torsional vibrations, Digest Journal of Nanomaterials and Biostructures, vol. 7, No. 3, 2012, pp. 1103-1115.
[21] Timoshenko S., Goodier, Theory of Elasticity, McGraw3 1aill, New York, vol. 1, No. 95, 1951, pp. 1.
[22] Hosaka H., Itao K., Kuroda S., Damping characteristics of beam-shaped micro-oscillators, Sensors and Actuators A: Physical, vol. 49, No. 1, 1995, pp. 87-95.
[23] Hsu J.C., Lee H.L., Chang W.J., Flexural vibration frequency of atomic force microscope cantilevers using the Timoshenko beam model, Nanotechnology, vol. 18, No. 28, 2007, pp. 285503.
[24] Derjaguin B.V., Muller V.M., Toporov Y.P., Effect of contact deformations on the adhesion of particles, Journal of Colloid and interface science, vol. 53, No. 2, 1975, pp. 314-326.
[25] Saltelli A., Chan K., Scott EM: Sensitivity analysis, Wiley, vol. 79, 2000, pp. 80.
[26] Korayem M., Damircheli M., The effect of fluid properties and geometrical parameters of cantilever on the frequency response of atomic force microscopy, Precision Engineering, vol. 38, No. 2, 2014, pp. 321-329.