Geometrical Parameters of Rectangular AFM Cantilevers Producing Highest Sensitivity in Excitation of Second Mode in Air Environment
الموضوعات :
1 - Department of Mechanical Engineering,
Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran
الکلمات المفتاحية: Geometry, AFM, Higher modes self-excitation,
ملخص المقالة :
Today, improving the quality of the images acquired by the atomic force microscope (AFM) and obtaining the close properties of various samples are among the most important and challenging issues tackled by researchers. One of the key mechanisms of achieving these objectives is the excitation of higher modes, which raises the sensitivity of the AFM and consequently improves the resolution. To attain this goal, it is imperative to design or select a type of cantilever which is able to excite the second mode and produce maximum sensitivity in higher modes, especially the second mode. In this paper, an AFM cantilever with rectangular cross section has been investigated in air medium. The cantilever has been modeled by the Timoshenko beam model and the normal and tangential forces between cantilever tip and sample have been considered in the simulations. By changing the geometrical parameters of the AFM’s cantilever and tip including length, width, thickness of cantilever, the angle between cantilever and sample surface, mass of tip, length of tip and Radius of tip, the frequency ratio of the second mode to first mode varies. The geometrical parameters that produce the minimum frequency ratio can increase the self-excitation probability of the second mode due to the excitation of the first mode simultaneously. The optimum geometrical parameters are derived that can increase the chance of higher mode excitation. The results indicate that the sensitivity of the second mode to sample stiffness also increases optimal geometrical parameters that yield the minimum frequency ratio; and, as a result, a higher contrast is achieved and it leads users to utilize the cantilevers with optimum geometry for achieving best contrast in imaging and properties estimation of unknown samples.
[1] Martin, Y., C. Williams, and H. K., Wickramasinghe, “Atomic Force Microscope–Force Mapping and Profiling on a Sub 100‐Å Scaleˮ, Journal of Applied Physics, Vol. 61, No. 10, 1987, pp. 4723-4729.
[2] Stark, M., et al., “From Images to Interactions: High-Resolution Phase Imaging in Tapping-Mode Atomic Force Microscopyˮ, Biophysical journal, Vol. 80, No. 6, 2001, pp. 3009-3018.
[3] Xu, X., et al., “Unmasking Imaging Forces on Soft Biological Samples in Liquids when using Dynamic Atomic Force Microscopy, A Case Study on Viral Capsidsˮ, Biophysical journal, Vol. 95, No. 5, 2008, pp. 2520-2528.
[4] Stark, M., et al., “Inverting Dynamic Force Microscopy: From Signals to Time-Resolved Interaction Forcesˮ, Proceedings of the National Academy of Sciences, Vol. 99, No. 13, 2002, pp. 8473-8478.
[5] Legleiter, J., et al., “Scanning Probe Acceleration Microscopy (SPAM) in Fluids: Mapping Mechanical Properties of Surfaces at the Nanoscaleˮ, Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, No. 13, 2006, pp. 4813-4818.
[6] Hillenbrand, R., M. Stark, and R. Guckenberger, “Higher-Harmonics Generation in Tapping-Mode Atomic-Force Microscopy: Insights into the Tip–Sample Interactionˮ, Applied Physics Letters, Vol. 76, No. 23, 2000, pp. 3478-3480.
[7] Sahin, O., A. Atalar, “Simulation of Higher Harmonics Generation in Tapping-Mode Atomic Force Microscopyˮ, Applied Physics Letters, Vol. 79, No. 26, 2001, pp. 4455-4457.
[8] Stark, R.W., “Spectroscopy of Higher Harmonics in Dynamic Atomic Force Microscopyˮ, Nanotechnology, Vol. 15, No. 3, 2004, pp. 347.
[9] Sharos, L., et al., “Enhanced Mass Sensing using Torsional and Lateral Resonances in Microcantileversˮ, Applied Physics Letters, Vol. 84, No. 23, 2004, pp. 4638-4640.
[10]Basak, S., A. Raman, “Dynamics of Tapping Mode Atomic Force Microscopy in Liquids: Theory and Experimentsˮ, Applied Physics Letters, Vol. 91, No. 6, 2007, pp. 064107.
[11]Melcher, J., et al., “Origins of Phase Contrast in the Atomic Force Microscope in Liquidsˮ, Proceedings of the National Academy of Sciences, Vol. 106, No. 33, 2009, pp.13655-13660.
[12]Garcia, R., E. T. Herruzo, “The Emergence of Multifrequency Forces Microscopyˮ, Nature nanotechnology, Vol. 7, No. 4, 2012, pp. 217-226.
[13]Rodrıguez, T. R., R. Garcı́a, “Compositional Mapping of Surfaces in Atomic Force Microscopy by Excitation of the Second Normal Mode of the Microcantileverˮ, Applied Physics Letters, Vol. 84, No. 3, 2004, pp. 449-451.
[14]Sadewasser, S., Villanueva, G. and Plaza, J. “Special Cantilever Geometry for the Access of Higher Oscillation Modes in Atomic Force Microscopyˮ, Applied physics letters, Vol. 89, No. 3, 2006, pp. 033106.
[15]Damircheli, M., M. Korayem, “Dynamic Analysis of the AFM by Applying the Timoshenko Beam Theory in the Tapping Mode and Considering the Impact of the Interaction Forces in a Liquid Environmentˮ, Canadian Journal of Physics, Vol. 92, No. 6, 2013, pp. 472-483.
[16]Johnson, K., “Contact Mechanicsˮ, Cambridge University Press, Cambridge, 1985, UK.
[17]Derjaguin, B., V. Muller, and Y. P. Toporov, “Effect of Contact Deformations on the Adhesion of Particlesˮ, Journal of Colloid and interface science, Vol. 53, No. 2, 1975, pp. 314-326.
[18]Song, Y., B. Bhushan, “Finite-Element Vibration Analysis of Tapping-Mode Atomic Force Microscopy in Liquidˮ, Ultramicroscopy, Vol. 107, No. 2, 2007, pp. 1095-1104.
