Research Papers: Design of Mechanisms and Robotic Systems

A Systematic Method for Developing Harmonic Cantilevers for Atomic Force Microscopy

[+] Author and Article Information
Benliang Zhu

Guangdong Province Key Laboratory
of Precision Equipment
and Manufacturing Technology,
School of Mechanical and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China
e-mail: meblzhu@scut.edu.cn

Soren Zimmermann

Department of Computing Science—AMiR,
University of Oldenburg,
Oldenburg D-26111, Germany
e-mail: soeren.zimmermann@uni-oldenburg.de

Xianmin Zhang

Guangdong Province Key Laboratory of
Precision Equipment and
Manufacturing Technology,
School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China
e-mail: zhangxm@scut.edu.cn

Sergej Fatikow

Department of Computing Science—AMiR,
University of Oldenburg,
Oldenburg D-26111, Germany
e-mail: fatikow@uni-oldenburg.de

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 15, 2016; final manuscript received September 1, 2016; published online October 14, 2016. Assoc. Editor: Massimo Callegari.

J. Mech. Des 139(1), 012303 (Oct 14, 2016) (6 pages) Paper No: MD-16-1361; doi: 10.1115/1.4034836 History: Received May 15, 2016; Revised September 01, 2016

This paper proposes a method for developing harmonic cantilevers for tapping mode atomic force microscopy (AFM). The natural frequencies of an AFM cantilever are tuned by inserting gridiron holes with specific sizes and locations, such that the higher order resonance frequencies can be assigned to be integer harmonics generated by the nonlinear tip–sample interaction force. The cantilever is modeled using the vibration theory of the Timoshenko beam with a nonuniform cross section. The designed cantilever is fabricated by modifying a commercial cantilever through focused ion beam (FIB) milling. The resonant frequencies of the designed cantilever are verified using a commercial AFM.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Binnig, G. , Quate, C. F. , and Gerber, C. , 1986, “ Atomic Force Microscope,” Phys. Rev. Lett., 56(9), p. 930. [CrossRef] [PubMed]
Eaton, P. , and West, P. , 2010, Atomic Force Microscopy, Oxford University Press, New York.
Garcia, R. , and Perez, R. , 2002, “ Dynamic Atomic Force Microscopy Methods,” Surf. Sci. Rep., 47(6), pp. 197–301. [CrossRef]
Mrinalini, R. S. M. , Sriramshankar, R. , and Jayanth, G. , 2015, “ Direct Measurement of Three-Dimensional Forces in Atomic Force Microscopy,” IEEE/ASME Trans. Mechatronics, 20(5), pp. 2184–2193. [CrossRef]
Taffetani, M. , Raiteri, R. , Gottardi, R. , Gastaldi, D. , and Vena, P. , 2015, “ A Quantitative Interpretation of the Response of Articular Cartilage to Atomic Force Microscopy-Based Dynamic Nanoindentation Tests,” ASME J. Biomech. Eng., 137(7), p. 071005. [CrossRef]
Meyer, E. , 1992, “ Atomic Force Microscopy,” Prog. Surf. Sci., 41(1), pp. 3–49. [CrossRef]
Zhong, Q. , Inniss, D. , Kjoller, K. , and Elings, V. , 1993, “ Fractured Polymer/Silica Fiber Surface Studied by Tapping Mode Atomic Force Microscopy,” Surf. Sci. Lett., 290(1), pp. L688–L692.
Stark, R. W. , and Heckl, W. M. , 2003, “ Higher Harmonics Imaging in Tapping-Mode Atomic-Force Microscopy,” Rev. Sci. Instrum., 74(12), pp. 5111–5114. [CrossRef]
Platz, D. , Tholén, E. A. , Pesen, D. , and Haviland, D. B. , 2008, “ Intermodulation Atomic Force Microscopy,” Appl. Phys. Lett., 92(15), p. 153106. [CrossRef]
Stark, M. , Stark, R. W. , Heckl, W. M. , and Guckenberger, R. , 2000, “ Spectroscopy of the Anharmonic Cantilever Oscillations in Tapping-Mode Atomic-Force Microscopy,” Appl. Phys. Lett., 77(20), pp. 3293–3295. [CrossRef]
Hillenbrand, R. , Stark, M. , and Guckenberger, R. , 2000, “ Higher-Harmonics Generation in Tapping-Mode Atomic-Force Microscopy: Insights Into the Tip–Sample Interaction,” Appl. Phys. Lett., 76(23), pp. 3478–3480. [CrossRef]
Preiner, J. , Tang, J. , Pastushenko, V. , and Hinterdorfer, P. , 2007, “ Higher Harmonic Atomic Force Microscopy: Imaging of Biological Membranes in Liquid,” Phys. Rev. Lett., 99(4), p. 046102. [CrossRef] [PubMed]
Sahin, O. , Quate, C. F. , Solgaard, O. , and Atalar, A. , 2004, “ Resonant Harmonic Response in Tapping-Mode Atomic Force Microscopy,” Phys. Rev. B, 69(16), p. 165416. [CrossRef]
Legleiter, J. , Park, M. , Cusick, B. , and Kowalewski, T. , 2006, “ Scanning Probe Acceleration Microscopy (Spam) in Fluids: Mapping Mechanical Properties of Surfaces at the Nanoscale,” Proc. Natl. Acad. Sci. U.S.A., 103(13), pp. 4813–4818. [CrossRef] [PubMed]
Sahin, O. , Magonov, S. , Su, C. , Quate, C. F. , and Solgaard, O. , 2007, “ An Atomic Force Microscope Tip Designed to Measure Time-Varying Nanomechanical Forces,” Nat. Nanotechnol., 2(8), pp. 507–514. [CrossRef] [PubMed]
Lai, C.-Y. , Barcons, V. , Santos, S. , and Chiesa, M. , 2015, “ Periodicity in Bimodal Atomic Force Microscopy,” J. Appl. Phys., 118(4), p. 044905. [CrossRef]
Zhang, W.-M. , Meng, G. , and Peng, Z.-K. , 2011, “ Nonlinear Dynamic Analysis of Atomic Force Microscopy Under Bounded Noise Parametric Excitation,” IEEE/ASME Trans. Mechatronics, 16(6), pp. 1063–1072. [CrossRef]
Rodriguez, T. R. , and García, R. , 2004, “ Compositional Mapping of Surfaces in Atomic Force Microscopy by Excitation of the Second Normal Mode of the Microcantilever,” Appl. Phys. Lett., 84(3), pp. 449–451. [CrossRef]
Sriramshankar, R. , and Jayanth, G. , 2015, “ Design and Evaluation of Torsional Probes for Multifrequency Atomic Force Microscopy,” IEEE/ASME Trans. Mechatronics, 20(4), pp. 1843–1853. [CrossRef]
Garcia, R. , and Herruzo, E. T. , 2012, “ The Emergence of Multifrequency Force Microscopy,” Nat. Nanotechnol., 7(4), pp. 217–226. [CrossRef] [PubMed]
Sahin, O. , Yaralioglu, G. , Grow, R. , Zappe, S. , Atalar, A. , Quate, C. , and Solgaard, O. , 2004, “ High-Resolution Imaging of Elastic Properties Using Harmonic Cantilevers,” Sens. Actuators A: Phys., 114(2), pp. 183–190. [CrossRef]
Li, H. , Chen, Y. , and Dai, L. , 2008, “ Concentrated-Mass Cantilever Enhances Multiple Harmonics in Tapping-Mode Atomic Force Microscopy,” Appl. Phys. Lett., 92(15), p. 151903. [CrossRef]
Cai, J. , Xia, Q. , Luo, Y. , Zhang, L. , and Wang, M. Y. , 2015, “ A Variable-Width Harmonic Probe for Multifrequency Atomic Force Microscopy,” Appl. Phys. Lett., 106(7), p. 071901. [CrossRef]
Weaver, W., Jr. , Timoshenko, S. P. , and Young, D. H. , 1990, Vibration Problems in Engineering, Wiley, New York.
Chen, G. , and Ma, F. , 2015, “ Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model,” ASME J. Mech. Des., 137(2), p. 022301. [CrossRef]
Xia, Q. , Zhou, T. , Wang, M. Y. , and Shi, T. , 2014, “ Shape and Topology Optimization for Tailoring the Ratio Between Two Flexural Eigenfrequencies of Atomic Force Microscopy Cantilever Probe,” Frontiers Mech. Eng., 9(1), pp. 50–57. [CrossRef]
Dugush, Y. , and Eisenberger, M. , 2002, “ Vibrations of Non-Uniform Continuous Beams Under Moving Loads,” J. Sound Vib., 254(5), pp. 911–926. [CrossRef]
Ahmadi, M. , and Nikkhoo, A. , 2014, “ Utilization of Characteristic Polynomials in Vibration Analysis of Non-Uniform Beams Under a Moving Mass Excitation,” Appl. Math. Modell., 38(7), pp. 2130–2140. [CrossRef]
Eichhorn, V. , Bartenwerfer, M. , and Fatikow, S. , 2012, “ Nanorobotic Assembly and Focused Ion Beam Processing of Nanotube-Enhanced AFM Probes,” IEEE Trans. Autom. Sci. Eng., 9(4), pp. 679–686. [CrossRef]


Grahic Jump Location
Fig. 1

The top–down view of an AFM cantilever with n inserted holes

Grahic Jump Location
Fig. 2

Values of the size (a) and position (x) of the inserted holes can ensure f2 or f3 to be exactly integers. The corresponding integers are labeled on the curves. Note that the crossover points between the solid and dotted lines can ensure both f2 and f3 are integer, such as points A, B, C, and D.

Grahic Jump Location
Fig. 3

Relationships between g2, g3 and x1 and x2 when a=30 μ m

Grahic Jump Location
Fig. 4

Relationships between ω2/ω1, ω3/ω1 and x1 and x2 when a=40 μ m

Grahic Jump Location
Fig. 5

SEM image of the cantilever after inserting two groups of holes by using FIB

Grahic Jump Location
Fig. 6

Normalized frequency response of the cantilevers before and after matching




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In