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.

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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



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