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SPECIAL SECTION ON NANOMATERIALS AND NANOMECHANICS

Nonlocality Effect in Atomic Force Microscopy Measurement and Its Reduction by an Approaching Method

[+] Author and Article Information
Ming Hu1

State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics,  Chinese Academy of Sciences, Beijing 100080, China and  Graduate School of Chinese Academy of Sciences, Beijing 100039, Chinahuming@lnm.imech.ac.cn

Haiying Wang, Yilong Bai

State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics,  Chinese Academy of Sciences, Beijing 100080, China

Mengfen Xia

State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics,  Chinese Academy of Sciences, Beijing 100080, China and Department of Applied Physics,  Peking University, Beijing 100871, China

Fujiu Ke

State Key Laboratory of Nonlinear Mechanics,  Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China Department of Physics,  Beijing University of Aerospace and Aeronautics, Beijing 100083, China

1

Corresponding author. Fax: +86-10-62579511

J. Eng. Mater. Technol 127(4), 444-450 (Feb 17, 2005) (7 pages) doi:10.1115/1.1925290 History: Received September 26, 2004; Revised February 17, 2005

In AFM measurements of surface morphology, the locality is a traditional assumption, i.e., the load recorded by AFM is simply the function of the distance between the tip of AFM and the point on a sample right opposite the tip [Giessibl, F. J., 2003, “Advances in Atomic Force Microscopy  ,” Rev. Mod. Phys., 75, pp. 949–983]. This paper presents that nonlocality effect may play an important role in atomic force microscopic (AFM) measurement. The nonlocality of AFM measurement results from two different finite scales: the finite scale of the characteristic intermolecular interaction distance and the geometric size of AFM tip. With a coupled molecular-continuum method, we analyzed this nonlocality effect in detail. It is found that the nonlocality effect can be formulated by a few dimensionless parameters characterizing the ratio of the following scales: the characteristic intermolecular interaction distance between the AFM tip and the sample, the characteristic size of the tip and the characteristic nano-structure and∕or the nanoscale roughness on the surface of a sample. The present work also suggests a data processing algorithm—the approaching method, which can reduce the nonlocality effect in AFM measurement of surface morphology effectively.

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

(a) Sd vs λ curves for various a changing from 10 to 40; (b) Sd vs a curves with λ varying from 60 to 100. Both figures are calculated under constant scanning force 0.1nN.

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Figure 8

Constant Sd=5.5% curve fitted by the polynomial. The points are calculated under constant scanning force 0.1nN.

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Figure 10

Comparison of the approaching and the scanning results of surface morphology. The former are calculated by the approaching method and the latter are scanned by the single-atom tip under constant force 0.1nN. Both a and λ are 10.

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Figure 13

Schematic of the secondary approaching method. The tip contacts the surface at point A and B is the point opposite to the tip. AC is the tangent of the sample surface.

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Figure 11

Comparison of the approaching and the scanning results of surface morphology. The former two are calculated by the first and second approaching methods respectively and the latter are directly scanned by the finite size tip with R=1 under constant force 0.1nN. Both a and λ are 10.

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Figure 12

Schematic of a finite size tip contacting the sample

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Figure 1

Schematic diagram of an AFM tip interacting with a specified rough surface

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Figure 2

Schematic of the interaction between the tip and a single particle

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Figure 3

Schematic of the Gaussian integral process

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Figure 4

Schematic of a finite size tip probing a curved sample surface

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Figure 5

Constant height curve as a single-atom particle moves along the surface in one asperity period (see the inset) with a=50 and λ=100

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Figure 6

Comparison of the real (real line) and measured (dash–dotted line) surface morphology scanned by a single particle in one asperity period with a=50, λ=100, and ffixed=1.953

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Figure 9

Comparison of the real (real line) and measured (dashed–dotted line) surface morphology scanned by a finite size tip with R=10 in one asperity period with a=50 and λ=100 under constant load ffixed=1.953(0.1nN)

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