Characterization of Intermittent Contact in Tapping-Mode Atomic Force Microscopy

[+] Author and Article Information
Xiaopeng Zhao1

Department of Biomedical Engineering, Duke University, Durham, NC 27708xzhao@duke.edu

Harry Dankowicz

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801danko@uiuc.edu


Author to whom correspondence should be addressed.

J. Comput. Nonlinear Dynam 1(2), 109-115 (Sep 04, 2005) (7 pages) doi:10.1115/1.2162864 History: Received February 22, 2005; Revised September 04, 2005

Tapping-mode atomic force microscopy has wide applications for probing the nanoscale surface and subsurface properties of a variety of materials in a variety of environments. Strongly nonlinear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact with the sample, however, result in strong dynamical instabilities. These can result in a sudden loss of stability of low-contact-velocity oscillations of the atomic-force-microscope tip in favor of oscillations with high contact velocity, coexistence of stable oscillatory motions, and destructive, nonrepeatable, and unreliable characterization of the nanostructure. In this paper, dynamical systems tools for piecewise-smooth systems are employed to characterize the loss of stability and associated parameter-hysteresis phenomena.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic of a tapping-mode atomic force microscope

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Figure 2

Model of the tapping-mode atomic force microscope. Here, we represent the oscillation of the dither piezo by an equivalent excitation force f(t)=mγcosωt.

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Figure 3

Dependence of the oscillation amplitude on the equilibrium tip-sample separation. Here, the solid line represents stable solutions and the dotted line represents unstable solutions. The insets show enlargements of the circled area.

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Figure 4

Dependence of penetration on the equilibrium tip-sample separation. Here, penetration is defined as −(xmin+l) for a periodic orbit. SN1 and SN2 represent saddle-node bifurcations and A–E represent points of grazing bifurcation. The inset shows an enlargement around point C.

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Figure 5

Dependence of the phase shift on the equilibrium tip-sample separation. Here, solid lines represent stable solutions, dotted lines represent unstable solutions, SN1 and SN2 represent saddle-node bifurcations, and A–E represent points of grazing bifurcations. The inset shows an enlargement near point C. The phase shift of the free oscillation (without interaction with the sample surface) is −90deg.

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Figure 6

Trajectory segments in the vicinity of a grazing trajectory. Here, the flow on the right of D is governed by F1 while the flow on the left is governed by F2. Solid curves represent the real flow, and dashed curves correspond to virtual flow under F1 as if the discontinuity surface D is absent.

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Figure 7

Numerical prediction of the grazing bifurcation from the discontinuity mapping as obtained by the Newton-Raphson method and parameter continuation (solid for stable and dotted for unstable) and numerical results obtained for the original system of differential equations (solid for stable and dashed for unstable): (a) dependence of penetration on the equilibrium tip-sample separation and (b) dependence of the real part of the largest-in-magnitude eigenvalue on the equilibrium tip-sample separation.




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