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Research Papers

Influence of Local Material Properties on the Nonlinear Dynamic Behavior of an Atomic Force Microscope Probe

[+] Author and Article Information
Wei Huang

Department of Mechanical Engineering and Materials Science, Nonlinear Phenomena Laboratory, Rice University, Houston, TX 77005wei.huang@rice.edu

Andrew J. Dick1

Department of Mechanical Engineering and Materials Science, Nonlinear Phenomena Laboratory, Rice University, Houston, TX 77005andrew.j.dick@rice.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(4), 041009 (Apr 14, 2011) (9 pages) doi:10.1115/1.4003732 History: Received April 15, 2010; Revised February 24, 2011; Published April 14, 2011; Online April 14, 2011

In this paper, a study of the characteristics of period-doubling bifurcations in the dynamic behavior of an atomic force microscope probe for off-resonance excitation is presented. Using a three-mode approximation and excitation at two-and-a-half times the fundamental frequency, the relationship between the characteristics of the period-doubling bifurcation and the material properties is studied by using numerical simulations. Simulations are first used to successfully reproduce nonlinear response data collected experimentally by using a commercial atomic force microscope system and then to conduct a parametric study in order to examine the influence of variations in other system parameters on the relationship. These parameters are the excitation magnitude, the damping level, the cantilever stiffness, and the characteristics of the force model. Based upon the results of the parametric study, a new operation mode for obtaining localized material properties through an efficient scanning process is proposed. A preliminary scan simulation demonstrates the successful implementation of the relationship and its potential for providing localized material property information with nanoscale resolution.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

((A)–(D)) Time series plots and ((E)–(H)) corresponding phase portrait plots depicting experimental response transition for AFM cantilever probe. The displacement values presented in the experimental results correspond to the deflection at the tip of the probe as measured by the AFM. ((I)–(L)) Time series plots and ((M)–(P)) corresponding phase portrait plots depicting simulated response transition for AFM cantilever probe. The displacement values presented in the simulated results represent the summation of the relative probe response and the motion of the base excitation, ŵ(L̂,t̂)+X̂(t̂).

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Figure 2

Diagram of AFM cantilever probe model

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Figure 3

Spectral information for simulated responses for (a) period-one response and ((b)–(d)) period-two responses

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Figure 4

Bifurcation diagram constructed from Poincaré sections of system’s response for Ê∗=8.518×10−2 GPa. The dashed vertical lines and labels identify the Poincaré sections that correspond to the data presented in the previous plots.

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Figure 5

Comparison of the bifurcation diagrams constructed from the system’s response for a range of different values of Ê∗

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Figure 6

Separation distance of period-doubling bifurcation versus the model parameter Ê∗

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Figure 7

Critical separation distance corresponding to period-doubling versus effective elastic modulus for three oscillation amplitudes

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Figure 8

Critical separation distance corresponding to period-doubling versus effective elastic modulus for four cantilevers with different force constant values

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Figure 9

Comparison of DMT force curve and empirical force curve

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Figure 10

Comparison of bifurcation diagrams with DMT force model and empirical force model

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Figure 11

Measurement of subharmonic amplitude for simulated scanning operation

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Figure 12

Comparison of true effective modulus profile with profile identified through simulated scanning operation

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