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Research Papers

Response Measurement Accuracy for Off-Resonance Excitation in Atomic Force Microscopy

[+] Author and Article Information
R. Parker Eason

 Nonlinear Phenomena Laboratory, Dept. of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005parker.eason@rice.edu

Andrew J. Dick1

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

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(1), 011010 (Dec 05, 2011) (9 pages) doi:10.1115/1.4005361 History: Received January 05, 2011; Revised September 17, 2011; Accepted September 21, 2011; Published December 05, 2011; Online December 05, 2011

Displacement measurement in atomic force microscopy (AFM) is most commonly obtained indirectly by measuring the slope of the AFM probe and applying a calibration factor. Static calibration techniques operate on the assumption that the probe response approximates single mode behavior. For off-resonance excitation or different operating conditions the contribution of higher modes may become significant. In this paper, changes to the calibrated slope-displacement relationship and the corresponding implications on measurement accuracy are investigated. A model is developed and numerical simulations are performed to examine the effect of laser spot position, tip mass, quality factor and excitation frequency on measurement accuracy. Free response conditions and operation under nonlinear tip-sample forces are considered. Results are verified experimentally using a representative macroscale system. A laser spot positioned at a nominal position between x = 0.5 and 0.6 is determined to minimize optical lever measurement error under conditions where the response is dominated by contributions from the first two modes, due to excitation as well as other factors.

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Figures

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Figure 1

Schematic of the components that comprise the optical lever deflection measurement system in AFM

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Figure 2

Simplified model of a rectangular cantilever probe

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Figure 3

Empirical force model: multiwall carbon nanotube on biomolecule

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Figure 4

Measurement error versus normalized excitation frequency. Curves correspond to results obtained at different spot positions.

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Figure 5

Measurement error versus normalized excitation frequency. Curves correspond to results obtained at different mass ratios.

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Figure 6

Displacement and slope profiles for excitation conditions ω ex= ω 1 , γ=  0 (SOLID), ω ex= ω 2.5 , γ =  0 (DASHED), and ω ex = ω 2.5 , γ=  0.03 (DASH-DOT)

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Figure 7

Measurement error versus quality factor at nominal excitation frequencies ωex  /ω1  =  1.0 (× ), ωex /ω1  = 1.5 (o), ωex  /ω1 = 2.0 (+ ), and ωex /ω1  = 2.5 (*)

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Figure 8

Contour plot of measurement error versus mass ratio and spot position. Trend line (DASHED) shows Xpo versus spot position. Labels identify positive and negative measurement error regions for grayscale prints.

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Figure 9

Measurement error versus separation distance and spot position at four excitation frequencies. Trend line (DOTTED) shows Xpo versus separation distance. Labels identify positive and negative measurement error regions for grayscale prints.

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Figure 10

Top view schematic of the macroscale experimental setup

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Figure 11

(a) Displacements calculated from experimental vibrometer measurements (MARKERS) and corresponding best-fit curves for excitation conditions ωex = ω1 , γ=  0 (TRIANGLE– SOLID), ωex = ω2.5 , γ=  0 (PLUS–DASHED) and ωex = ω2.5 , γ=  0.03 (SQUARE–DASH-DOT). (b) Slope profiles calculated by differentiating the corresponding best-fit curves.

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Figure 12

Measurement error versus normalized excitation frequency, calculated from experimental data. Curves correspond to results obtained at different spot positions.

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Figure 13

Measurement error versus normalized excitation frequency, calculated from experimental data. Curves correspond to results obtained at different mass ratios.

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Figure 14

Contour plot of measurement error versus mass ratio and spot position, calculated from experimental data. Positive and negative regions are separated by a dashed line and labeled.

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