Frequency Domain Identification of Tip-sample van der Waals Interactions in Resonant Atomic Force Microcantilevers

[+] Author and Article Information
Shuiqing Hu, Arvind Raman

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

Stephen Howell, Ron Reifenberger

Department of Physics, Purdue University, West Lafayette, IN 47907

Matthew Franchek

Department of Mechanical Engineering, University of Houston, 4800 Calhoun Road, Houston, Texas, 77204-4792

J. Vib. Acoust 126(3), 343-351 (Jul 30, 2004) (9 pages) doi:10.1115/1.1760560 History: Received February 01, 2003; Revised February 01, 2004; Online July 30, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
Scanning electron micrograph of the diving-board microcantilever (Olympus tip OMCL-AC240TS) used in the experiment. The figure in the inset shows a zoomed in image of the tip taken after the experiments were performed.
Grahic Jump Location
Estimated Hamaker constants from the simulation data using the one- and three-term Harmonic Balance methods and using data at different excitation frequencies around resonance. The dashed line indicates the input value of the Hamaker constant A=2.96×10−19 J used in this simulation.
Grahic Jump Location
A schematic diagram of the experimental setup for using “Jumping mode” AFM to measure real time base piezo deflection, tip deflection and tip-sample separation signals
Grahic Jump Location
A typical example of the input-output signals required to implement a Hamaker Spectrometer. In (a), a plot of the experimental tip deflection signal is given. In (b), the motion of the Z piezo in the Jumping mode operation is plotted. In (c), the resulting power spectral density of the tip vibration signal obtained during the “noncontact sampling” time indicated in the box.
Grahic Jump Location
Estimated values for the Hamaker constants obtained from this study. In (a) the estimated Si-HOPG Hamaker constant using the one-term Harmonic Balance technique, as a function of the number of data sets at different excitation frequencies near resonance. In (b) the estimated Si-Au Hamaker constant using the one-term Harmonic Balance technique, as a function of the number of data sets at different excitation frequencies near resonance. In (c) the estimated Si-SiC Hamaker constant using the one-term Harmonic Balance technique, as a function of the number of data sets at different excitation frequencies near resonance. In all plots, the horizontal dashed lines correspond to the range of literature values for the Hamaker constants. The experiments on each sample were repeated twice. The mean of the two measurements along with the error bars are shown above. The error bars are the sum of all the estimated uncertainties discussed in Sec. 4.6.
Grahic Jump Location
Frequency dependence of primary, secondary and zeroth harmonics of tip deflection towards sample with base excitation amplitude Y=y/η*=0.0035. (The dotted line denotes the unstable solution and solid line denotes the stable solution.)
Grahic Jump Location
Frequency dependence of maximum and minimum tip deflection towards sample, and the phase of the first harmonic of the response with respect to excitation for base excitation amplitude Y=y/η*=0.0035. The dotted line denotes the unstable solution and solid line denotes the stable solution. Fold points are indicated by circles while period doubling bifurcations are marked by squares.
Grahic Jump Location
Schematic diagram of the cantilever configurations as the cantilever vibrates about its elastostatic equilibrium




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