A beam model is developed and discretized to study the dynamic behavior of the cantilever probe of an atomic force microscope. Atomic interaction force models are used with a multimode approximation in order to simulate the probe’s response. The system is excited at two-and-a-half times the fundamental frequency and with a dual-frequency signal consisting of the AFM probe’s fundamental frequency and two-and-a-half times the fundamental frequency. A qualitative change in the response in the form of period doubling is observed for the harmonic off-resonance excitation when significantly influenced by repulsive surface forces. Through the use of dual-frequency excitation, standard response characteristics are maintained, while the inclusion of the off-resonance frequency component results in an identifiable qualitative change in the response. By monitoring specific frequency components, the influence of attractive and repulsive surface forces may be distinguished. This information could then be used to distinguish between imaging regimes when bistability occurs or to operate at the separation distance between surface force regimes to minimize force levels.
Issue Section:
Research Papers
1.
Binnig
, G.
, Quate
, C. F.
, and Gerber
, C.
, 1986, “Atomic Force Microscope
,” Phys. Rev. Lett.
0031-9007, 56
(9
), pp. 930
–933
.2.
Martin
, Y.
, Williams
, C. C.
, and Wickramasinghe
, H. K.
, 1987, “Atomic Force Microscope-Force Mapping and Profiling on a Sub 100 Angstrom Scale
,” J. Appl. Phys.
0021-8979, 61
(10
), pp. 4723
–4729
.3.
García
, R.
, and Perez
, R.
, 2002, “Dynamic Atomic Force Microscopy Methods
,” Surf. Sci. Rep.
0167-5729, 47
(6–8
), pp. 197
–301
.4.
Zhong
, Q.
, Inniss
, D.
, Kjoller
, K.
, and Elings
, V. B.
, 1993, “Fractured Polymer/Silica Fiber Surface Studied by Tapping Mode Atomic Force Microscopy
,” Surf. Sci. Lett.
0167-2584, 290
, pp. L688
–L692
.5.
Gleyzes
, P.
, Kuo
, P. K.
, and Boccara
, A. C.
, 1991, “Bistable Behavior of a Vibrating Tip Near a Solid Surface
,” Appl. Phys. Lett.
0003-6951, 58
(25
), pp. 2989
–2997
.6.
Dankowicz
, H.
, 2006, “Nonlinear Dynamics as an Essential Tool for Non-Destructive Characterization of Soft Nanostructures Using Tapping-Mode Atomic Force Microscopy
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 364
, pp. 3505
–3520
.7.
Dankowicz
, H.
, Zhao
, X.
, and Misra
, S.
, 2007, “Near-Grazing Dynamics in Tapping-Mode Atomic-Force Microscopy
,” Int. J. Non-Linear Mech.
0020-7462, 42
, pp. 697
–709
.8.
Akamine
, S.
, Barrett
, R. C.
, and Quate
, C. F.
, 1990, “Improved Atomic Force Microscope Images Using Microcantilevers With Sharp Tips
,” Appl. Phys. Lett.
0003-6951, 57
(3
), pp. 316
–318
.9.
Fotino
, M.
, 1993, “Tip Sharpening by Normal and Reverse Electrochemical Etching
,” Rev. Sci. Instrum.
0034-6748, 64
(1
), pp. 159
–167
.10.
Neuzil
, P.
, and Nagarajan
, R.
, 2006, “The Formation of Sharp AFM Tips by Single Step Etching
,” J. Micromech. Microeng.
0960-1317, 16
, pp. 1298
–1300
.11.
Burt
, D. P.
, Dobson
, P. S.
, Donaldson
, L.
, and Weaver
, J. M. R.
, 2008, “A Simple Method for High Yield Fabrication of Sharp Silicon Tips
,” Microelectron. Eng.
0167-9317, 85
(3
), pp. 625
–630
.12.
Wong
, S. S.
, Joselevich
, E.
, Woolley
, A. T.
, Cheung
, C. L.
, and Lieber
, C. M.
, 1998, “Covalently Functionalized Nanotubes as Nanometre-Sized Probes in Chemistry and Biology
,” Nature (London)
0028-0836, 394
(6688
), pp. 52
–55
.13.
Hafner
, J. H.
, Cheung
, C. L.
, Woolley
, A. T.
, and Lieber
, C. M.
, 2001, “Structural and Functional Imaging With Carbon Nanotube AFM Probes
,” Prog. Biophys. Mol. Biol.
0079-6107, 77
(1
), pp. 73
–110
.14.
Choi
, N.
, Uchihashi
, T.
, Nishijima
, H.
, Ishida
, T.
, Mizutani
, W.
, Akita
, S.
, Nakayama
, Y.
, Ishikawa
, M.
, and Tokumoto
, H.
, 2000, “Atomic Force Microscopy of Single-Walled Carbon Nanotubes Using Carbon Nanotube Tip
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 39
(6B
), pp. 3707
–3710
.15.
Kuwahara
, M.
, Abe
, H.
, Tokumoto
, H.
, Shima
, T.
, Tominaga
, J.
, and Fukuda
, H.
, 2004, “Practical Use of a Carbon Nanotube Attached to a Blunt Apex in an Atomic Force Microscope
,” Mater. Charact.
1044-5803, 52
, pp. 43
–48
.16.
Solares
, S. D.
, 2008, “Characterization of Deep Nanoscale Surface Trenches With AFM Using Thin Carbon Nanotube Probes in Amplitude-Modulation and Frequency-Force-Modulation Modes
,” Meas. Sci. Technol.
0957-0233, 19
, p. 015503
.17.
Zhang
, W.
, Xi
, Z.
, Zhang
, G.
, Li
, G.
, and Guo
, D.
, 2008, “Multiple Telescoping Extension of Multiwalled Carbon Nanotubes and Its Application in Atomic Force Microscopy
,” J. Phys. Chem. C
1932-7447, 112
, pp. 14714
–14717
.18.
Tay
, A. B. H.
, and Thong
, J. T. L.
, 2004, “Fabrication of Super-Sharp Nanowire Atomic Force Microscope Probes Using a Field Emission Induced Growth Technique
,” Rev. Sci. Instrum.
0034-6748, 75
(10
), pp. 3248
–3255
.19.
Solares
, S. D.
, 2007, “Frequency and Force Modulation Atomic Force Microscopy: Low-Impact Tapping-Mode Imaging Without Bistability
,” Meas. Sci. Technol.
0957-0233, 18
, pp. L9
–L14
.20.
Solares
, S. D.
, 2007, “Single Biomolecule Imaging With Frequency and Force Modulation in Tapping-Mode Atomic Force Microscopy
,” J. Phys. Chem. B
1089-5647, 111
(9
), pp. 2125
–2129
.21.
Solares
, S. D.
, and Crone
, J. C.
, 2007, “Real-Time Simulations of Isolated Biomolecule Characterization With Frequency and Force Modulation Atomic Force Microscopy
,” J. Phys. Chem.
0022-3654, 111
, pp. 10029
–10034
.22.
Jarvis
, S. P.
, Lantz
, M. A.
, Durig
, U.
, and Tokumoto
, H.
, 1999, “Off Resonance ac Mode Force Spectroscopy and Imaging With an Atomic Force Microscope
,” Appl. Surf. Sci.
0169-4332, 140
(3–4
), pp. 309
–313
.23.
Oral
, A.
, Grimble
, R. A.
, Ozer
, H. O.
, Hoffmann
, P. M.
, and Pethica
, J. B.
, 2001, “Quantitative Atom-Resolved Force Gradient Imaging Using Noncontact Atomic Force Microscopy
,” Appl. Phys. Lett.
0003-6951, 79
(12
), pp. 1915
–1917
.24.
Hoffmann
, P. M.
, Oral
, A.
, Grimble
, R. A.
, Ozer
, H. O.
, Jeffery
, S.
, and Pethica
, J. B.
, 2009, “Direct Measurement of Interatomic Force Gradients Using an Ultra-Low-Amplitude Atomic Force Microscope
,” Proc. R. Soc. London, Ser. A
0950-1207, 457
, pp. 1161
–1174
.25.
Hoffmann
, P. M.
, 2003, “Dynamics of Small Amplitude, Off-Resonance AFM
,” Appl. Surf. Sci.
0169-4332, 210
(1–2
), pp. 140
–145
.26.
Jeffery
, S.
, Hoffmann
, P. M.
, Pethica
, J. B.
, Ramanujan
, C.
, Ozer
, H. O.
, and Oral
, A.
, 2004, “Direct Measurement of Molecular Stiffness and Damping in Confined Water Layers
,” Phys. Rev. B
0556-2805, 70
(5
), p. 054114
.27.
Özer
, H. O.
, O’Brien
, S. J.
, Norris
, A.
, Sader
, J. E.
, and Pethica
, J. B.
, 2005, “Dissipation Imaging With Low Amplitude Off-Resonance Atomic Force Microscopy
,” Jpn. J. Appl. Phys., Part 1
0021-4922, 44
(7B
), pp. 5325
–5327
.28.
Balachandran
, B.
, 2003, “Dynamics of an Elastic Structure Subjected to Harmonic and Aharmonic Impactor
,” J. Vib. Control
1077-5463, 9
(3–4
), pp. 265
–279
.29.
Stark
, R. W.
, and Heckl
, W. M.
, 2000, “Fourier Transformed Atomic Force Microscopy: Tapping Mode Atomic Force Microscopy Beyond the Hookian Approximation
,” Surf. Sci.
0039-6028, 457
, pp. 219
–228
.30.
Sahin
, O.
, and Atalar
, A.
, 2001, “Simulation of Higher Harmonics Generation in Tapping-Mode Atomic Force Microscopy
,” Appl. Phys. Lett.
0003-6951, 79
(26
), pp. 4455
–4457
.31.
Stark
, R. W.
, and Heckl
, W. M.
, 2003, “Higher Harmonics Imaging in Tapping-Mode Atomic Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 74
(12
), pp. 5111
–5114
.32.
Sahin
, O.
, Quate
, C. F.
, Solgaard
, O.
, and Atalar
, A.
, 2004, “Resonant Harmonic Response in Tapping-Mode Atomic Force Microscopy
,” Phys. Rev. B
0556-2805, 69
(16
), p. 165416
.33.
Stark
, R. W.
, Schitter
, G.
, Stark
, M.
, Guckenberger
, R.
, and Stemmer
, A.
, 2004, “State-Space Model of Freely Vibrating and Surface-Coupled Cantilever Dynamics in Atomic Force Microscopy
,” Phys. Rev. B
0556-2805, 69
(8
), p. 085412
.34.
Crittenden
, S.
, Raman
, A.
, and Reifenberger
, R.
, 2005, “Probing Attractive Forces at the Nanoscale Using Higher-Harmonic Dynamic Force Microscopy
,” Phys. Rev. B
0556-2805, 72
, p. 235422
.35.
Dick
, A. J.
, Balachandran
, B.
, Yabuno
, H.
, Numatsu
, M.
, Hayashi
, K.
, Kuroda
, M.
, and Ashida
, K.
, 2009, “Utilizing Nonlinear Phenomena to Locate Grazing in the Constrained Motion of a Cantilever Beam
,” Nonlinear Dyn.
0924-090X, 57
, pp. 335
–349
.36.
Dick
, A. J.
, and Solares
, S. D.
, 2008, “Utilizing Period-Doubling Bifurcations to Locate Grazing in Atomic Force Microscopy
,” Proceedings of the Sixth ENOC, EuroMech
.37.
Dick
, A. J.
, 2008, “Near-Grazing Based Intermittent Contact Mode Atomic Force Microscopy
,” Proceedings of ASME 2008 IMECE
, Boston, Paper No. IMECE2008-68795, pp. 1
–9
.38.
Mayo
, S. L.
, Olafson
, B. D.
, and Goddard
, W. A.
, III, 1990, “Dreiding: A Generic Force Field for Molecular Simulations
,” J. Phys. Chem.
0022-3654, 94
, pp. 8897
–8909
.39.
Muller
, D. J.
, Schabert
, F. A.
, Buldt
, G.
, and Engel
, A.
, 1995, “Imaging Purple Membranes in Aqueous Solutions at Sub-Nanometer Resolution by Atomic Force Microscopy
,” Biophys. J.
0006-3495, 68
(5
), pp. 1681
–1686
.40.
Stark
, R. W.
, 2004, “Optical Lever Detection in Higher Eigenmode Dynamic Atomic Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 75
(11
), pp. 5053
–5055
.41.
Stark
, M.
, Guckenberger
, R.
, Stemmer
, A.
, and Stark
, R. W.
, 2005, “Estimating the Transfer Function of the Cantilever in Atomic Force Microscopy: A System Identification Approach
,” J. Appl. Phys.
0021-8979, 98
, p. 114904
.42.
Doedel
, E. J.
, 1981, “Auto, a Program for Automatic Bifurcation Analysis of Autonomous Systems
,” Congr. Numer.
0384-9864, 30
, pp. 265
–384
.43.
Lee
, S. I.
, Howell
, S. W.
, Raman
, A.
, and Reifenberger
, R.
, 2002, “Nonlinear Dynamics of Microcantilevers in Tapping Mode Atomic Force Microscopy: A Comparison Between Theory and Experiment
,” Phys. Rev. B
0556-2805, 66
, p. 115409
.44.
Rutzel
, S.
, Lee
, S. I.
, and Raman
, A.
, 2003, “Nonlinear Dynamics of Atomic-Force-Microscope Probes Driven in Lennard-Jones Potential
,” Proc. R. Soc. London, Ser. A
0950-1207, 459
, pp. 1925
–1948
.45.
Kikukawa
, A.
, Hosaka
, S.
, and Imura
, R.
, 1996, “Vacuum Compatible High-Sensitive Kelvin Probe Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 67
(4
), pp. 1463
–1467
.46.
Stark
, R. W.
, Naujoks
, N.
, and Stemmer
, A.
, 2007, “Multifrequency Electrostatic Force Microscopy in the Repulsive Regime
,” Nanotechnology
0957-4484, 18
, p. 065502
.47.
Proksch
, R.
, 2006, “Multifrequency, Repulsive-Mode Amplitude-Modulated Atomic Force Microscopy
,” Appl. Phys. Lett.
0003-6951, 89
, p. 113121
.48.
Rodriguez
, B. J.
, Callahan
, C.
, Kalinin
, S. V.
, and Proksch
, R.
, 2007, “Dual-Frequency Resonance-Tracking Atomic Force Microscopy
,” Nanotechnology
0957-4484, 18
, p. 475504
.49.
Lozano
, J. R.
, and Garcia
, R.
, 2008, “Theory of Multifrequency Atomic Force Microscopy
,” Phys. Rev. Lett.
0031-9007, 100
, p. 076102
.50.
Chawla
, G.
, and Solares
, S. D.
, 2009, “Single-Cantilever Dual-Frequency Modulation Atomic Force Microscopy
,” Meas. Sci. Technol.
0957-0233, 20
, p. 015501
.51.
Stark
, R. W.
, 2009, “Dynamics of Repulsive Dual-Frequency Atomic Force Microscopy
,” Appl. Phys. Lett.
0003-6951, 94
, p. 063109
.52.
Thota
, P.
, MacLaren
, S.
, and Dankowicz
, H.
, 2007, “Controlling Bistability in Tapping-Mode Atomic Force Microscopy Using Dual-Frequency Excitation
,” Appl. Phys. Lett.
0003-6951, 91
, p. 093108
.53.
Platz
, D.
, Tholen
, E. A.
, Pesen
, D.
, and Haviland
, D. B.
, 2008, “Intermodulation Atomic Force Microscopy
,” Appl. Phys. Lett.
0003-6951, 92
(15
), p. 153106
.54.
Rodrı́guez
, T. R.
, and Garcia
, R.
, 2002, “Tip Motion in Amplitude Modulation (Tapping-Mode) Atomic Force Microscopy: Comparison Between Continuous and Point-Mass Models
,” Appl. Phys. Lett.
0003-6951, 80
(9
), pp. 1646
–1648
.55.
Melcher
, J.
, Hu
, S.
, and Raman
, A.
, 2007, “Equivalent Point-Mass Models of Continuous Atomic Force Microscope Probes
,” Appl. Phys. Lett.
0003-6951, 91
, p. 053101
.56.
Derjaguin
, B. V.
, Muller
, V. M.
, and Toporov
, Y. P.
, 1975, “Effects of Contact Deformations on the Adhesion of Particles
,” J. Colloid Interface Sci.
0021-9797, 53
(2
), pp. 314
–326
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
