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Modeling of Tip-Cantilever Dynamics in Atomic Force Microscopy

Chapter
Part of the NanoScience and Technology book series (NANO)

Abstract

Atomic force microscopy (AFM) is commonly used for atomic and nanoscale surface measurements. Two operational modes of AFM exist: static mode and dynamic mode. In dynamic AFM mode, a cantilever is driven to vibrate by its holder or the sample. The changes of cantilever vibration parameters (amplitude, resonance frequency, and phase angle) due to tip-sample interaction are used to reveal surface properties. Analytical and numerical models that can accurately simulate surface-coupled cantilever dynamics are essential for explaining AFM scanning images and evaluating the sample’s material properties. In this chapter, the existing dynamic modes of AFM are categorized in terms of cantilever deflection and excitation mechanism. Cantilever models for cantilever response simulation are summarized. Using these models, the important relations of cantilever frequency shift, vibration amplitude and phase angle with tip-sample interaction in various dynamic modes are derived, with an emphasis on newly-developed torsional resonance (TR) mode and lateral excitation (LE) mode. Some specific issues, such as the excitation of higher-order vibration modes in TappingMode (TM), the effects of tip eccentricity on cantilever responses in TR and LE modes, and how the cantilever dynamics affects the atomic-scale topographic and friction maps obtained in friction force microscopy (FFM) measurements, are investigated. Based on the derived relations between cantilever responses and tip-sample interaction, methods for quantitative evaluation of the sample’s mechanical parameters are described.

Keywords

Atomic Force Microscopy Graphite Surface Sample Interaction Torsional Resonance Friction Force Microscopy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Albrecht TR, Grütter P, Horne D, Rugar D (1991) Frequency Modulation Detection Using High-Q Cantilevers for Enhanced Force Microscopy Sensitivity. J Appl Phys 69:668–673CrossRefGoogle Scholar
  2. 2.
    Albrecht TR, Quate CF (1987) Atomic Resolution Imaging of a Nonconductor by Atomic Force Microscopy. J Appl Phys 62:2599–2602CrossRefGoogle Scholar
  3. 3.
    Amelio S, Goldade AV, Rabe U, Scherer V, Bhushan B, Arnold W (2001) Measurements of Elastic Properties of Ultra-Thin Diamond-Like Carbon Coatings Using Atomic Force Acoustic Microscopy. Thin Solid Films 392:75–84CrossRefGoogle Scholar
  4. 4.
    Arinero R, Lévêque G (2003) Vibration of the Cantilever in Force Modulation Microscopy Analysis by a Finite Element Model. Rev Sci Instrum 74:104–111CrossRefGoogle Scholar
  5. 5.
    Bhushan B (2005) Introduction to Nanotribology and Nanomechanics, Springer, Berlin Heidelberg New YorkGoogle Scholar
  6. 6.
    Bhushan B (2006) Springer Handbook of Nanotechnology, 2nd edn, Springer, Berlin Heidelberg New YorkGoogle Scholar
  7. 7.
    Bhushan B, Kasai T (2004) A Surface Topography-Independent Friction Measurement Technique Using Torsional Resonance Mode in an AFM. Nanotechnology 15:923–935CrossRefGoogle Scholar
  8. 8.
    Bhushan B, Qi J (2003) Phase Contrast Imaging of Nanocomposites and Molecularly Thick Lubricant Films in Magnetic Media. Nanotechnology 14:886–895CrossRefGoogle Scholar
  9. 9.
    Binning G, Gerber Ch (1987) Stoll E, Albrecht TR, and Quate CF, Atomic Resolution with Atomic Force Microscope. Europhys Lett 3:1281–1286Google Scholar
  10. 10.
    Butt HJ, Jaschke M (1995) Calculation of Thermal Noise in Atomic Force Microscopy. Nanotechnology 6:1–7CrossRefGoogle Scholar
  11. 11.
    Caron A, Rabe U, Reinstädtler M (2004) Imaging Using Lateral Bending Modes of Atomic Force Microscopy Cantilevers. Appl Phys Lett 85:6398–6400CrossRefGoogle Scholar
  12. 12.
    Chen N, Bhushan B (2005) Morphological, Nanomechanical and Cellular Structural Characterization of Human Hair and Condition Distribution Using Torsional Resonance Mode with an Atomic Force Microscopy. J Microscopy 220:96–112CrossRefGoogle Scholar
  13. 13.
    Chen J, Workman RK, Sarid D, Höper R (1994) Numerical simulations of a scanning force microscope with a large-amplitude vibrating cantilever. Nanotechnology 5:199–204CrossRefGoogle Scholar
  14. 14.
    Cleveland JP, Anczykowski B, Schmid AE, Elings VB (1998) Energy Dissipation in Tapping-Mode Atomic Force Microscopy. Appl Phys Lett 72:2613–2615CrossRefGoogle Scholar
  15. 15.
    Derjaguin BV, Muller VM, Toporov YP (1975) Effect of Contact Deformations on the Adhesion of Particles. J Colloid Interface Sci 53:314–326CrossRefGoogle Scholar
  16. 16.
    Dupas E, Gremaud G, Kulik A, Loubet JL (2001) High-Frequency Mechanical Spectroscopy with an Atomic Force Microscope. Rev Sci Instrum 72:3891–3897CrossRefGoogle Scholar
  17. 17.
    Fujisawa S, Yokoyama K, Sugawara Y, Morita S (1998) Analysis of Experimental Load Dependence of Two-Dimensional Atomic-Scale Friction. Phys Rev B 58:4909–4916CrossRefGoogle Scholar
  18. 18.
    García R, Pérez R (2002) Dynamic Atomic Force Microscopy Methods. Surf Sci Rep 47:197–301CrossRefGoogle Scholar
  19. 19.
    Giessibl FJ (1995) Atomic Resolution of the Silicon (111) — 7×7 Surface by Atomic Force Microscopy. Science 267:68–71CrossRefGoogle Scholar
  20. 20.
    Giessibl FJ (1997) Forces and Frequency Shifts in Atomic-Resolution Dynamic-Force Microscopy. Phys Rev B 56:16010–16015CrossRefGoogle Scholar
  21. 21.
    Gorman DJ (1975) Free Vibration Analysis of Beams and Shafts, Wiley, New YorkGoogle Scholar
  22. 22.
    Hölscher H, Schwarz UD, Wiesendanger R (1996) Simulation of a Scanned Tip on a NaF (001) Surface in Friction Force Microscopy. Europhys Lett 36:19–24CrossRefGoogle Scholar
  23. 23.
    Hölscher H, Schwarz UD, Wiesendanger R (1997) Modelling of the Scan Process in Lateral Force Microscopy. Surf Sci 375:395–402CrossRefGoogle Scholar
  24. 24.
    Hölscher H, Schwarz UD, Zwörner O, Wiesendanger R (1998) Consequence of the Stick-Slip Movement for the Scanning Force Microscopy Imaging of Graphite. Phys Rev B 57:2477–2481CrossRefGoogle Scholar
  25. 25.
    Huang L, Su C (2004) A Torsional Resonance Mode AFM for In-Plane Tip Surface Interfaces. Ultramicroscopy 100:277–285CrossRefGoogle Scholar
  26. 26.
    Hurley DC, Shen K, Jenett NM, Turner JA (2003) Atomic Force Acoustic Microscopy Methods to Determine Thin-Film Elastic Properties. J Appl Phys 94:2347–2354CrossRefGoogle Scholar
  27. 27.
    Johnson KL (1985) Contact Mechanics, Cambridge University Press, UKGoogle Scholar
  28. 28.
    Johnson KL, Kendall K, Roberts AD (1971) Surface Energy and the Contact of Elastic Solids. Proc R Soc London Ser A 324:301–313CrossRefGoogle Scholar
  29. 29.
    Johnson KL, Woodhouse J (1998) Stick-Slip Motion in the Atomic Force Microscopy. Tribol Lett 5:155–160CrossRefGoogle Scholar
  30. 30.
    Kasai T, Bhushan B, Huang L, Su C (2004) Topography and Phase Imaging Using the Torsional Resonance Mode. Nanotechnology 15:731–742CrossRefGoogle Scholar
  31. 31.
    Kitamura S, Iwatsuki M (1995) Observation of Silicon Surfaces Using Ultrahigh-Vacuum Noncontact Atomic Force Microscopy. Jpn J Appl Phys 35:L668–L671CrossRefGoogle Scholar
  32. 32.
    Lee SI, Howell SW, Raman A, Reifenberger R (2002) Non-Linear Dynamics of Microcantilevers in TappingMode Atomic Force Microscopy: A Comparison between Theory and Experiment. Phys Rev B 66:115409 1–10CrossRefGoogle Scholar
  33. 33.
    Maivald P, Butt HJ, Gould SAC, Prater CB, Drake B, Gurley JA, Elings VB, Hansma PK (1991) Using Force Modulation to Image Surface Elasticities with the Atomic Force Microscopy. Nanotechnology 2:103–106CrossRefGoogle Scholar
  34. 34.
    Marti O, Colchero J, Mlynek J (1990) Combined Scanning Force and Friction Microscopy of Mica. Nanotechnology 1:141–144CrossRefGoogle Scholar
  35. 35.
    Marti O, Drake B, Hansma PK (1987) Atomic Force Microscopy of Liquid-Covered Surfaces: Atomic Resolution Images. Appl Phys Lett 51:484–486CrossRefGoogle Scholar
  36. 36.
    Mate CM, McClelland GM, Erlandsson R, Chiang S (1987) Atomic-Scale Friction of a Tungsten Tip on a Graphite Surface. Phys Rev Lett 59:1942–1945CrossRefGoogle Scholar
  37. 37.
    Meyer G, Amer N (1990) Simultaneous Measurement of Lateral and Normal Forces with an Optical-Beam-Deflection Atomic Force Microscopy. Appl Phys Lett 57:2089–2091CrossRefGoogle Scholar
  38. 38.
    Mizes HA, Park SI, Harrison WA (1987) Multiple-Tip Interpretation of Anomalous Scanning-Tunneling-Microscopy Images of Layered Materials. Phys Rev B 36:R4491–4494CrossRefGoogle Scholar
  39. 39.
    MultiMode SPM Instructor Manual, Version 4.31ce (1997) Digital Instruments, Santa Barbara, CAGoogle Scholar
  40. 40.
    Rabe U, Arnold W (1994) Acoustic Microscopy by Atomic Force Microscopy. Appl Phys Lett 64:1493–1495CrossRefGoogle Scholar
  41. 41.
    Rabe U, Janser K, Arnold W (1996) Vibrations of Free and Surface-Coupled Atomic Force Microscope Cantilevers: Theory and Experiment. Rev Sci Instrum 67:3281–3293CrossRefGoogle Scholar
  42. 42.
    Rabe U, Turner J, Arnold W (1998) Analysis of the High-Frequency Response of Atomic Force Microscope Cantilevers. Appl Phys A 66:S227–S282CrossRefGoogle Scholar
  43. 43.
    Rabe U, Amelio S, Kester E, Scherer V, Hirsekorn S, Arnold W (2000) Quantitative Determination of Contact Stiffness Using Atomic Force Acoustic Microscopy. Ultrasonics 38:430–437CrossRefGoogle Scholar
  44. 44.
    Rabe U, Amelio S, Kopycinska M, Hirsekorn S, Kempf M, Göken M, Arnold W (2002) Imaging and Measurement of Local Mechanical Material Properties by Atomic Force Acoustic Microscopy. Surf Interf Anal 33:65–70CrossRefGoogle Scholar
  45. 45.
    Reinstädtler M, Kasai T, Rabe U, Bhushan B, Arnold W (2005a) Imaging and Measurement of Elasticity and Friction Using the TRmode. J Phys D Appl Phys 38:R269–R282CrossRefGoogle Scholar
  46. 46.
    Reinstädtler M, Rabe U, Scherer V, Hartmann U, Goldade A, Bhushan B, Arnold W (2003) On the Nanoscale Measurement of Friction Using Atomic-Force Microscope Cantilever Torsional Resonances. Appl Phys Lett 82:2604–2606CrossRefGoogle Scholar
  47. 47.
    Reinstädtler M, Rabe U, Goldade A, Bhushan B, Arnold W (2005b) Investigating Ultra-Thin Lubricant Layers Using Resonant Friction Force Microscopy. Tribol Int 38:533–541CrossRefGoogle Scholar
  48. 48.
    Ruan J, Bhushan B (1994) Atomic-Scale and Microscale Friction Studies of Graphite and Diamond Using Friction Force Microscopy. J Appl Phys 76:5022–5035CrossRefGoogle Scholar
  49. 49.
    San Paulo A, García R (2001) Tip-Surface forces, Amplitude, and Energy Dissipation in Amplitude-Modulation (TappingMode) Force Microscopy. Phys Rev B 64:193411 1–4CrossRefGoogle Scholar
  50. 50.
    Sasaki N, Kobayashi K, Tsukada M (1996) Atomic-Scale Friction Image of Graphite in Atomic-Force Microscopy. Phys Rev B 54:2138–2149CrossRefGoogle Scholar
  51. 51.
    Scherer V, Arnold W, Bhushan B (1999) Lateral Force Microscopy Using Acoustic Friction Microscopy. Surf Interf Anal 27:578–587CrossRefGoogle Scholar
  52. 52.
    Scott WW, Bhushan B (2003) Use of Phase Imaging in Atomic Force Microscopy for Measurement of Viscoelastic Contrast in Polymer Nanocomposites and Molecularly-Thick Lubricant Films. Ultramicroscopy 97:151–169CrossRefGoogle Scholar
  53. 53.
    Song Y, Bhushan B (2005) Quantitative Extraction of In-Plane Surface Properties Using Torsional Resonance Mode of Atomic Force Microscopy. J Appl Phys 97:083533 1–5CrossRefGoogle Scholar
  54. 54.
    Song Y, Bhushan B (2006a) Dynamic Analysis of Torsional Resonance Mode of Atomic Force Microscopy and its Application to In-Plane Surface Property Extraction. Microsyst Technol 12:129–230CrossRefGoogle Scholar
  55. 55.
    Song Y, Bhushan B (2006b) Simulation of Dynamic Modes of Atomic Force Microscopy Using a 3D Finite Element Model. Ultramicroscopy 106:847–873CrossRefGoogle Scholar
  56. 56.
    Song Y, Bhushan B (2006c) Coupling of Lateral Bending and Torsion in Torsional Resonance and Lateral Excitation Modes of Atomic Force Microscopy. J Appl Phys 99:094911 1–12CrossRefGoogle Scholar
  57. 57.
    Song Y, Bhushan B (2006d) Atomic-scale topographic and friction force imaging and cantilever dynamics in friction force microscopy. Phys Rev B, in pressGoogle Scholar
  58. 58.
    Stark RW, Schitter G, Startk M, Guckenberger R, Stemmer A (2004) State-Space Model of Freely Vibrating and Surface-Coupled Cantilever Dynamics in Atomic Force Microscopy. Phys Rev B 69:085412 1–9CrossRefGoogle Scholar
  59. 59.
    Tamayo J, García R (1998) Relationship between Phase Shift and Energy Dissipation in Tapping-Mode Scanning Force Microscopy. Appl Phys Lett 73:2926–2928CrossRefGoogle Scholar
  60. 60.
    Turner JA (2004) Non-linear Vibrations of a Beam with Cantilever-Hertzian Contact Boundary Conditions. J Sound Vib 275:177–195CrossRefGoogle Scholar
  61. 61.
    Turner JA, Wiehn JS (2001) Sensitivity of Flexural and Torsional Vibration Modes of Atomic Force Microscopy Cantilevers to Surface Stiffness Variations, Nanotechnology 12:322–330CrossRefGoogle Scholar
  62. 62.
    Turner JA, Hirsekorn S, Rabe U, Arnold W (1997) High-Frequency Response of Atomic-Force Microscope Cantilevers. J Appl Phys 82:966–979CrossRefGoogle Scholar
  63. 63.
    Wang L (1998) Analytical Descriptions of the Tapping-Mode Atomic Force Microscopy Response. Appl Phys Lett 73:3781–3783CrossRefGoogle Scholar
  64. 64.
    Wang L (1999) The Role of Damping in Phase Imaging in TappingMode Atomic Force Microscopy. Surf Sci 429:178–185CrossRefGoogle Scholar
  65. 65.
    Wright OB, Nishiguchi N (1997) Vibration Dynamics of Force Microscopy: Effect of Tip Dimensions. Appl Phys Lett 71:626–628CrossRefGoogle Scholar
  66. 66.
    Yamanaka K, Nakano S (1996) Ultrasonic Atomic Force Microscope with Overtone Excitation of Cantilever. Jpn J Appl Phys 35:3787–3792CrossRefGoogle Scholar
  67. 67.
    Yamanaka K, Nakano S (1998) Quantitative Elasticity Evaluation by Contact Resonance in an Atomic Force Microscopy. Appl Phys A 66:S313–S317CrossRefGoogle Scholar
  68. 68.
    Yamanaka K, Tomita E (1995) Lateral Force Modulation Atomic Force Microscopy for Selective Imaging of Friction Force. Jpn J Appl Phys 34:2879–2882CrossRefGoogle Scholar
  69. 69.
    Yamanaka K, Ogiso H, Kolosov O (1994) Ultrasonic Force Microscopy for Nanometer Resolution Substrate Imaging. Appl Phys Letts 64:178–180CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Nanotribology Lab for Information Storage and MEMS/NEMS (NLIM)The Ohio State UniversityColumbusUSA
  2. 2.Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) W 390 Scott LaboratoryOhio State UniversityColumbusUSA

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