Analytical solutions of the frequency shifts of several modes in AFM scanning an inclined surface, subjected to the Lennard-Jones force

International Journal of Solids and Structures

Volumn 44, Issue 3-4, 2007, Pages 799-810

  Lin, Shueei Muh ^a   Liauh, Chihng Tsung ^a   Wang, Wen Rong ^a   Ho, Shing Huei ^a  

^a KUN SHAN UNIVERSITY   (Taiwan)

Author keywords

AFM; Analytical solution; Inclined surface

Indexed keywords

ATOMIC FORCE MICROSCOPY; BOUNDARY CONDITIONS; PERTURBATION TECHNIQUES; STRAIN RATE; SUBSTRATES; SURFACE TOPOGRAPHY;

ANALYTICAL SOLUTION; FREQUENCY SHIFTS; INCLINED SURFACE; LENNARD-JONES FORCE;

SURFACE STRUCTURE;

EID: 33750996139     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.05.024     Document Type: Article

References (19)

1. Garcia R., and Perez R. Dynamic atomic force microscopy methods. Surface Science Report 47 (2002) 197-301
2. Giessibl F.J. Forces and frequency shifts in atomic-resolution dynamic-force microscopy. Physical Review B 56 (1997) 16010-16015
3. Giessibl F.J. Advances in atomic force microscopy. Reviews of Modern Physics 75 (2003) 949-983
4. Glatzel Th., Sadeeasser S., and Lux-Steiner M.Ch. Amplitude or frequency modulation-detection in Kelvin probe force microscopy. Applied Surface Science 210 (2003) 84-89
5. Hölscher H., Schwarz U.D., and Wiesendanger R. Calculation of the frequency shift in dynamic force microscopy. Applied Surface Science 140 (1999) 344-351
6. Lin S.M. The instability and vibration of rotating beams with arbitrary pretwist and an elastically restrained root. ASME Journal of Applied Mechanics 68 (2001) 844-853
7. Lin S.M. Exact Solution of the frequency shift in dynamic force microscopy. Applied Surface Science 250 (2005) 228-237
8. Lin, S.M., Lee S.Y. and Chen B.S., in press. Closed-form solutions for the frequency shift of V-shaped probes scanning an inclined surface. Applied Surface Science, in press.
9. Meirovitch L. Analytical Methods in Vibrations (1967), Collier-Macmillan Limited, London
10. Rabe U., Janser K., and Amold W. Vibrations of free and surface-coupled force microscope cantilevers: Theory and experiment. American Institute of Physics 67 (1966) 3281-3293
11. Rodriguez T.R., and Garcia R. Tip motion in amplitude modulation (tapping-mode) atomic-force microscopy: Comparison between continuous and point-mass models. Applied Physics Letters 80 (2002) 1646-1648
12. Sader J.E., Uchihashi T., Higgins M.J., Farrell A., Nakayama Y., and Jarvis S.P. Quantitative force measurements using frequency modulation atomic force microscopy-theoretical foundations. Nanotechnology 16 (2005) s94-s101
13. Sarid D. Scanning force microscopy with applications to electric, magnetic and atomic forces (1994), Oxford University Press
14. Sasaki N., Tsukada M., Tamura R., Abe K., and Sato N. Dynamics of the cantilever in noncontact atomic force microscopy. Applied Physics A : Materials 66 (1998) 287-291
15. Sokolov I.Y., Henderson G.S., and Wicks F.J. Model dependence of AFM simulations in non-contact mode. Surface Science 457 (2000) 267-272
16. Sommerhalter Ch., Glatzel Th., Mattes Th.W., Jäger-Waldau A., and Lux-Steiner M.Ch. Kelvin probe force microscopy in ultrahigh vacuum using amplitude modulation detection of the electrostatic forces. Applied Surface Science 157 (2000) 32-36
17. Stark R.W., and Heckl W.M. Fourier transformed atomic force microscopy: tapping mode atomic force microscopy beyond the Hookian approximation. Surface Science 457 (2000) 219-228
18. Stark R.W., Drobek T., and Heckl W.M. Tapping-mode atomic force microscopy and phase-imaging in higher modes. Applied Physics Letters 74 (1999) 3296-3298
19. Weigert S., Dreier M., and Hegner M. Frequency shifts of cantilevers vibrating in various media. Applied Physics Letters 69 (1996) 2834-2836