Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy

Nonlinear Dynamics

Volumn 54, Issue 1-2, 2008, Pages 93-122

  Hornstein, S ^a   Gottlieb, O ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Atomic Force Microscopy (AFM); Escape bifurcation; Melnikov Holmes stability; Moon Chirikov overlap; Nonlinear microbeam; Scan dynamics

Indexed keywords

ATOMIC FORCE MICROSCOPY; ATOMIC PHYSICS; ATOMS; CONTINUUM MECHANICS; DAMPING; DYNAMICAL SYSTEMS; DYNAMICS; EQUATIONS OF MOTION; IMAGING TECHNIQUES; MICROSCOPIC EXAMINATION; NONLINEAR EQUATIONS; SCANNING PROBE MICROSCOPY; SCHRODINGER EQUATION; SYSTEM STABILITY;

APPROXIMATE STABILITY; ATOMIC FORCE MICROSCOPY (AFM); CONTINUUM MODELING; ESCAPE BIFURCATION; HAMILTON'S PRINCIPLE; IMPROVED STABILITY; MELNIKOV-HOLMES STABILITY; MODE OF OPERATIONS; MOON-CHIRIKOV OVERLAP; NON-LINEAR DYNAMICS; NONLINEAR EQUATIONS OF MOTION; NONLINEAR MICROBEAM; PARAMETRIC EXCITATIONS; SCAN CONTROL; SCAN DYNAMICS; STABILITY AND CONTROL; ULTRA-HIGH VACUUM;

PROCESS CONTROL;

EID: 50249185231     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9335-5     Document Type: Article

References (41)

1. Binning, G., Quate, C.F., Gerber, C.: Atomic force microscope. Phys. Rev. Lett. 56(9), 930-936 (1986)
2. Giessible, F.J.: Advances in Atomic force microscopy. Rev. Mod. Phys. 75(3), 949-983 (2003)
3. Sarid, D.: Scanning Force Microscopy: With Applications to Electric, Magnetic, and Atomic Forces. Oxford University Press, New York (1991)
4. Paulo, A.S., Garcia, R.: Unifying theory of tapping-mode atomic-force microscopy. Phys. Rev. B 66, 041406(R) (2002)
5. Durig, U., Zuger, O., Stalder, A.: Interaction force detection in scanning probe microscopy: methods and applications. J. Appl. Phys. 72(5), 1778-1798 (1992)
6. Mertz, J., Marti, O., Mlynek, J.: Regulation of a microcantilever response by force feedback. Appl. Phys. Lett. 62(19), 2344-2346 (1993)
7. Ashhab, M., Salapaka, M.V., Dahleh, M., Mezic, I.: Dynamical analysis and control of microcantilevers. Automatica 35, 1663-1670 (1999)
8. Perez, H., Zou, Q., Devasia, S.: Design and control of optimal scan trajectories: Scanning tunneling microscope example. ASME J. Dyn. Syst. Meas. Control 126, 187-197 (2004)
9. Minne, S.C., Manalis, S.R., Quate, C.F.: Bringing Scanning Probe Microscopy Up to Speed. Kluwer, Boston (1999)
10. Schitter, G., Fantner, G.E., Kindt, J.H., Thurner, P.J., Hansma, P.K.: On recent developments for high-speed atomic force microscopy. In: Proceedings of the 2005 IEEE/ASME, International Conference on Advanced Intelligent Mechatronics, Monterey, CA, July 2005
11. Manalis, S.R., Minne, S.C., Quate, C.F.: Atomic force microscopy for high speed imaging using cantilevers with an integrated actuator and sensor. Appl. Phys. Lett. 68(6), 871-874 (1996)
12. Thompson, J.M.T.: Chaotic phenomena triggering the escape from a potential well. Proc. R. Soc. Lond. A 421, 195-225 (1989)
13. Thompson, J.M.T.: Nonlinear Dynamics and Chaos. Wiley, New York (2002)
14. Erlandsson, R., Olsson, L.: Force interaction in low-amplitude ac-mode atomic force microscopy: cantilever simulation and comparison with data from Si(111)7×7. Appl. Phys. A 66, S879-S883 (1998)
15. Couturier, G., Nony, L., Boisgard, R., Aimé, J.P.: Stability of an oscillating tip in noncontact atomic force microscopy: theoretical and numerical investigations. J. Appl. Phys. 91(4), 2537-2543 (2002)
16. Stark, R.W., Heckl, W.M.: Fourier transformed atomic force microscopy: tapping mode atomic force microscopy beyond the Hookian approximation. Surf. Sci. 457, 219-228 (2000)
17. Rodriguez, T.R., Garcia, R.: Tip motion in amplitude modulation (tapping-mode) atomic-force microscopy: Comparison between continuous and point-mass models. Appl. Phys. Lett. 80(9), 1646-1648 (2002)
18. Turner, J.A., Hirsekorn, S., Rabe, U., Arnold, W.: High-frequency response of atomic-force microscope cantilevers. Appl. Phys. Lett. 82(3), 966-979 (1997)
19. Turner, J.A.: Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions. J. Sound Vib. 275(1), 177-191 (2004)
20. Wolf, K., Gottlieb, O.: Nonlinear dynamics of a noncontacting atomic force microscope cantilever actuated by a piezoelectric layer. J. Appl. Phys. 91(7), 4701-4709 (2002)
21. Heim, L.O., Kappl, M., Butt, H.J.: Tilt of atomic force microscope cantilevers: Effect on spring constant and adhesion measurements. Langmuir 20, 2760-2764 (2004)
22. Cannara, R.J., Eglina, M., Carpick, R.W.: Lateral force calibration in atomic force microscopy: A new lateral force calibration method and general guidelines for optimization. Rev. Sci. Instrum. 77, 053701 (2006)
23. Stiernstedt, J., Rutland, M.W., Attard, P.: A novel technique for the in situ calibration and measurement of friction with the atomic force microscope. Rev. Sci. Instrum. 76, 083710 (2005)
24. Crespo da Silva, M.C., Glynn, C.C.: Nonlinear flexural-flexural-torsional dynamics of inextensional beams. I. Equation of motion. II. Forced motions. J. Struct. Mech. 6(4), 437-461 (1978)
25. Israelachvili, J.: Intermolecular and Surface Forces. Academic Press, London (1992)
26. Sarid, D., Ruskell, T.G., Workman, R.K., Chen, D.: Driven nonlinear atomic force microscopy cantilevers: from noncontact to tapping modes of operation. J. Vac. Sci. Technol. B 14(2), 864-867 (1996)
27. Nayfeh, A.H., Pai, P.F.: Non-linear non-planar parametric responses of an inextensional beam. Int. J. Non-Linear Mech. 24, 139-158 (1989)
28. Crespo da Silva, M.C.: Equations for nonlinear analysis of 3D motions of beams. Appl. Mech. Rev. 44(11), 51-59 (1991)
29. Cannara, R.J., Brukman, M.J., Carpick, R.W.: Cantilever tilt compensation for variable-load atomic force microscopy. Rev. Sci. Instrum. 76, 053706 (2005)
30. Meirovitch, L.: Fundamentals of Vibrations. McGraw-Hill, Boston (2001)
31. Stupnicka, W.S., Plaut, R.H., Hsieh, J.C.: Period doubling and chaos in unsymmetric structures under parametric excitation. J. Appl. Mech. 56(4), 947-952 (1989)
32. Guckenheimer, J., Holmes, P.J.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York (1983)
33. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics. Wiley, New York (1995)
34. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)
35. Maris, J.P., Piednoir, A., Zambelli, T., Bouju, X., Gauthier, S.: Experimental investigation of resonance curves in dynamic force microscopy. Nanotechnology 14, 1036-1042 (2003)
36. Albrecht, T.R., Grutter, P., Horne, D., Rugar, D.: Frequency modulation detection using high Q cantilevers for enhanced force microscope sensitivity. J. Appl. Phys. 69(2), 668-673 (1991)
37. Gottlieb, O., Champneys, A.R.: Global bifurcations of nonlinear thermoelastic microbeams subject to electrodynamic actuation. In: Rega, G., Vestroni, F. (eds.) Chaotic Dynamics and Control of Systems and Processes in Mechanics, pp. 117-126. Kluwer Academic, Dordrecht (2004)
38. Yagasaki, K.: Chaotic dynamic of a quasi-periodically forced beam. Trans. J. Appl. Mech. 59, 161-167 (1992)
39. Ashhab, M., Salapaka, M.V., Dahleh, M., Mezíc, I.: Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy. Nonlinear Dyn. 20(3), 197-220 (1999)
40. Moon, F.C.: Chaotic and Fractal Dynamics. Wiley, New York (1992)
41. Moon, F.C.: Experiments on chaotic motions of a forced nonlinear oscillator: Strange attractors. J. Appl. Mech. 47, 638-644 (1980)