Dynamic properties of AFM cantilevers and the calibration of their spring constants

Journal of Micromechanics and Microengineering

Volumn 16, Issue 8, 2006, Pages 1720-1733

  Mendels, David A ^a   Lowe, Martin ^a   Cuenat, Alexandre ^a   Cain, Markys G ^a   Vallejo, Elena ^b   Ellis, David ^b   Mendels, François ^c  

^a NATIONAL PHYSICAL LABORATORY   (United Kingdom)

^b IDAC Ltd   (United Kingdom)

^c Cognoscens ^*  (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC FORCE MICROSCOPY; DAMPING; DYNAMIC MECHANICAL ANALYSIS; MATHEMATICAL MODELS; NATURAL FREQUENCIES; RESIDUAL STRESSES;

SCANNING VIBROMETRY; SPRING CONSTANTS; TIMOSHENKO BEAM EQUATION;

CANTILEVER BEAMS;

EID: 33746306996     PISSN: 09601317     EISSN: 13616439     Source Type: Journal    
DOI: 10.1088/0960-1317/16/8/037     Document Type: Article

References (39)

1. Binnig G, Quate C F and Gerber C 1986 Atomic force microscope Phys. Rev. Lett. 56 930-3
2. Burnham N A, Chen X, Hodges C S, Matei G A, Thoreson E J, Roberts C J, Davies M C and Tendler S J B 2003 Comparison of calibration methods for atomic-force microscopy cantilevers Nanotechnology 14 1-6
3. Clifford C A and Seah M P 2005 The determination of atomic force microscope cantilever spring constants via dimensional methods for nanomechanical analysis Nanotechnology 16 1666-80
4. Meyer E, Lüthi R, Howald L, Bammerlin M, Guggisberg M and Güntherodt H-J 1997 Instrumental aspects and contrast mechanisms of friction force microscopy Micro/Nanotribology and its Applications (NATO ASI Series E) vol 330 ed B Bhushan pp 193-215
5. Toikka G, Hayes R A and Ralston J 1997 The application of lateral force microscopy to particle removal in aqueous polymer solutions J. Adhes. Sci. Technol. 11 1479-592
6. Drobek T, Stark R W, Gräber M and Heckl W M 1999 Overtone atomic force microscopy studies of decagonal quasicrystal surfaces New J. Phys. 1 15.1-11
7. Reinstädtler M, Kasai T, Rabe U, Bhushan B and Arnold W 2005 Imaging and measurement of elasticity and friction using the TR mode J. Phys. D: Appl. Phys. 38 R269-82
8. Sader J E, Larson I, Mulvaney P and White L R 1995 Method for the calibration of atomic force microscope cantilevers Rev. Sci. Instrum. 66 3789-98
9. Cleveland J P, Manne S, Bocek D and Hansma P K 1993 A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy Rev. Sci. Instrum. 64 403-5
10. Tortonese M and Kirk M 1997 Characterization of application-specific probes for SPMs Proc. SPIE, 'Micromachining and Imaging' vol 3009 ed T A Michalske and M A Wendman pp 53-60
11. Stark R W, Drobek T and Heckl W M 2001 Thermomechanical noise of a free V-shaped cantilever for atomic-force microscopy Ultramicroscopy 86 207-15
12. Sader J E, Chon J W M and Mulvaney P 1999 Calibration of rectangular atomic force microscope cantilevers Rev. Sci. Instrum. 70 3967-9
13. Butt H-J and Jaschke M 1995 Calculation of thermal noise in atomic force microscopy Nanotechnology 6 1-7
14. Timoshenko S P and Goodier J N 1970 Theory of Elasticity (New York: McGraw-Hill)
15. Yu W and Hodges D H 2004 Elasticity solutions versus asymptotic sectional analysis of homogeneous, isotropic, prismatic beams J. Appl. Mech. 71 15-23
16. Timoshenko S P 1921 On the correction for shear of the differential equation for transverse vibration of prismatic bars Phil. Mag. 41 744-6
17. Timoshenko S P 1922 On the transverse vibrations of bars of uniform cross-section Phil. Mag. 43 125-31
18. Kaneko T 1975 On Timoshenko's correction of shear in vibrating beams J. Phys. D: Appl. Phys. 8 1927-36
19. Mendels D-A, Vallejo E and Ellis D 2006 A comparative parametric study of the sensitivity of AFM probes to their environment and boundaries (in preparation)
20. Shen K, Hurley D C and Turner J A 2004 Dynamic behaviour of dagger-shaped cantilevers for atomic force microscopy Nanotechnology 15 1582-9
21. Jensen B D, de Boer M P, Masters N D, Bitsie F and LaVan D A 2001 Interferometry of actuated microcantilevers to determine material properties and test structure nonidealities in MEMS J. MEMS 10 336-46
22. Rajakumar C and Rogers C R 1992 The Lanczos algorithm applied to unsymmetric generalized eigenvalue problem Int. J. Numer. Methods Eng. 32 1009-26
23. Mendels D-A, Leterrier Y and Mnson J-A E 2002 The influence of internal stresses on the microbond test: 2. Experimental interpretation including the effect of relaxation J. Compos. Mater. 36 1655-74
24. Zhang Y, Ren Q and Zhao Y-P 2004 Modelling analysis of surface stress on a rectangular cantilever beam J. Phys. D: Appl. Phys. 37 2140-5
25. Petersen K E and Guarnieri C R 1979 Young's modulus measurements of thin films using micromechanics J. Appl. Phys. 50 6761-6
26. Kiesewetter L, Zhang J-M, Houdeau D and Steckenborn A 1992 Determination of Young's moduli of micromechanical thin films using the resonance method Sensors Actuators A 35 153-9
27. Orsulak C, Coakley T and Zecchine M 2005 Characterizing AFM cantilevers with dynamic MEMS measurement Veeco Application Note 536 (Tucson, AZ: Veeco Instruments Inc.)
28. Ozdoganlar O B, Hansche B D and Carne T G 2003 Experimental modal analysis for microsystems Proc. 21st International Modal Analysis Conf. (IMAC) (Kissimmee, FL, USA, 3-6 February 2003)
29. Epp D S, Ozdoganlar O B, Chaplya P M, Hansche B D and Carne T G 2004 A base excitation test facility for dynamic testing of microsystems Proc. 21st International Modal Analysis Conf. (IMAC) (Dearborn, Detroit, USA, 26-29 January 2004)
30. Sonka M, Hlavac V and Boyle R 1998 Image Processing: Analysis and Machine Vision 2nd edn (Pacific Grove, CA: Thomson Learning and Brooks/Cole Publishing)
31. Soille P 1999 Morphological Image Analysis (Berlin: Springer)
32. George A 1999 Elastic constants and moduli of diamond cubic Si doping dependence of elastic constants Properties of Crystalline Silicon ed R Hull (NJ: IEEE) p 102
33. Mendels D-A 2006 Adhesion of multi-layered coatings by the nano-scratch test Wear submitted
34. Mendels D-A, Evanno N M P and Cuenat A 2005 Determination of the elastic properties of multi-layered foils by the four-point micro-bending test Phil. Mag. 85 1765-82
35. Dareing D W, Thundat T, Jeon S and Nicholson M 2005 Modal analysis of microcantilever sensors with environmental damping J. Appl. Phys. 97 084902
36. Kanazawa K K 2005 Some basics for operating and analyzing data using the thickness shear mode resonator Analyst 130 1459-64
37. McFarland A W, Poggi M A, Doyle M J, Bottomley L A and Colton J S 2005 Influence of surface stress on the resonance behavior of microcantilevers Appl. Phys. Lett. 87 053505
38. Timoshenko S P 1936 Theory of Elastic Instability (Engineering Societies Monographs) 1st edn (New York: McGraw-Hill)
39. Korn G A and Korn T M 1968 Mathematical Handbook for Scientists and Engineers: Legendre's Normal Elliptic Integrals (New York: McGraw-Hill) pp 833-40