Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Review of Scientific Instruments

Volumn 83, Issue 10, 2012, Pages

  Sader, John E ^a,b   Sanelli, Julian A ^a   Adamson, Brian D ^a   Monty, Jason P ^a   Wei, Xingzhan ^a,c   Crawford, Simon A ^a   Friend, James R ^d,e   Marusic, Ivan ^a   Mulvaney, Paul ^a,c   Bieske, Evan J ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b California Institute of Technology   (United States)

^c UNIVERSITY OF MELBOURNE   (Australia)

^d MELBOURNE CENTRE FOR NANOFABRICATION   (Australia)

^e RMIT UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY GEOMETRY; ARBITRARY SHAPE; ATOMIC FORCE MICROSCOPE CANTILEVERS; CALIBRATION METHOD; CONVERSION FACTOR; DESIGN AND APPLICATION; HYDRODYNAMIC FUNCTIONS; MICRO-CANTILEVERS; NANOMECHANICAL SYSTEMS; NON-IDEALITIES; QUALITY FACTORS; QUANTITATIVE MEASUREMENT; SMALL ASPECT RATIO; SPRING CONSTANTS; STATIC AND DYNAMIC; TRAPEZOIDAL CROSS SECTIONS; V-SHAPE;

AIR; ATOMIC FORCE MICROSCOPY; CALIBRATION; HYDRODYNAMICS; NATURAL FREQUENCIES; SPRINGS (COMPONENTS);

NANOCANTILEVERS;

ARTICLE; ATOMIC FORCE MICROSCOPY; CALIBRATION; ELASTICITY; EQUIPMENT; HYDRODYNAMICS; MECHANICS; UNCERTAINTY;

CALIBRATION; ELASTICITY; HYDRODYNAMICS; MECHANICAL PROCESSES; MICROSCOPY, ATOMIC FORCE; UNCERTAINTY;

EID: 84868360475     PISSN: 00346748     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4757398     Document Type: Conference Paper

References (58)

1. R. Garcia and R. Perez, Surf. Sci. Rep. 47, 197 (2002). 10.1016/S0167-5729(02)00077-8
2. F. J. Giessibl, Rev. Mod. Phys. 75, 949 (2003). 10.1103/RevModPhys.75.949
3. H.-J. Butt, B. Cappella, and M. Kappl, Surf. Sci. Rep. 59, 1 (2005). 10.1016/j.surfrep.2005.08.003
4. J. E. Sader and L. White, J. Appl. Phys. 74, 1 (1993). 10.1063/1.354137
5. J. M. Neumeister and W. A. Ducker, Rev. Sci. Instrum. 65, 2527 (1994). 10.1063/1.1144646
6. C. A. Clifford and M. P. Seah, Nanotechnology 16, 1666 (2005). 10.1088/0957-4484/16/9/044
7. J. Lubbe, L. Doering, and M. Reichling, Meas. Sci. Technol. 23, 045401 (2012). 10.1088/0957-0233/23/4/045401
8. H.-J. Butt, P. Siedle, K. Seifert, K. Fendler, T. Seeger, E. Bamberg, A. L. Weisenhorn, K. Goldie, and A. Engel, J. Microsc. 169, 75 (1993). 10.1111/j.1365-2818.1993.tb03280.x
9. T. J. Senden and W. A. Ducker, Langmuir 10, 1003 (1994). 10.1021/la00016a600
10. C. T. Gibson, G. S. Watson, and S. Myhra, Nanotechnology 7, 259 (1996). 10.1088/0957-4484/7/3/014
11. M. Tortonese and M. Kirk, Proc. SPIE 3009, 53 (1997). 10.1117/12.271229
12. A. Torii, M. Sasaki, K. Hane, and S. Okuma, Meas. Sci. Technol. 7, 179 (1996). 10.1088/0957-0233/7/2/010
13. J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma, Rev. Sci. Instrum. 64, 403 (1993). 10.1063/1.1144209
14. J. L. Hutter and J. Bechhoefer, Rev. Sci. Instrum. 64, 1868 (1993). 10.1063/1.1143970
15. J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999). 10.1063/1.1150021
16. H.-J. Butt and M. Jaschke, Nanotechnology 6, 1 (1995). 10.1088/0957-4484/6/1/001
17. R. Levy and M. Maaloum, Nanotechnology 13, 33 (2002). 10.1088/0957-4484/13/1/307
18. A. D. Slattery, J. S. Quinton, and C. Gibson, Nanotechnology 23, 285704 (2012). 10.1088/0957-4484/23/28/285704
19. J. E. Sader, in Encyclopedia of Surface and Colloid Science, edited by, A. Hubbard, (Dekker, New York, 2002), pp. 846-856.
20. S. M. Cook, T. E. Schäffer, K. M. Lang, K. M. Chynoweth, M. Wigton, R. W. Simmonds, and K. M. Lang, Nanotechnology 17, 2135 (2006). 10.1088/0957-4484/17/9/010
21. M. L. B. Palacio and B. Bhushan, Crit. Rev. Solid State Mater. Sci. 35, 73 (2010). 10.1080/10408430903546691
22. J. te Riet, A. J. Katan, C. Rankl, S. W. Stahl, A. M. van Buul, I. Y. Phang, A. Gomez-Casado, P. Schön, J. W. Gerritsen, A. Cambi, A. E. Rowan, G. J. Vancso, P. Jonkheijm, J. Huskens, T. H. Oosterkamp, H. Gaub, P. Hinterdorfer, C. G. Figdor, and S. Speller, Ultramicroscopy 111, 1659 (2011). 10.1016/j.ultramic.2011.09.012
23. J. E. Sader, J. Appl. Phys. 84, 64 (1998). 10.1063/1.368002
24. C. P. Green, H. Lioe, J. P. Cleveland, R. Proksch, P. Mulvaney, and J. E. Sader, Rev. Sci. Instrum. 75, 1988 (2004). 10.1063/1.1753100
25. J. E. Sader, J. Pacifico, C. P. Green, and P. Mulvaney, J. Appl. Phys. 97, 124903 (2005). 10.1063/1.1935133
26. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics (Addison-Wesley, San Francisco, 2002).
27. S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1969).
28. Λ(Re) is strictly the imaginary component of the hydrodynamic function, as defined in Ref.. It is referred to as the hydrodynamic function in this article for simplicity.
29. P. W. Bridgman, Dimensional Analysis (Yale University Press, New Haven, 1931).
30. D. R. Brumley, M. Willcox, and J. E. Sader, Phys. Fluids 22, 052001 (2010). 10.1063/1.3397926
31. R. Cox, F. Josse, S. M. Neinrich, O. Brand, and I. Dufour, J. Appl. Phys. 111, 014907 (2012). 10.1063/1.3674278
32. H. Frentrup and M. S. Allen, Nanotechnology 22, 295703 (2011). 10.1088/0957-4484/22/29/295703
33. T. Pettersson, N. Nordgren, M. W. Rutland, and A. Feiler, Rev. Sci. Instrum. 78, 093702 (2007). 10.1063/1.2779215
34. J. W. M. Chon, P. Mulvaney, and J. E. Sader, J. Appl. Phys. 87, 3978 (2000). 10.1063/1.372455
35. R. Proksch, T. E. Schaeffer, J. P. Cleveland, R. C. Callahan, and M. B. Viani, Nanotechnology 15, 1344 (2004). 10.1088/0957-4484/15/9/039
36. J. Stiernstedt, M. W. Rutland, and P. Attard, Rev. Sci. Instrum. 76, 083710 (2005). 10.1063/1.2006407
37. K.-H. Chung, S. Scholz, G. A. Shaw, J. A. Kramar, and J. R. Pratt, Rev. Sci. Instrum. 79, 095105 (2008). 10.1063/1.2987695
38. COMSOL Multiphysics, Gottingen, Germany.
39. J. E. Sader, I. Larson, P. Mulvaney, and L. R. White, Rev. Sci. Instrum. 66, 3789 (1995). 10.1063/1.1145439
40. J. E. Sader, Rev. Sci. Instrum. 66, 4583 (1995). 10.1063/1.1145292
41. R. J. Roark and W. C. Young, Formulas for Stress and Strain, 5th ed. (McGraw-Hill, New York, 1975).
42. T. E. Schaeffer, J. P. Cleveland, F. Ohnesorge, D. A. Walters, and P. K. Hansma, J. Appl. Phys. 80, 3622 (1996). 10.1063/1.363308
43. R. Proksch and S. V. Kalinin, Nanotechnology 21, 455705 (2010). 10.1088/0957-4484/21/45/455705
44. C. P. Green and J. E. Sader, Phys. Fluids 17, 073102 (2005). 10.1063/1.1995467
45. R. J. Clarke, O. E. Jensen, and J. Billingham, Phys. Rev. E 78, 056310 (2008). 10.1103/PhysRevE.78.056310
46. M. J. Higgins, R. Proksch, J. E. Sader, M. Polcik, S. Mc Endoo, J. P. Cleveland, and S. P. Jarvis, Rev. Sci. Instrum. 77, 013701 (2006). 10.1063/1.2162455
47. B. Ohler, Rev. Sci. Instrum. 78, 063701 (2007). 10.1063/1.2743272
48. J. R. Lozano, D. Kiracofe, J. Melcher, R. Garcia, and A. Raman, Nanotechnology 21, 465502 (2010). 10.1088/0957-4484/21/46/465502
49. J. Park, S. Nishida, P. Lambert, H. Kawakatsu, and H. Fujita, Lab Chip 11, 4187 (2011). 10.1039/c1lc20608g
50. Doppler shift of the laser reflected from the cantilever causes beating in the interferometer signal, the frequency of which is directly proportional to the cantilever velocity; no additional calibration is necessary.
51. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 2nd ed. (Pergamon, Oxford, NY, 1970).
52. Power spectral density data were derived from the time series measurements using MATLAB code, Mathworks, Natick, MA.
53. J. E. Sader, B. D. Hughes, J. A. Sanelli, and E. J. Bieske, Rev. Sci. Instrum. 83, 055106 (2012). 10.1063/1.4709496
54. SI reference data for viscosity and density were obtained from the National Institute of Standards and Technology; see http://webbook.nist.gov/ chemistry/name-ser.html
55. J. E. Sader, J. Sanelli, B. D. Hughes, J. P. Monty, and E. J. Bieske, Rev. Sci. Instrum. 82, 095104 (2011). 10.1063/1.3632122
56. W. E. Newell, Science 161, 1320 (1968). 10.1126/science.161.3848.1320
57. F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, J. Vac. Sci. Technol. B 10, 19 (1992). 10.1116/1.586300
58. R. Sandberg, A. Boisen, and W. Svendsen, Rev. Sci. Instrum. 76, 125101 (2005). 10.1063/1.2140284