DOI QR코드

DOI QR Code

Effect of Contact Stiffness on Lateral Force Calibration of Atomic Force Microscopy Cantilever

원자 현미경 탐침의 수평방향 힘 교정에 미치는 접촉 강성의 영향

  • Tran, Da Khoa (School of Mechanical Engineering, University of Ulsan) ;
  • Jeon, Ki-Joon (School of Electrical Engineering University of Ulsan) ;
  • Chung, Koo-Hyun (School of Mechanical Engineering, University of Ulsan)
  • Received : 2012.07.16
  • Accepted : 2012.09.03
  • Published : 2012.12.31

Abstract

Atomic force microscopy (AFM) has been used for imaging surfaces and measuring surface forces at the nano-scale. Force calibration is important for the quantitative measurement of forces at the nano-scale using AFM. Normal force calibration is relatively straightforward, whereas the lateral force calibration is more complicated since the lateral stiffness of the cantilever is often comparable to the contact stiffness. In this work, the lateral force calibrations of the rectangular cantilever were performed using torsional Sader's method, thermal noise method, and wedge calibration method. The lateral optical lever sensitivity for the thermal noise method was determined from the friction loop under various normal forces as well. Experimental results showed that the discrepancies among the results of the different methods were as large as 30% due to the effect of the contact stiffness on the lateral force calibration of the cantilever used in this work. After correction for the effect of contact stiffness, all the calibration results agreed with each other, within experimental uncertainties.

Acknowledgement

Supported by : 울산대학교

References

  1. Binnig, G., Quate, C. F., and Gerber, C., "Atomic Force Microscope," Phys Rev Lett, Vol. 56, pp. 930-933, 1986. https://doi.org/10.1103/PhysRevLett.56.930
  2. Chung, K. H., Bhadriraju, K., Spurlin, T. A., Cook, R. F., and Plant, A. L., "Nanomechanical Properties of Thin Films of Type I Collagen Fibrils," Langmuir, Vol. 26, pp. 3629-3636, 2010. https://doi.org/10.1021/la903073v
  3. Mahaffy, R. E., Shih, C. K., MacKintosh, F. C., and KAos, J., "Scanning Probe-Based Frequency-Dependent Microrheology of Polymer Gels and Biological Cells," Phys Rev Lett, Vol. 85, pp. 880-883, 2000. https://doi.org/10.1103/PhysRevLett.85.880
  4. Stan, G., Krylyuk, S., Davydov, A. V., Levin, I., and Cook, R. F., "Ultimate Bending Strength of Si Nanowires," Nano Lett., Vol. 12, pp. 2599-2604, 2012. https://doi.org/10.1021/nl300957a
  5. Giesbers, A. J. M., Zeitler, U., Neubeck, S., Freitag, F., Novoselov, K. S., and Maan, J. C., "Nanolithography and Manipulation of Graphene using an Atomic Force Microscope," Solid State Commun, Vol. 147, pp. 366-369, 2008. https://doi.org/10.1016/j.ssc.2008.06.027
  6. Hutter, J. L. and Bechhoefer, J., "Calibration of Atomic-Force Microscope Tips," Rev. Sci. Instrum., Vol. 64, pp. 1868-1873, 1993. https://doi.org/10.1063/1.1143970
  7. Sader, J. E., Chon, J. W. M., and Mulvaney, P., "Calibration of Rectangular Atomic Force Microscope Cantilevers," Rev. Sci. Instrum., Vol. 70, pp. 3967- 3969, 1999. https://doi.org/10.1063/1.1150021
  8. Higgins, M. J., Proksch, R., Sader, J. E., Polcik, M., Endoo, S. M., Cleveland, J. P., and Jarvis, S. P., "Noninvasive Determination of Optical Lever Sensitivity in Atomic Force Microscopy," Rev. Sci. Instrum., Vol. 77, pp. 013701, 2006. https://doi.org/10.1063/1.2162455
  9. Wagner, K., Cheng, P., and Vezenov, D., "Noncontact Method for Calibration of Lateral Forces in Scanning Force Microscopy," Langmuir, Vol. 27, pp. 4635-4644, 2011. https://doi.org/10.1021/la1046172
  10. Torii, A., Sasaki, M., Hane, K., and Okuma, S., "A Method for Determining the Spring Constant of Cantilevers for Atomic Force Microscopy," Meas Sci Technol, Vol. 7, pp. 179-184, 1996. https://doi.org/10.1088/0957-0233/7/2/010
  11. Gates, R. S. and Reitsma, M. G., "Precise Atomic Force Microscope Cantilever Spring Constant Calibration using a Reference Cantilever Array," Rev. Sci. Instrum., Vol. 78, pp. 086101, 2007. https://doi.org/10.1063/1.2764372
  12. Cleveland, J. P., Manne, S., Bocek, D., and Hansma, P. K., "A Nondestructive Method for Determining the Spring Constant of Cantilevers for Scanning Force Microscopy," Rev. Sci. Instrum., Vol. 64, pp. 403-405, 1993. https://doi.org/10.1063/1.1144209
  13. Chung, K. H., Shaw, G. A., and Pratt, J. R., "Accurate Noncontact Calibration of Colloidal Probe Sensitivities in Atomic Force Microscopy," Rev. Sci. Instrum., Vol. 80, pp. 065107, 2009. https://doi.org/10.1063/1.3152335
  14. Cain, R. G., Biggs, S., and Page, N. W., "Force Calibration in Lateral Force Microscopy," J. Colloid Interface Sci., Vol. 227, pp. 55-65, 2000. https://doi.org/10.1006/jcis.2000.6840
  15. Sader, J. E. and Green, C. P., "In-Plane Deformation of Cantilever Plates with Applications to Lateral Force Microscopy," Rev. Sci. Instrum., Vol. 75, pp. 878-883, 2004. https://doi.org/10.1063/1.1667252
  16. Cannara, R. J., Eglin, M., and Carpick, R. W., "Lateral Force Calibration in Atomic Force Microscopy: A New Lateral Force Calibration Method and General Guidelines for Optimization," Rev. Sci. Instrum., Vol. 77, pp. 053701, 2006. https://doi.org/10.1063/1.2198768
  17. Ogletree, D. F., Carpick, R. W., and Salmeron, M., "Calibration of Frictional Forces in Atomic Force Microscopy," Rev. Sci. Instrum., Vol. 67, pp. 3298- 3306, 1996. https://doi.org/10.1063/1.1147411
  18. Varenberg, M., Etsion, I., and Halperin, G., "An Improved Wedge Calibration Method for Lateral Force in Atomic Force Microscopy," Rev. Sci. Instrum., Vol. 74, pp. 3362-3367, 2003. https://doi.org/10.1063/1.1584082
  19. Li, Q., Kim, K., and Rydberg, A., "Lateral Force Calibration of an Atomic Force Microscope with a Diamagnetic Levitation Spring System," Rev. Sci. Instrum., Vol. 77, pp. 065105, 2006. https://doi.org/10.1063/1.2209953
  20. Chung, K. H. and Reitsma, M. G., "Note: Lateral Force Microscope Calibration using Multiple Location Pivot Loading of Rectangular Cantilevers," Rev. Sci. Instrum., Vol. 81, pp. 026104, 2010. https://doi.org/10.1063/1.3276709
  21. Wang, F. and Zhao, X., "Effect of Contact Stiffness on Wedge Calibration of Lateral Force in Atomic Force Microscopy," Rev. Sci. Instrum., Vol. 78, pp. 043701, 2007. https://doi.org/10.1063/1.2720723
  22. Green, C. P., Lioe, H., Cleveland, J. P., Proksch, R., Mulvaney, P., and Sader, J. E., "Normal and Torsional Spring Constants of Atomic Force Microscope Cantilevers," Rev. Sci. Instrum., Vol. 75, pp. 1988-1996, 2004. https://doi.org/10.1063/1.1753100
  23. Sader, J. E., "Frequency Response of Cantilever Beams Immersed in Viscous Fluids with Applications to the Atomic Force Microscope," J. Appl. Phys., Vol. 84, pp. 64-76, 1998. https://doi.org/10.1063/1.368002
  24. Carpick, R. W., Ogletree, D. F., and Salmeron, M., "Lateral Stiffness: A New Nanomechanical Measurement for the Determination of Shear Strengths with Friction Force Microscopy," Appl. Phys. Lett., Vol. 70, pp. 1548-1550, 1997. https://doi.org/10.1063/1.118639