Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy

Abstract

Efforts to reliably measure AFM lateral forces have been impeded by the difficulties in obtaining appropriate calibration standards, applying those force standards to the apex of the tip, and quantifying calibration uncertainty. Here we propose a new method, Traceable Lateral Force Calibration (TLFC), which combines the reliability of direct methods with the convenience of indirect/semi-direct methods. Like other direct methods, ours comprise three essential steps: (1) fabrication of a spring (the Traceable Reference Lever or TRL); (2) calibration of the TRL spring constant; (3) conversion of measurable TRL deflections into absolute lateral force measurements based on its pre-calibrated spring constant (TLFC method). The TRL device, a simple two-axis cantilever, is easy to design, fabricate, and directly pre-calibrate with a standard laboratory microbalance. Following pre-calibration, the TRL device becomes a convenient absolute standard for AFM lateral force measurements. This paper describes the complete method and demonstrates its primary merits, which include (1) traceability to measurement standards; (2) ease of use by outside user groups; (3) absolute measurement errors < 10% for moderately stiff cantilevers (> 1 N/m normal stiffness); (4) robustness over a wide range of common loads, instruments, probes, and environments. While the method and proof-of-concept devices described in this paper were designed primarily for moderate to high load cantilevers (> 1 N/m), we discuss how a next generation of compliant TRL devices can be used with the TLFC method to reliably calibrate arbitrary AFM cantilevers (< < 1 N/m) and forces.

Graphical Abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3 
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. 1.

    Primary metrological requirements include traceability to absolute standards and full accounting of measurement error sources.

  2. 2.

    Note that Eqs. 3 and 4 are only used for theoretical guidance. Experimental uncertainties are obtained by directly propagating the errors in each measurement into each measurand using Eqs. 1 and 2 per standard practice [8].

References

  1. 1.

    Munz, M.: Force calibration in lateral force microscopy: a review of the experimental methods. J. Phys. D 43, 063001 (2010). https://doi.org/10.1088/0022-3727/43/6/063001

    CAS  Article  Google Scholar 

  2. 2.

    Attard, P., Stiernstedt, J., Rutland, M.W.: Measurement of friction coefficients with the atomic force microscope. J. Phys. Conf. Ser. 61, 51–55 (2007). https://doi.org/10.1088/1742-6596/61/1/011

    Article  Google Scholar 

  3. 3.

    Liu, W., Bonin, K., Guthold, M.: Easy and direct method for calibrating atomic force microscopy lateral force measurements. Rev. Sci. Instrum. (2007). https://doi.org/10.1063/1.2745733

    Article  Google Scholar 

  4. 4.

    Varenberg, M., Etsion, I., Halperin, G.: An improved wedge calibration method for lateral force in atomic force microscopy. Rev. Sci. Instrum. 74, 3362–3367 (2003). https://doi.org/10.1063/1.1584082

    CAS  Article  Google Scholar 

  5. 5.

    Cannara, R.J., Eglin, 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. (2006). https://doi.org/10.1063/1.2198768

    Article  Google Scholar 

  6. 6.

    Wang, H.: Lateral force calibration in atomic force microscopy: minireview. Sci. Adv. Mater. 9, 56–64 (2017). https://doi.org/10.1166/sam.2017.2738

    CAS  Article  Google Scholar 

  7. 7.

    Green, C.P., Lioe, H., Cleveland, J.P., Proksch, R., Mulvaney, P., Sader, J.E.: Normal and torsional spring constants of atomic force microscope cantilevers. Rev. Sci. Instrum. 75, 1988–1996 (2004). https://doi.org/10.1063/1.1753100

    CAS  Article  Google Scholar 

  8. 8.

    Guide to the Expression of Uncertainty in Measurement, (1993)

  9. 9.

    Ogletree, D.F., Carpick, R.W., Salmeron, M.: Calibration of frictional forces in atomic force microscopy. Rev. Sci. Instrum. 67, 3298 (1996). https://doi.org/10.1063/1.1147411

    CAS  Article  Google Scholar 

  10. 10.

    Khare, H.S., Burris, D.L.: The extended wedge method: atomic force microscope friction calibration for improved tolerance to instrument misalignments, tip offset, and blunt probes. Rev. Sci. Instrum. (2013). https://doi.org/10.1063/1.4804163

    Article  Google Scholar 

  11. 11.

    Ortuso, R.D., Sugihara, K.: Detailed study on the failure of the wedge calibration method at nanonewton setpoints for friction force microscopy. J. Phys. Chem. C 122, 11464–11474 (2018). https://doi.org/10.1021/acs.jpcc.8b03583

    CAS  Article  Google Scholar 

  12. 12.

    Asay, D.B., Kim, S.H.: Direct force balance method for atomic force microscopy lateral force calibration. Rev. Sci. Instrum. (2006). https://doi.org/10.1063/1.2190210

    Article  Google Scholar 

  13. 13.

    Li, Q., Kim, K.S., Rydberg, A.: Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system. Rev. Sci. Instrum. (2006). https://doi.org/10.1063/1.2209953

    Article  Google Scholar 

  14. 14.

    Barkley, S.S., Deng, Z., Gates, R.S., Reitsma, M.G., Cannara, R.J.: Quantitative comparison of two independent lateral force calibration techniques for the atomic force microscope. Rev. Sci. Instrum. (2012). https://doi.org/10.1063/1.3685243

    Article  Google Scholar 

  15. 15.

    Qu, C., Liu, B., Ma, M., Zheng, Q.: Design and optimization of the diamagnetic lateral force calibration method. Rev. Sci. Instrum. (2018). https://doi.org/10.1063/1.5041854

    Article  Google Scholar 

  16. 16.

    Ando, Y., Shiraishi, N.: Development of a microlateral force sensor and its evaluation using lateral force microscopy. Rev. Sci. Instrum. (2007). https://doi.org/10.1063/1.2714038

    Article  Google Scholar 

  17. 17.

    Cumpson, P.J., Hedley, J., Clifford, C.A.: Microelectromechanical device for lateral force calibration in the atomic force microscope: lateral electrical nanobalance. J. Vac. Sci. Technol. B 23, 1992–1997 (2005). https://doi.org/10.1116/1.2044809

    CAS  Article  Google Scholar 

  18. 18.

    Garabedian, N.T., Khare, H.S., Carpick, R.W., Burris, D.L.: AFM at the macroscale : methods to fabricate and calibrate probes for millinewton force measurements. Tribol. Lett. 67, 1–10 (2019). https://doi.org/10.1007/s11249-019-1134-2

    Article  Google Scholar 

  19. 19.

    Álvarez-Asencio, R., Thormann, E., Rutland, M.W.: Note: Determination of torsional spring constant of atomic force microscopy cantilevers: combining normal spring constant and classical beam theory. Rev. Sci. Instrum. 84, 1–4 (2013). https://doi.org/10.1063/1.4820345

    CAS  Article  Google Scholar 

  20. 20.

    Carpick, R.W., Ogletree, D.F., Salmeron, M.: Lateral stiffness: a new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl. Phys. Lett. 70, 1548–1550 (1997). https://doi.org/10.1063/1.118639

    CAS  Article  Google Scholar 

  21. 21.

    Borovsky, B.P., Garabedian, N.T., McAndrews, G.R., Wieser, R.J., Burris, D.L.: Integrated QCM-microtribometry: friction of single-crystal MoS2 and gold from μm/s to m/s. ACS Appl. Mater. Interfaces. 11, 40961–40969 (2019). https://doi.org/10.1021/acsami.9b15764

    CAS  Article  Google Scholar 

  22. 22.

    Stoyanov, P., Chromik, R.R.: Scaling effects on materials tribology : from macro to micro scale. Materials (2017). https://doi.org/10.3390/ma10050550

    Article  Google Scholar 

  23. 23.

    Miller, B.P., Theodore, N.D., Brukman, M.J., Wahl, K.J., Krim, J.: A nano-to macroscale tribological study of PFTS and TCP lubricants for Si MEMS applications. Tribol. Lett. 38, 69–78 (2010). https://doi.org/10.1007/s11249-009-9573-9

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge financial support from the NSF 1434435 for financial support of this work.

Author information

Affiliations

Authors

Corresponding author

Correspondence to David L. Burris.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bhattacharjee, A., Garabedian, N.T., Evans, C.L. et al. Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy. Tribol Lett 68, 111 (2020). https://doi.org/10.1007/s11249-020-01349-y

Download citation

Keywords

  • Lateral force calibration
  • Friction
  • FFM
  • AFM
  • Nanotribology