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Direct Stress-Strain Measurements from Bulged Membranes Using Topography Image Correlation

Abstract

This paper discusses an experimental method to characterize thin films as they are encountered in micro-electronic devices. The method enables the measurement of the stress and strain of pressure deflected bulged membranes without using a priori defined bulge equations. An enrichment to the Global Digital Image Correlation method is detailed to capture the membrane strain and curvature while robustly dealing with acquisition noise. The accuracy of the method is analyzed and compared to the standard bulge test method. The method is applied to a proof of principle experiment to investigate its applicability and accuracy. Additionally, it is shown for two experimental cases that the method provides accurate results, although the bulge equations do not hold.

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References

  1. 1.

    Nix W (1989) Mechanical properties of thin films. Metall Trans A 20A:2217–2245

    Article  Google Scholar 

  2. 2.

    Vinci R, Vlassak J (1996) Mechanical behavior of thin films. Annu Rev Mater Sci 26:431–462

    Article  Google Scholar 

  3. 3.

    Arzt E (1998) Size effects in materials due to microstructural and dimensional constraints: a comparative review. Acta Mater 46:5611–5626

    Article  Google Scholar 

  4. 4.

    Gruber P, Böhm J, Onuseit F, Wanner A, Spolenak R, Arzt E (2008) Size effects on yield strength and strain hardening for ultra-thin cu films with and without passivation: a study by synchrotron and bulge test techniques. Acta Mater 56:2318–2335

    Article  Google Scholar 

  5. 5.

    Beams J (1959) Mechanical properties of thin films of gold and silver. Wiley, New York

    Google Scholar 

  6. 6.

    Tabata O, Kawahata K, Sugiyama S, Igarashi I (1989) Mechanical property measurements of thin films using load-deflection of composite rectangular membranes. Sensors Actuators 20:135–141

    Article  Google Scholar 

  7. 7.

    Timoshenko S, Woinowsky-Krieger S (1987) Theory of plates and shells. McGraw-Hill, New York

    Google Scholar 

  8. 8.

    Vlassak J, Nix W (1992) A new bulge test technique for the determination of young’s modulus and poisson’s ratio of thin films. J Mater Res 7:3242–3249

    Article  Google Scholar 

  9. 9.

    Xiang Y, Chen X, Vlassak J (2005) Plane-strain bulge test for thin films. J Mater Res 20:2360–2370

    Article  Google Scholar 

  10. 10.

    Neggers J, Hoefnagels J, Geers M (2012) On the validity regime of the bulge equations. J Mater Res 27:1245–1250

    Article  Google Scholar 

  11. 11.

    Madou MJ (2002) Fundamentals of Microfabrication. CRC Press LLC, Boca Raton

    Google Scholar 

  12. 12.

    Rogers J, Someya T, Huang Y (2010) Materials and mechanics for stretchable electronics Science. 327:1603–1607

  13. 13.

    Han K, Ciccotti M, Roux S (2010) Measuring nanoscale stress intensity factors with an atomic force microscope. Europhys Lett 89:1–5

    Article  Google Scholar 

  14. 14.

    Chu T, Ranson W, Sutton M (1985) Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech:232–244

  15. 15.

    Bruck H, McNeill S, Sutton M, Peters W (1989) Digital image correlation using newton-raphson method of partial differential correction. Exp Mech:261–267

  16. 16.

    Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties - a review. Strain 42:69–80

    Article  Google Scholar 

  17. 17.

    Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52:1503–1519

    Article  Google Scholar 

  18. 18.

    Schreier H, Braasch J, Sutton M (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39:2915–2921

    Article  Google Scholar 

  19. 19.

    Schreier H, Sutton M (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. Exp Mech 42:303–310

    Article  Google Scholar 

  20. 20.

    Neggers J, Hoefnagels JPM, Hild F, Roux S, Geers MGD (2012) A global digital image correlation enhanced full-field bulge test. Procedia IUTAM 4:73–81

    Article  Google Scholar 

  21. 21.

    Hill R (1950) A theory of the plastic bulging of a metal diaphragm by lateral pressure. Phil Mag 4:1133–1142

    Google Scholar 

  22. 22.

    Hsu F, Schwab C, Rigamonti D, Humphrey J (1994) Identification of response functions from axisymmetric membrane inflation tests: implications for biomechanics. Int J Solids Struct 31:3375–3386

    Article  MATH  Google Scholar 

  23. 23.

    Avril S, Bonnet M, Bretelle A-S, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements,. Exp Mech 48:381–402

    Article  Google Scholar 

  24. 24.

    Maynadier A, Poncelet M, Lavernhe K, Roux S (2011) One-shot measurement of thermal and kinematic fields: infra-red image correlation (iric). Exp Mech 52:241–255

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Dutch Technology Foundation (STW) and the Dutch Organization for Scientific Research (NWO).

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Correspondence to J. Neggers.

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Neggers, J., Hoefnagels, J.P.M., Hild, F. et al. Direct Stress-Strain Measurements from Bulged Membranes Using Topography Image Correlation. Exp Mech 54, 717–727 (2014). https://doi.org/10.1007/s11340-013-9832-4

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Keywords

  • Digital image correlation
  • Surface profilometry
  • Thin film
  • Membrane
  • Full-field measurement
  • Strain
  • Stress