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Plane-strain Bulge Test for Thin Films

Published online by Cambridge University Press:  03 March 2011

Y. Xiang ,
X. Chen  and
J.J. Vlassak
Y. Xiang
Affiliation:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138-2901
X. Chen
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027-6699
J.J. Vlassak*
Affiliation:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138-2901
*
a) Address all correspondence to this author. e-mail: vlassak@esag.deas.harvard.edu
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Abstract

The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.

Keywords

Mechanical propertiesThin film
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 9 , September 2005 , pp. 2360 - 2370
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1Nix, W.D.: Mechanical properties of thin-films. Metall. Trans. A 20, 2217 (1989).CrossRefGoogle Scholar
2Spearing, S.M.: Materials issues in microelectromechanical systems (MEMS). Acta Mater. 48, 179 (2000).CrossRefGoogle Scholar
3Vinci, R.P. and Vlassak, J.J.: Mechanical behavior of thin films. Ann. Rev. Mater. Sci. 26, 431 (1996).CrossRefGoogle Scholar
4Arzt, E.: Size effects in materials due to microstructural and dimensional constraints: A comparative review. Acta Mater. 46, 5611 (1998).CrossRefGoogle Scholar
5Venkatraman, R. and Bravman, J.C.: Separation of film thickness and grain-boundary strengthening effects in Al thin-films on Si. J. Mater. Res. 7, 2040 (1992).CrossRefGoogle Scholar
6Freund, L.B. and Suresh, S.: Thin Film Materials: Stress, Defect Formation, and Surface Evolution (Cambridge University Press, New York, 2003), p. 6.Google Scholar
7Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).CrossRefGoogle Scholar
8Chen, X. and Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, 2974 (2001).CrossRefGoogle Scholar
9Tsui, T.Y., Vlassak, J.J. and Nix, W.D.: Indentation plastic displacement field: Part I. The case of soft films on hard substrates. J. Mater. Res. 14, 2196 (1999).CrossRefGoogle Scholar
10Baker, S.P., Keller-Flaig, R.M. and Shu, J.B.: Bauschinger effect and anomalous thermomechanical deformation induced by oxygen in passivated thin Cu films on substrates. Acta Mater. 51, 3019 (2003).CrossRefGoogle Scholar
11Haque, M.A. and Saif, M.T.A.: Deformation mechanisms in free-standing nanoscale thin films: A quantitative in situ transmission electron microscope study. Proc. Natl. Acad. Sci. USA. 101, 6335 (2004).CrossRefGoogle ScholarPubMed
12Huang, H.B. and Spaepen, F.: Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers. Acta Mater. 48, 3261 (2000).CrossRefGoogle Scholar
13Read, D.T., Cheng, Y.W., Keller, R.R. and McColskey, J.D.: Tensile properties of free-standing aluminum thin films. Scripta Mater. 45, 583 (2001).CrossRefGoogle Scholar
14Espinosa, H.D., Prorok, B.C. and Peng, B.: Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52, 667 (2004).CrossRefGoogle Scholar
15Vlassak, J.J. and Nix, W.D.: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7, 3242 (1992).CrossRefGoogle Scholar
16Beams, J.W. Mechanical properties of thin films of gold and silver, in Structure and Properties of Thin Films, edited by Neugebauer, C.A., Newkirk, J.B., and Vermilyea, D.A. (John Wiley and Sons, New York, 1959), p. 183.Google Scholar
17Tabata, O., Kawahata, K., Sugiyama, S. and Igarashi, I.: Mechanical property measurements of thin-films using load deflection of composite rectangular membranes. Sens. Actuators 20, 135 (1989).CrossRefGoogle Scholar
18Hencky, H.: About the stress state in circular plates with negligible bending stiffness. Z. Math. Phys. 63, 311 1915 , in German.Google Scholar
19Vlassak, J.J. New experimental techniques and analysis methods for the study of mechanical properties of materials in small volumes. Ph.D. Dissertation, Stanford University, Stanford, CA, 1994.Google Scholar
20Levy, S. Large deflection theory for rectangular plates, in Non-linear Problems in Mechanics of Continua, edited by Reissner, E., Prager, W., and Stoker, J.J. (Proc. Symposia. Appl. Math. I, Am. Math. Soc., New York, 1949), p. 197.CrossRefGoogle Scholar
21Lin, P. The in-situ measurement of mechanical properties of multi-layer coatings. Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1990.Google Scholar
22Timoshenko, S. and Woinowsky-Krieger, S.: Theory of Plates and Shells (McGraw-Hill, New York, 1959), p. 580.Google Scholar
23Itozaki, H. Mechanical properties of composition modulated copper-palladium foils. Ph.D. Dissertation, Northwestern University, Evanston, IL, 1982.Google Scholar
24Small, M.K. and Nix, W.D.: Analysis of the accuracy of the bulge test in determining the mechanical properties of thin-films. J. Mater. Res. 7, 1553 (1992).CrossRefGoogle Scholar
25Small, M.K., Vlassak, J.J. and Nix, W.D. Re-examining the bulge test: Methods for improving accuracy and reliability, in Thin Films: Stresses and Mechanical Properties III, edited by Nix, W.D., Bravman, J.C., Arzt, E., and Freund, L.B. (Mater. Res. Soc. Symp. Proc. 239, Pittsburgh, PA, 1992), p. 257.Google Scholar
26Xiang, Y., Chen, X. and Vlassak, J.J. The mechanical properties of electroplated Cu thin films measured by means of the bulge test technique, in Thin Films: Stresses and Mechanical Properties IX, edited by Ozkan, C.S., Freund, L.B., Cammarata, R.C., and Gao, H. (Mater. Res. Soc. Symp. Proc. 695, Warrendale, PA, 2002), p. 189.Google Scholar
27Maseeh, F. and Senturia, S.D. Viscoelasticity and creep recovery of polyimide thin films, in Technical Digest. IEEE Solid-State Sensor and Actuator Workshop, edited by IEEE (IEEE, NY, 1990), p. 55.CrossRefGoogle Scholar
28Xiang, Y., Tsui, T.Y., Vlassak, J.J., and McKerrow, A.J.: Measuring the elastic modulus and ultimate strength of low-k dielectric materials by means of the bulge test, in the Proceedings of IEEE 2004 International Interconnect Technology Conference, edited by IEEE (IEEE, Piscataway, NJ, 2004), p. 133.Google Scholar
29Perez-Prado, M.T. and Vlassak, J.J.: Microstructural evolution in electroplated Cu thin films. Scripta Mater. 47, 817 (2002).CrossRefGoogle Scholar
30Xiang, Y. and Vlassak, J.J.: Bauschinger effect in thin metal films. Scripta Mater. 53, 177 (2005).CrossRefGoogle Scholar
31Dieter, G.E.: Mechanical Metallurgy, 3rd ed. (McGraw-Hill, New York, 1986), p. 287.Google Scholar
32Freund, L.B., personal communication (1995).Google Scholar
33Azrin, M. and Backofen, W.A.: The deformation and failure of a biaxially stretched sheet. Metall. Trans. 1, 2857 (1970).CrossRefGoogle Scholar