Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T11:40:02.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Measuring substrate-independent modulus of thin films

Published online by Cambridge University Press:  03 March 2011

Jennifer Hay  and
Bryan Crawford
Jennifer Hay*
Affiliation:
Agilent Technologies, Oak Ridge, Tennessee 37830
Bryan Crawford
Affiliation:
Agilent Technologies, Oak Ridge, Tennessee 37830
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Substrate influence is a common problem when using instrumented indentation (also known as nano-indentation) to evaluate the elastic modulus of thin films. Many have proposed models to be able to extract the film modulus (Ef) from the measured substrate-affected modulus, assuming that the film thickness (t) and substrate modulus (Es) are known. Existing analytic models work well if the film is more compliant than the substrate. However, no analytic model accurately predicts response when the modulus of the film is more than double the modulus of the substrate. In this work, a new analytic model is proposed. This new model is shown by finite-element analysis to be able to accurately predict composite response over the domain 0.1 < Ef/Es < 10. Finally, the new model is used to analyze experimental data for compliant films on stiff substrates and stiff films on compliant substrates.

Keywords

Elastic propertiesThin filmNano-indentation
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 6 , 28 March 2011 , pp. 727 - 738
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2.Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
3.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).CrossRefGoogle Scholar
4.Shield, T.W. and Bogy, D.B.: Some axisymmetric problems for layered elastic media: Part 1—Multiple region contact solutions for simply connected indenters. J. Appl. Mech. 56, 798 (1989).CrossRefGoogle Scholar
5.Gao, H., Chiu, C.-H., and Lee, J.: Elastic contact versus indentation modeling of multi-layered materials. Int. J. Solids Struct. 29, 2471 (1992).Google Scholar
6.Menčík, J., Munz, D., Quandt, E., Weppelmann, E.R., and Swain, M.V.: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12, 2475 (1997).CrossRefGoogle Scholar
7.Song, H.: Selected mechanical problems in load- and depth-sensing indentation testing. Ph.D. Thesis, Rice University (1999).Google Scholar
8.Rar, A., Song, H., and Pharr, G.M.: Assessment of new relation for the elastic compliance of a film–substrate system, 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. 431.Google Scholar
9.Xu, H. and Pharr, G.M.: An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scr. Mater. 55, 315 (2006).CrossRefGoogle Scholar
10.Bec, S., Tonck, A., Georges, J.M., Georges, E., and Loubet, J.L.: Improvements in the indentation method with a surface force apparatus. Philos. Mag. A 74, 1061 (1996).CrossRefGoogle Scholar
11.Roche, S., Bec, S., and Loubet, J.L.: Analysis of the elastic modulus of a thin polymer film, in Mechanical Properties Derived from Nanostructuring Materials, edited by Bahr, D.F., Kung, H., Moody, N.R., and Wahl, K.J. (Mater. Res. Soc. Symp. Proc. 778, Warrendale, PA, 2003), p. 117.Google Scholar
12.Hay, J.L.: Measuring substrate-independent modulus of dielectric films by instrumented indentation. J. Mater. Res. 24, 667 (2009).CrossRefGoogle Scholar
13.Saha, R. and Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, 23 (2002).CrossRefGoogle Scholar
14.Ni, W.Y. and Cheng, Y.T.: Modeling conical indentation in homogeneous materials and in hard films on soft substrates. J. Mater. Res. 20, 521 (2005).CrossRefGoogle Scholar
15.Hay, J.L.: Introduction to instrumented indentation testing. Exp. Tech. 33, 66 (2009).CrossRefGoogle Scholar
16.Hay, J.L., Agee, P., and Herbert, E.G.: Continuous stiffness measurements during instrumented indentation testing. Exp. Tech. 34, 86 (2010).CrossRefGoogle Scholar
17.Pharr, G.M., Strader, J.H., and Oliver, W.C.: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res. 24, 653 (2009).CrossRefGoogle Scholar