Skip to main content Accessibility help

Measuring substrate-independent modulus of thin films

  • Jennifer Hay (a1) and Bryan Crawford (a1)


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.


Corresponding author

a)Address all correspondence to this author. e-mail:


Hide All
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).
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).
3.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).
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).
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).
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).
7.Song, H.: Selected mechanical problems in load- and depth-sensing indentation testing. Ph.D. Thesis, Rice University (1999).
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.
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).
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).
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.
12.Hay, J.L.: Measuring substrate-independent modulus of dielectric films by instrumented indentation. J. Mater. Res. 24, 667 (2009).
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).
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).
15.Hay, J.L.: Introduction to instrumented indentation testing. Exp. Tech. 33, 66 (2009).
16.Hay, J.L., Agee, P., and Herbert, E.G.: Continuous stiffness measurements during instrumented indentation testing. Exp. Tech. 34, 86 (2010).
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).



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed