Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T11:24:55.276Z Has data issue: false hasContentIssue false

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Published online by Cambridge University Press:  31 January 2011

Han Li
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
Joost J. Vlassak*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

A data analysis procedure has been developed to estimate the contact area in an elasto-plastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu's elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods.

Type
Articles
Copyright
Copyright © Materials Research Society 2009

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 indentation experiments. J. Mater. Res. 7(6), 1564 (1992).Google Scholar
2.Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
3.Burnett, P.J. and Rickerby, D.S.: The mechanical properties of wear-resistent coatings. 1. Modeling of hardness behavior. Thin Solid Films 148(1), 41 (1987).CrossRefGoogle Scholar
4.Fabes, D.B., Oliver, W.C., McKee, R.A., and Walker, F.J.: The determination of film hardness from the composite response of film and substrate to nanometer scale indentations. J. Mater. Res. 7(11), 3056 (1992).CrossRefGoogle Scholar
5.Pharr, G.M. and Oliver, W.C.: Measurement of thin-film mechanical properties using nanoindentation. MRS Bull. 17(7), 28 (1992).Google Scholar
6.Mencik, 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(9), 2475 (1997).CrossRefGoogle Scholar
7.Saha, R. and Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50(1), 23 (2002).CrossRefGoogle Scholar
8.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23(12), 1657 (1987).Google Scholar
9.Gao, H.J., Chiu, C.H., and Lee, J.: Elastic contact versus indentation modeling of multilayered materials. Int. J. Solids Struct. 29 (20), 2471 (1992).Google Scholar
10.Yu, H.Y., Sanday, S.C., and Rath, B.B.: The effect of substrate on the elastic properties of films determined by the indentation test-Axisymmetrical Boussinesq problem. J. Mech. Phys. Solids 38(6), 745 (1990).Google Scholar
11.Chen, X. and Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16(10), 2974 (2001).CrossRefGoogle Scholar
12.Han, S.M., Saha, R., and Nix, W.D.: Determining hardness of thin films in elastically mismatched film-on-substrate systems using nanoindentation. Acta Mater. 54(6), 1571 (2006).Google Scholar
13.Xu, H.T. 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(4), 315 (2006).CrossRefGoogle Scholar
14.Elgendi, S.E.: Chebyshev solution of differential, integral and integro-differential equations. Comput. J. 12(3), 282 (1969).Google Scholar
15.Pharr, G.M., Oliver, W.C., and Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7 (3), 613617 (1992).Google Scholar
16.Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42(8), 1223 (1994).CrossRefGoogle Scholar
17.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17(10), 2660 (2002).Google Scholar
18.Harding, J.W. and Sneddon, I.N.: The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. Math Proc. Cambridge Philos. Soc. 41(1), 16 (1945).CrossRefGoogle Scholar
19.Hill, R. and Storåkers, B.: A concise treatment of axisymmetric indentation in elasticity, in Elasticity: Mathematical Methods and Applications, edited by Eason, G. and Ogden, R.W. (Harwood, Chichester, UK, 1990), pp. 199209.Google Scholar
20. iMechanica. 2008. Harvard School of Engineering and Applied Sciences. Available at http://imechanica.org/node/4050 (accessed Jan. 20, 2009).Google Scholar
21.Oliver, 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(1), 3 (2004).CrossRefGoogle Scholar
22.Xiang, Y., Chen, X., and Vlassak, J.J.: Plane-strain bulge test for thin films. J. Mater. Res. 20(9), 2360 (2005).CrossRefGoogle Scholar
23.Vlassak, J.J. and Nix, W.D.: A new bulge test technique for the determination of Young modulus and Poisson ratio of thin films. J. Mater. Res. 7(12), 3242 (1992).CrossRefGoogle Scholar
24.Jaccodine, R.J. and Schlegel, W.A.: Measurement of strains at Si-SiO2 interface. J. Appl. Phys. 37(6), 2429 (1966).CrossRefGoogle Scholar
25.Carlotti, G., Doucet, L., and Dupeux, M.: Comparative study of the elastic properties of silicate glass films grown by plasma enhanced chemical vapor. J. Vac. Sci. Technol., B 14(6), 3460 (1996).CrossRefGoogle Scholar
26.Petersen, K.E. and Guarnieri, C.R.: Young's modulus measurement of thin films using micromechanics. J. Appl. Phys. 50(11), 6761 (1979).CrossRefGoogle Scholar
27.Petersen, K.E.: Dynamic micromechanics on silicon-Techniques and devices. IEEE Trans. Electron Devices 25(10), 1241 (1978).Google Scholar
28.Blech, I. and Cohen, U.: Effects of humidity on stress in thin silicon dioxide films. J. Appl. Phys. 53(6), 4202 (1982).CrossRefGoogle Scholar
29.Saha, R., Xue, Z.Y., Huang, Y., and Nix, W.D.: Indentation of a soft metal film on a hard substrate: Strain gradient hardening effects. J. Mech. Phys. Solids 49(9), 1997 (2001).Google Scholar
30.Chen, X., Xiang, Y., and Vlassak, J.J.: Novel technique for measuring the mechanical properties of porous materials by nanoinden-tation. J. Mater. Res. 21(3), 715 (2006).Google Scholar
31.Tsui, T.Y., Oliver, W.C., and Pharr, G.M.: Influences of stress on the measurement of mechanical properties using nanoindentation: Part I. Experimental studies in an aluminum alloy. J. Mater. Res. 11(3), 752 (1996).Google Scholar