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

  • Han Li (a1) and Joost J. Vlassak (a1)


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.


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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).
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).
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).
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).
5.Pharr, G.M. and Oliver, W.C.: Measurement of thin-film mechanical properties using nanoindentation. MRS Bull. 17(7), 28 (1992).
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).
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).
8.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23(12), 1657 (1987).
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).
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).
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).
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).
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).
14.Elgendi, S.E.: Chebyshev solution of differential, integral and integro-differential equations. Comput. J. 12(3), 282 (1969).
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).
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).
17.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17(10), 2660 (2002).
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).
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.
20. iMechanica. 2008. Harvard School of Engineering and Applied Sciences. Available at (accessed Jan. 20, 2009).
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).
22.Xiang, Y., Chen, X., and Vlassak, J.J.: Plane-strain bulge test for thin films. J. Mater. Res. 20(9), 2360 (2005).
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).
24.Jaccodine, R.J. and Schlegel, W.A.: Measurement of strains at Si-SiO2 interface. J. Appl. Phys. 37(6), 2429 (1966).
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).
26.Petersen, K.E. and Guarnieri, C.R.: Young's modulus measurement of thin films using micromechanics. J. Appl. Phys. 50(11), 6761 (1979).
27.Petersen, K.E.: Dynamic micromechanics on silicon-Techniques and devices. IEEE Trans. Electron Devices 25(10), 1241 (1978).
28.Blech, I. and Cohen, U.: Effects of humidity on stress in thin silicon dioxide films. J. Appl. Phys. 53(6), 4202 (1982).
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).
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).
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).



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