Nanoindentation of a 10 nm thick thin film
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Nanoindentation of a 10 nm thick thin film Takeshi Sawa, Yasushi Akiyama,a) Atsushi Shimamoto,b) and Kohichi Tanakac) Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata, 940-2188, Japan (Received 2 October 1998; accepted 23 March 1999)
In a nanometer order nanoindentation test, roundness or truncation of the indenter tip cannot be avoided. In this paper, we have analyzed the indentation problem of a rounded triangular indentation into a layered elastic half-space by a finite element analysis and then established a method to estimate the intrinsic elastic modulus of the film from the nanoindentation data. The method was applied to analyze the nanoindentation data of a less-than-10 nm penetration depth on a 10 nm thick diamondlike carbon film deposited on a 50 nm thick magnetic layer.
I. INTRODUCTION
Nanoindentation is a simple and effective means for evaluating the mechanical properties of thin films. In the method, the applied load, P, and the penetration depth, h, of the indenter are continuously monitored, and the mechanical properties are determined from the thus obtained P-h relationship. For evaluating the intrinsic mechanical property of a thin film layered on a substrate, as a rule of thumb, the penetration depth should be less than one tenth of the film thickness. However, the precise indentation measurement on one-tenth of the film thickness is impossible for 10 nm order thickness films. Doerner and Nix1 suggested that the effective comp , in a layered solid can be posite Young’s modulus, Eeff described as a function of plane strain Young’s modulus, 1yE p s1 2 n 2 dyE, of the relevant materials: 1 1 1 p s1 2 e 2bst/hd d 1 p e2bst/hd , p Es Eeff Ef
(1)
where b is an unknown parameter, t the film thickness, E Young’s modulus, and n Poisson’s ratio. Subscripts f and s refer to the film and substrate properties, respectively. They determined b based on measurements of tungsten films on silicon substrates. King2 analyzed the problem of triangular punches indenting a layered solid via a singular integral equation, and numerically obtained b as a function of contact radius normalized by t. Menˇcik et al.3 examined the application of five approximation functions for determining elastic modulus of thin layers using nanoindentation. They showed that Gao’s function4 gives better fitting to experimental data a)
Present address: Nippon Seiki Corp., Nagaoka, Niigata, Japan. Present address: Nano TEM Co. Ltd., 2-2-2 Nakajima Nagaoka, Niigata, Japan. c) Address all correspondence to this author. e-mail: [email protected] b)
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http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 6, Jun 1999
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than the Doerner and Nix function in determining the thin film modulus. A triangular indenter is commonly used for nanoindentation measurement for the reason that the three facets theoretically converge to a single point. However, in practice, the truncation or roundness of the
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