Plane-strain Bulge Test for Thin Films
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X. Chen Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027-6699
J.J. Vlassaka) Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138-2901 (Received 21 January 2005; accepted 19 April 2005)
The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.
I. INTRODUCTION
Thin films have many important applications in modern industries.1,2 For example, thin films with thicknesses well below 1 m are widely used as functional and structural elements in ultra-large-scale integrated circuits and microelectromechanical systems, as well as in newly emerging nano-devices and biomedical devices. Thicker films are often used as wear-resistant coatings on cutting tools, protective coatings in data storage devices, and thermal-barrier coatings on turbine blades. To take full advantage of these materials and to further improve their reliability, the mechanical behavior of thin films must be well understood. It is well known that many materials behave very differently in thin film form than
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0313 2360
http://journals.cambridge.org
J. Mater. Res., Vol. 20, No. 9, Sep 2005 Downloaded: 16 Mar 2015
they do in the bulk.3 For example, thin metal films are often found to support much higher stresses than the same material in bulk form, and their yield stress scales inversely with film thickness if the film surface is passivated.4,5 Besides the size effects associated with film thickn
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