Two interferometric methods for the mechanical characterization of thin films by bulging tests. Application to single cr
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Two interferometric methods for the mechanical characterization of thin films by bulging tests. Application to single crystal of silicon E. Bonnotte, P. Delobelle, and L. Bornier Laboratoire de M´ecanique Appliqu´ee R. Chal´eat, UA CNRS, UFR Sciences et Techniques, 24 chemin de l’Epitaphe, 25030 Besancon Cedex, France
B. Trolard and G. Tribillon Laboratoire d’Optique, UA CNRS, UFR Sciences et Techniques, Route de Gray, La Bouloie, 25030 Besancon Cedex, France (Received 16 February 1996; accepted 8 May 1997)
Two optical methods are presented for the mechanical characterization of thin films, namely real time holographic interferometry and a fringe projection method called “contouring.” These two methods are coupled to the interferometry by the phase measurements, thus allowing the displacement field to be measured at all points on the membrane. We discuss the solutions retained in terms of their precision and sensitivity. These methods are then applied to membrane bulging tests, a type of test that is widely used in micro-mechanical studies. The measurements are performed on silicon single crystal and the results are compared to the solutions calculated by finite element methods. In both cases, the good agreement between theory and experiments allows the experimental apparatus to be validated.
I. INTRODUCTION
The design and realization of mechanisms of submillimetric or micrometric size is a growing field requiring developments in several scientific disciplines.1,2 In general, the mechanical architecture of microsystems can be likened to an assembly of plates, beams, or membranes fixed on a more massive substrate and submitted to mechanical loadings such as tensile, bending, and pressure loads. These considerations have led us to develop three kinds of tests for materials having small dimensions, namely: a uniaxial tensile test, a four point bending test, and finally a membrane bulging test which can be used not only for ductile materials but also for those that are highly brittle. This article is concerned with this third type of test which is widely used in the domain of very thin materials.3–7 Indeed, while being relatively easy to perform, this test allows the quantification of certain mechanical properties of the materials used in the microtechnical domain which prove to be strongly dependent on the fabrication process.3–9 However, the main experimental difficulty of this test resides in the quasi-instantaneous and contactless measurement of the membrane deformation. Classically, interferometry is used to measure the out-of-plane displacement at a particular point of the film, generally at its center,3–5 and it can lead in some cases to significant errors, as will be illustrated later. It can also be noted that the theoretical interpretation of the relation pressure2234
http://journals.cambridge.org
J. Mater. Res., Vol. 12, No. 9, Sep 1997
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displacement at the center of the membrane, in the case of large displacements, must be rigorousl
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