Mechanical Characterization of Thin Films Using Full-Field Measurement of Diaphragm Deflection
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MECHANICAL CHARACTERIZATION OF THIN FILMS USING FULL-FIELD MEASUREMENT OF DIAPHRAGM DEFLECTION R. I. Pratt and G. C. Johnson,
Department of Mechanical Engineering, University of California, Berkeley, CA 94720.
ABSTRACT A new method for evaluating the elastic moduli and residual stresses in thin films is presented. This technique is based on measurement of the complete deflected shape of pressurized diaphragms made of the material to be evaluated. It offers important advantages over previous techniques in which only the displacement of the center of the diaphragm is measured as a function" of pressure. The experimental apparatus uses a laser beam and its reflection from the sample surface to determine relative height. Measurements are made over an area of the sample by performing a two-dimensional scan of the sample under the laser beam. The most important advantage of determining the entire deformed shape of the diaphragm is that the shape is known rather than assumed. This way, the particular theory chosen to analyze the structural response does not also dictate a deformed shape based solely on the maximum deflection at the midpoint. Plate theory, as opposed to the more traditional membrane theory, is used to account for the dominance of bending behavior at low pressure and near the diaphragm edges. An energy method is employed to estimate stiffness and residual stress. The accuracy of this approximate method is directly related to how closely the assumed mode shape used in the analysis approximates the true response of the structure. Since these surface profiles are measured experimentally, the resulting property estimates are obtained with increased confidence. 1.0 BACKGROUND The mechanical properties of thin films as well as their intrinsic stress have long been recognized as important parameters in the manufacture of reliable micro-electro-mechanical devices. Robust techniques for determining these parameters are not, as yet, well developed. The primary reason for this is that due to the small volume of material involved, conventional techniques used in bulk materials are not generally applicable. It is for this reason that new techniques must be developed and existing techniques must be improved. The use of diaphragms as structures for mechanical characterization of thin films has become quite popular. Fabrication of these diaphragms is relatively simple and the equipment required for pressurization is readily available. Early techniques [1-3] measured the displacement of the midpoint of the diaphragm as a function of pressure. The functional form of the displacement over the entire diaphragm was then assumed and its magnitude was scaled according to this measured maximum value. More recent work [4] has included an additional parameter in the assumed transverse displacement in hopes of being able to match the actual displacement more closely. This is indeed an improvement, but does not take full advantage of the fact that the displacement field itself can be measured. Because of the static nature of the exp
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