Static and Dynamic Characterization of Buckled Composite SiO 2 - Au Microbridges
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ABSTRACT Theoretical and experimental investigations have been made to study the nonlinear static and dynamic behavior of composite Si0 2-Au microbridges. Measurements of maximal deflection amplitude were carried out on arrays of clamped-clamped SiO 2-Au beams buckling under the effect of thin film effective residual stress. The static analysis adresses the issue of microfabricated beam buckling from an energy point of view. SiO 2-Au and Au effective residual stresses are evaluated by considering the measured buckling maximal deflection and by through an adequate approximation of the shape of the microbeam deflection curve. The dynamic approach is based on a direct analytical model yielding an exact solution to the linear problem associated with the nonlinear vibrations of initially buckled clamped-clamped structures. Several experimental multi-mode dynamic responses of composite buckled beams are also given to illustrate the validity and accuracy of this analytical model.
INTRODUCTION Over the years, methods derived from the MEMS field generated in situ techniques for residual stress determination in microelectronic thin films. These techniques rely on the deformation of microfabricated structures as suspended membranes, asymmetrical released structures or micromachined beams [1-3]. The theoretical models that support these mechanical testing techniques systematically associate residual stress with extemally applied loads and bending moments. In this paper, the energy method that we had already proposed for the study of the residual stress in single-layer microstructures [4], is used for composite micromachined beams. Also, buckled states cause micromachined clamped-clamped beams to operate in a nonlinear range that could affect the device dynamic response. Hence, buckled beams have been the subjects of a great number of studies investigating the nonlinear vibrations of mechanical structures. To determine approximate solutions to the nonlinear vibrations of buckled beams, most analytical methods rely on a minimization of residual techniques such as Galerkin's method[5,6]. Geijselaers et al.[7] experimentally validate this model [6] at the microscale. Alternatively, the theoretical direct method leads to an exact solution to the linear problem associated with nonlinear vibrations of a structure around its nth buckling mode. Our approach experimentally validates the direct method proposed by Nayfeh et at [8] for initially budded clamped-clamped beams at the microscale. SAMPLE PREPARATION An n-type (110) oriented Cz-grown silicon wafer was used as substrate. A (110) rather than (100) oriented wafer was chosen to facilitate the release of microstructures [9] by generating vertical walls at the clamped ends. The process started by performing thermal steam oxidation to obtain a 0.45 jim thick silicon dioxide at a temperature of 1100 0C. Then, the oxide was buffer HF-pattemed to form the micromachined beam areas. In addition, during HF etching, Si0 2 was totally removed from the back side of the wafer. Arrays of SiO 2 m
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