IUVSTA 15th International Vacuum Congress (IVC-15), AVS 48th International Symposium (AVS-48), 11th International Conference on Solid Surfaces (ICSS-11)
    Microelectromechanical Systems (MEMS) Thursday Sessions
       Session MM-ThM

Paper MM-ThM3
The Beam vs. Plate Distinction for Si Strips Mechanically Loaded in Bending

Thursday, November 1, 2001, 9:00 am, Room 130

Session: Characterization of MEMS Materials
Presenter: S.K. Kaldor, Columbia University
Authors: S.K. Kaldor, Columbia University
I.C. Noyan, IBM T.J. Watson Research Division
Correspondent: Click to Email

Silicon structures used in microelectromechanical systems (MEMS) are generally anisotropic and possess dimensions that make it difficult to determine whether a beam or plate solution is more appropriate. Since a plate has an increased stiffness over that of a beam, errors of up to 10% in predicted displacements and stresses can occur if the proper bending solution is not employed. For single crystal Si samples loaded in four-point bending, we report both finite element modeling results and x-ray curvature measurements that illustrate the effects of boundary conditions (bending jig rollers used to apply displacements), specimen anisotropy, and specimen dimensions. We find that the transverse, or anticlastic, bending effects, which are ignored by 2-D solutions, should be considered as they can result in non-uniform loading across the sample width, and they are important in deciding whether a beam or plate solution should be used. While the sample's width-to-thickness ratio is typically the only criterion used to differentiate between beam and plate structures, we show that it is necessary to consider not only the sample's width and thickness but also the amount of applied bending; this was first considered by Searle@footnote 1@ in 1908. We show that the Searle parameter, width@super 2@/(thickness * bending radius), can be used to accurately differentiate between beam and plate structures. Furthermore, the difference in stiffness between a beam and a plate depends on the Poisson's ratio of the bent material. Since Poisson's ratio in Si can vary from 0.06 to 0.36 with crystallographic orientation, controlling the bending direction of a single crystal is a possible method for tailoring the specimen's flexural rigidity. @FootnoteText@ @footnote 1@ G.F.C. Searle, "Experimental Elasticity," 2nd ed. Cambridge UP, 1920.