A Modeling Approach based on Laminated Plate Theory to Design Microbeams
Susan C. Mantell , Ellen Longmire, and Dan Wolters
University of Minnesota, US
Keywords: plate theory, residual stresses, displacement, model
MEMs microbeams consist of many thin material layers. This thin layered structure is very similar to that of laminated composite plates in which thin layers of fiber reinforced plastic are stacked and cured. Both the MEMs layered structure and the composites layered structure will have layers with different properties including modulus and coefficient of thermal expansion. Even an actuating layer in a MEMs structure can be modeled as part of a laminated plate. Researchers in composite materials have developed an approach, referred to as laminated plate theory, to solve mechanics problems in these layered structures. In laminated plate theory the mechanical response of the layered structure to imposed forces, strains or thermal loads can be predicted through series of matrix calculations. This approach can be extended to characterizing MEMs mechanical behavior. For example, laminated plate theory can be used to evaluate displacement of MEMs microbeams that are actuated by PZT. This approach can also be extended to predict residual stresses that occur during manufacture. In this work, PZT actuated beams were fabricated on either a silicon dioxide or silicon nitride structural layer (Figure 1). Actual beam response is compared with predictions from laminated plate theory (Table 1). In addition a study in which residual stresses during fabrication result in beams that are structurally sound vs. those that failed is presented. In this study of residual stresses laminated plate theory predicts whether residual stresses created during fabrication will cause the beam to fail.
NSTI Nanotech 2003 Conference Technical Program Abstract