|Ph.D Thesis||Department of Mechanical Engineering|
|Supervisor:||Prof. Altus Eli|
In many MEMS applications such as polysilicon microstructures, the size of the basic element (grain), compared with the structure’s scale is not negligible. In these cases, the random microstructure causes statistical dispersion of the response, experimentally observed by many researchers. However, treating the material as homogeneous with effective properties is not sufficient. In this work, we analytically study the relations between various microstructure properties and the generalized displacements of statically determinate beams, frequently used in MEMS. The beams are stochastically inhomogeneous both in the longitudinal direction and through the beam cross section. The analysis includes shear deformation effects, material coupling (nonisotropic behavior) and structural coupling, such as shear and bending deformations due to normal forces.
The governing equations in this work are presented in a special non-local tensorial form, which enables finding analytical expressions for the mean and covariance matrix of the generalized deflections in terms of well defined microstructural parameters of the material and their statistics.
Experiments were also conducted, where self-designed MUMPs polysilicon beams with clamped-clamped and clamped-free boundary conditions were examined using an Atomic Force Microscope (AFM). The results for the clamped-free beams show very good agreement with the theoretical prediction. The microstructure of these beams was found to be dominantly a 3D uniform grain orientation. The results for the clamped-clamped beams have shown higher than expected compliance. It is conjectured that this phenomenon is related to a strong influence of morphology on statically indeterminate beams, and to compression stresses in the polysilicon layer. The method for loading specimen beams using an Atomic Force Microscope and extracting their mechanical properties was thoroughly discussed.