Effect of stochastically anisotropic morphology on the mechanical behavior of microbeams

In many Micro-Electro-Mechanical-Systems (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 its response to load, experimentally observed by many researchers. The accompanying calculations, which generally treat the material as homogeneous and isotropic, do not model the structures properly. In this work, we analytically study the relations between morphological properties and the generalized displacements of statically determinate beams, frequently used in MEMS. The analysis includes shear deformation effects, material and structural couplings such as shear and bending deformations due to normal forces, and nonisotropic effects. The governing equations are presented in a special tensorial form, which enables finding analytical expressions for the mean and covariance matrix of the generalized deflections in terms of well defined morphological parameters and their statistics.