Stochastic modeling and response prediction of MEMS

Micro-Electro-Mechanical Systems (MEMS) are micro devices used as micro sensors and actuators with structural dimensions of the order of a micron. The focus in this dissertation is on MEMS made of planar, polycrystalline silicon and fabricated through integrated circuit-based processes. The process conditions often result in texture in the material that manifests as anisotropy in the mechanical properties. Due to the random orientations and shapes of the crystal grains, the constituent materials also exhibit inhomogeneity at the microscopic level. These material characteristics can have significant influences on the mechanical response of MEMS devices. With the increasing push towards miniaturization in MEMS, the potential for uncertainties in the mechanical response of nominally identical devices has increased. Without knowledge of these uncertainties, the successful implementation of production scale manufacture is hampered.; Homogenization techniques such as the first order Voigt and Reuss bounds are shown to be sufficiently close for MEMS made of polysilicon (containing large number of crystals within smallest structural dimensions) and their derivation for {dollar}{lcub}100{rcub}{dollar} and {dollar}{lcub}110{rcub}{dollar} textures are outlined. To account for the effects of random crystal shape and orientation, detailed approaches to the probabilistic modelling and analysis of the mechanical response of multicrystalline structural elements and devices are presented using simulation, random fields and stochastic finite element techniques. A mathematical model--the Voronoi Tesselation--is used to simulate random multicrystalline geometries which are then analyzed using finite elements. A more efficient continuous-parameter random field characterization of the crystalline micro-structure is also employed. The equivalent random field properties are used in conjunction with stochastic finite element methods to probabilistically compute the response of MEMS components and devices. These analysis techniques enable a quantitative estimation of response uncertainties for multicrystalline structural elements and devices.; Typical results show coefficients of variation (C.O.V.) of approximately 3% in the response of micro beams with grain sizes of the same order as their depths. For a folded beam lateral micro resonator, the natural frequency is found to have C.O.V.s that are lower than the C.O.V.s of the lateral stiffness of the constituent beams. The uncertainty in the natural frequency, however, is dependent on the length of the consituent beams and can reach as high as 6% for beams greater than 40 {dollar}mu{dollar}m in length.; This dissertation represents a first attempt to analytically and numerically characterize the uncertainty inherent in the properties and response of MEMS that arises from the natural randomness in the constituent materials.