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We present computationally efficient models and approaches to simulate the response of microstructures under mechanical shock. These approaches include a Galerkin-based reduced-order model and a hybrid approach utilizing the response of structures to static loads combined with the dynamic shock spectrum of a spring-mass-damper system. To demonstrate the accuracy and efficiency of these approaches, we apply them on cantilever and clamped-clamped microbeams, and compare their predictions with analytical and finite-element (FE) results. We conclude that the hybrid approach is computationally efficient and accurate for microstructures behaving linearly in both quasi-static and dynamic loading conditions. The hybrid approach enables using simple analytical expressions that can be easily utilized by microelectromechanical system designers to judge the reliability of their devices. We show that reduced-order models are capable of capturing accurately the dynamic behavior of microstructures under shock pulses of various amplitudes (low-g and high-g), damping conditions, structural boundaries, and can capture linear and nonlinear behavior. Our results indicate that modeling the shock force as a quasi-static force for microstructures with low-natural frequencies may lead to erroneous results. High-g loading cases are investigated. Significant increase in the computational cost of simulations is reported when using traditional FE models because of the activation of higher order modes. The developed reduced-order model employing at least six modes is shown to be efficient in such cases. Design parameters are investigated to determine their effect on the shock resistance of microstructures. It is concluded that increasing air damping and tensile residual stresses improves the shock resistance of microstructures. A case study for the response of an optical fiber switch to shock is presented. [2006-0131] Index Terms--Clamped, high-g shock, microbeams, microelectromechanical system (MEMS) reliability, nonlinearity, reduced-order models, shock spectrum.

This work presents a new strain sensor with a compact structure. The strain sensor comprises of a pair of cantilever beams with different lengths connected by a short tip. The residual strain causes two beams to deflect each other, thereby magnifying the deflection, which is measured by the tip. The displacement is independent of both Young's modulus and the film's thickness. An analytical model is derived to relate the measured displacement to residual strain. Finite-element modeling is also used to analyze the model. This work also thoroughly considers other factors that influence the designs and the implicit limitations of the strain sensors. Experimental results with an Si[O.sub.2] film as well as undoped LPCVD polysilicon films are used to demonstrate the effectiveness of the proposed structure. Index Terms - Residual strain, thin film.

A sticking (stiction) model for a cantilevered beam is derived. This model includes the effect of the bending moment, which stems from stress gradient along the vertical direction of structural polysilicon, and the temperature during the release process. The bending moment due to the stress gradient will play an important role to evaluate antisticking efficiency since liquid tension and surface energy of microstructures tend to become smaller by newly developed antisticking techniques. The effects of stress gradient and temperature were analyzed and verified with surface-micromachined polysilicon cantilevers. By modifying the substrate polysilicon with grain-hole formation technique, the effects of residual stress gradient in polysilicon on stiction could be observed in the condition of low work of adhesion. Index Terms - Grain hole, polysilicon, sticking, stress gradient, surface micromachining.