Abstract
In the fabrication of micro-electro-mechanical systems (MEMS) devices, manufacturing process variations are usually involved. For these devices sensitive to process variations such as doubly-clamped beams, mismatches between designs and final products will exist. As a result, it underlies yield problems and will be determined by design parameter ranges and distribution functions. Topographical changes constitute process variations, such as inclination, over-etching, and undulating sidewalls in the Bosch process. In this paper, analytical models are first developed for MEMS doubly-clamped beams, concerning the mentioned geometrical variations. Then, finite-element (FE) analysis is performed to provide a guidance for model verifications. It is found that results predicted by the models agree with those of FE analysis. Assigning process variations, predictions for performance as well as yield can be made directly from the analytical models, by means of probabilistic analysis. In this paper, the footing effect is found to have a more profound effect on the resonant frequency of doubly-clamped beams during the Bosch process. As the confining process has a variation of 10.0%, the yield will have a reduction of 77.3% consequently. Under these circumstances, the prediction approaches can be utilized to guide the further MEMS device designs.
Highlights
Precise processing control has turned into an issue, owing to the mass production of micro-electro-mechanical systems (MEMS) devices and their increasingly complicated manufacturing processes
Achievements have been reached to get a balance between precision and calculation—for example, the Sigma-Point approach applied to MEMS resonators with four orders of magnitude faster than Monte Carlo (MC) [23], the generalized polynomial chaos (GPC) framework to handle stochastic coupled electromechanical analysis with the same precision and one order of magnitude faster compared with MC [24], and the Taguchi parameter design and statistical process-control method to minimize variability in performance response to fluctuations [25]
Geometric features of MEMS devices usually do not comply with the design value, with the Geometric features of [34,35]
Summary
Precise processing control has turned into an issue, owing to the mass production of micro-electro-mechanical systems (MEMS) devices and their increasingly complicated manufacturing processes. Proposed the first-order second-moment (FOSM) and advanced FOSM reliability method, respectively, in a probabilistic way to obtain a linearized feasible region and maximize the yield For those non-linear actuated MEMS devices, high fidelity optimization schemes have been realized. Achievements have been reached to get a balance between precision and calculation—for example, the Sigma-Point approach applied to MEMS resonators with four orders of magnitude faster than MC [23], the generalized polynomial chaos (GPC) framework to handle stochastic coupled electromechanical analysis with the same precision and one order of magnitude faster compared with MC [24], and the Taguchi parameter design and statistical process-control method to minimize variability in performance response to fluctuations [25]. Given design specifications, reasonable suggestions can be made for parameter error ranges under process variations
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