Modeling of the Effect of Process Variations on a Micromachined Doubly-Clamped Beam

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.

Effects of the Manufacturing Process on the Reliability of the Multilayer Structure in MetalMUMPs Actuators: Residual Stresses and Variation of Design Parameters

“…Different thermal expansions and geometries generate thermal stresses that vary along layer films and depend on the material properties, e.g., the Young’s moduli, the coefficients of thermal expansion, the thermal conductivity, etc. Also in [ 24 ], the scholars reached a similar conclusion: when manufacturing MEMS, the manufacturing process variations led to mismatches between the original designs and the final products.…”

A Generalized Polynomial Chaos-Based Approach to Analyze the Impacts of Process Deviations on MEMS Beams

“…Like perturbation methods, they are also restricted to small uncertainties [ 25 ] and strongly dependent on the underlying operators. We previously developed adequate processing models to predict the device performance [ 26 ]. However, these approaches are not applicable to complex device models with different process deviation distributions.…”

Micro/Nano Manufacturing

“…(3) Quality control of micro systems and processes. Baruffi et al [7] demonstrated the application of the replica molding technology for quality control of micro milled surfaces; Cao et al [8] investigated the effect of profile errors on the surface of micro lenses on laser beam homogenization; Choi et al [9] presented a novel testing platform to characterize and predict the mechanical damage of miniaturized haptic actuator; Gao et al [10] modeled the effect of micro manufacturing process variations on the characteristics of a micro machined doubly-clamped beam.…”