Robust Optimization: Design in MEMS - University of California ...

8properties are largely dependent on how they are manufactured, similarly the propertiesof MEMS materials are dependent on how they are fabricated. With a number ofdevelopments occurring in the past 15 years, the characterization of mechanical, electrical,and thermal properties has barely scratched the surface for the overwhelmingcombinations of materials and processes. Further complicating the characterizationprocess is the difficulty of making measurements at the micrometer scale. For thesereasons, most microfabrication materials have large uncertainties associated with theirproperties. For example, Sharpe and Jackson [6] characterized polycrystalline siliconin the MUMPs R process and measured values of 162 ± 14 GPa for Young’s modulusand 1.56 ± 0.25 GPa for tensile strength, which are relative uncertainties of 9% and16%, respectively.Finally, there are several other sources of uncertainty such as surface roughness,side-wall etch angle, and grain size. These factors, however, are typically much morecomplicated and difficult to characterize than the aforementioned two.Uncertainty is clearly significant at the micro-scale, however it is often neglectedin the MEMS design process. In order to design highly reliable systems that can befabricated with high yields, it will be necessary to account for the effects of uncertaintyespecially with the current trends to make more complex and integrated systems. Inthis report we will address a strategy for robust design through optimization. Ourfocus will be on dimensional and material uncertainties.