Description of brittle failure of non-uniform MEMS geometries

The description of probability of failure of polysilicon micromachined components with complex geometries using a single set of Weibull parameters was investigated. Strength data from both uniform tension and from twelve non-uniform specimen geometries with central perforations were employed. These perforations allowed for twelve different combinations of stress concentration factors and radii of curvature. Two methods were applied to determine the Weibull parameters: in the first method, only the strength data from uniform tension specimens were used to determine the Weibull modulus and the material scale parameter. In the second approach, the strength data from all non-uniform tension geometries were used to calculate the material scale parameter and the Weibull modulus using the maximum likelihood method. The non-uniform stress state in each perforated specimen was taken into account through an elasticity finite element model and the use of the integral form of the Weibull probability function. Using the first method, an analysis considering active flaw populations at the top specimen surface or the specimen sidewalls indicated that the active flaw population is not the same at all scales: for 1-3 μm radius perforations and small stress concentration factor (K = 3) the active flaw population was located at the specimen top surface, e.g. surface roughness, which, as the analysis indicated, was also the case for uniform tension specimens. For higher stress concentration factors (nominal K = 6 and 8) the analysis indicated that the active flaw population was located at the hole sidewall surface. As a result, for a given material the geometry of the specimen and the local state of stress determine the active flaw population from all flaws generated during fabrication and processing. Therefore, it is important that all potential failure modes be considered when extrapolations to other geometries and loadings are made using the Weibull probability function.