Fracture strength of polysilicon at stress concentrations

Mechanical design of MEMS requires the ability to predict the strength of load-carrying components with stress concentrations. The majority of these microdevices are made of brittle materials such as polysilicon, which exhibit higher fracture strengths when smaller volumes or areas are involved. A review of the literature shows that the fracture strength of polysilicon increases as tensile specimens get smaller. Very limited results show that fracture strengths at stress concentrations are larger. This paper examines the capability of Weibull statistics to predict such localized strengths and proposes a methodology for design. Fracture loads were measured for three shapes of polysilicon tensile specimens - with uniform cross-section, with a central hole, and with symmetric double notches. All specimens were 3.5 μm thick with gross widths of either 20 or 50 μm. A total of 226 measurements were made to generate statistically significant information. Local stresses were computed at the stress concentrations, and the fracture strengths there were approximately 90% larger than would be predicted if there were no size effect (2600 MPa versus 1400 MPa). Predictions based on mean values are inadequate, but Weibull statistics are quite successful. One can predict the fracture strength of the four shapes with stress concentrations to within ±10% from the fracture strengths of the smooth uniaxial specimens. The specimens and test methods are described and the Weibull approach is reviewed and summarized. The CARES/Life probabilistic reliability program developed by NASA and a finite element analysis of the stress concentrations are required for complete analysis. Incorporating all this into a design methodology shows that one can take "baseline" material properties from uniaxial tensile tests and predict the overall strength of complicated components. This is commensurate with traditional mechanical design, but with the addition of Weibull statistics.