Fracture strength of polysilicon at stress concentrations

Abstract

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 mu m thick with gross widths of either 20 or 50 mu m. 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 +or-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

Quantized fracture mechanics

“…Similar experimental results are discussed in a recent paper (Bagdahn et al 2003). The fracture strengths of polysilicon thin films with and without holes of radius 2.5 mm for two different film widths (20 and 50 mm) were measured; deviations from the classical value, C /3, were found (note that for these finite plates, C /3.23 is expected from finite element analysis for the 20-mm width, and C /3.04 for the 2838 N. M. Pugno and R. S. Ruoff 50-mm width) (Bagdahn et al 2003).…”

“…The fracture strengths of polysilicon thin films with and without holes of radius 2.5 mm for two different film widths (20 and 50 mm) were measured; deviations from the classical value, C /3, were found (note that for these finite plates, C /3.23 is expected from finite element analysis for the 20-mm width, and C /3.04 for the 2838 N. M. Pugno and R. S. Ruoff 50-mm width) (Bagdahn et al 2003). In particular, we focus attention on the average values (the distribution of strengths follows a classical Weibull distribution) reported (Bagdahn et al 2003), and obtain a ratio for the experimental strength of the films with and without the hole of 0.54 (20-mm width) and 0.69 (50-mm width); from equation (7) (a % 2 mm, # ¼ ¼ 0) we obtain 0.56. This comparison emphasizes that at larger size scales a larger fracture quantum is expected, so that a much smaller hole would have little effect on the strength (here, a vacancy practically does not reduce the strength!…”

“…It is well known that Griffith's criterion (1920) is equivalent to the stress-intensity factor-based criterion (Westergaard 1939) for brittle crack propagation, if the stress-intensity K I and its critical value K IC (the fracture toughness of the material) are assumed to be equal (Irwin 1957). According to LEFM (for details, see Bazant and Cedolin 1991, Hellan 1985, Carpinteri 1997…”

Mechanical Effects of Galvanic Corrosion on Structural Polysilicon

“…As a final example, the roughness and grain boundary separations seen after HF immersion (Table IV and Fig. 8) are of the same order of magnitude as suggested in the literature for critical flaw sizes, i.e., 30-115 nm [11], [64]. This would be expected to influence the fracture and fatigue properties of polySi.…”

Vibration and shock reliability of MEMS: modeling and experimental validation

“…The model for lateral instability of comb-drives [24] was used to obtain the numerical values of the finger overlap required to drive the comb-drive into unstable domains, as a function of the voltage across the comb-drive, and cause lateral snap-in. Using (6) and (9), the critical conditions for lateral snapping of the combdrive due to axial shock inputs in the presence of a voltage are computed and are shown in figure 10 as a continuous curve. The figure is divided into two different regimes by a vertical line corresponding to 66.96 V. The region to the right of this line is the region where the prediction curve is directly valid.…”