Fracture initiation at sharp notches in single crystal silicon

Abstract

In the context of linear anisotropic elasticity, a universal singular stress field may exist in the region surrounding a sharp reentrant corner (notch). In general, both the radial and tangential variation of the stress fields differ for mode I (symmetric) and mode II (antisymmetric) deformations, and for general anisotropy the mode I and II deformations are coupled. A failure criterion based on critical values of the stress intensities may be appropriate in situations where the region around the corner dominated by the singular fields is large compared to the size of intrinsic flaws and any inelastic zones. We determined the mode I stress fields and stress intensities for two sets of notched silicon flexure specimens using a combination of an asymptotic analysis using the Stroh formalism, dimensional considerations, and continuum finite element analysis. We carried out a companion experimental study to assess the suitability of a critical stress intensity failure criterion. Specifically, assuming such a criterion is valid, we extracted critical values of the mode I stress intensities for a series of notched silicon flexure specimens with notch angles of 70.53° and 125.26°. The specimens were fabricated by anisotropic etching of silicon wafers in KOH, resulting in notch angles of 70.53° between (111) and (1̄1̄1) planes and 125.26° between (111) and (100) planes. The data show that good failure correlation is obtained through the use of a single parameter, the critical mode I stress intensity.