Dynamic crack modeling and analytical stress field analysis in single-crystal silicon using quantitative fractography

Single-crystal silicon is the fundamental building block enabling today's plethora of integrated electronic components. However, complex mechanical stresses, originating from either direct mechanical loading or thermal cycling, can result in fracture of the constituent silicon, one of the leading causes of semiconductor device failure. Although phenomenological relationships to estimate the fracture strength in silicon have been proposed in the past, no quantitative fractographic method addressing the intrinsic anisotropy of crystals exists. In this work, a fractographic approach using optical confocal microscopy and atomic force microscopy is developed to identify and analyze the cleavage planes associated with dynamic instabilities in single-crystal silicon. We analytically determined the dynamic crack propagation behavior and asymptotic stress field at the crack-tip for unstable, anisotropic, circular cracks in silicon. The fractographic features predicted by the analytical model are consistent with experimental observations, and correctly predict how the {1 1 1} planes define the fractographic mirror region (including mirror constant), as well as the {1 1 2} planes associated with fractographic Wallner lines. These findings have important consequences in reducing mechanical and thermomechanical failure in semiconductor devices, where the mechanical strength is highly dependent on crystallographic anisotropy.