Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon

Brittle materials such as silicon fail <i>via</i> the crack nucleation and propagation, which is characterized by the singular stress field formed near the crack tip according to Griffith or fracture mechanics theory. The applicability of these continuum-based theories is, however, uncertain and questionable in a nanoscale system due to its extremely small singular stress field of only a few nanometers. Here, we directly characterize the mechanical behavior of a nanocrack <i>via</i> the development of <i>in situ</i> nanomechanical testing using a transmission electron microscope and demonstrate that Griffith or fracture mechanics theory can be applied to even 4 nm stress singularity despite their continuum-based concept. We show that the fracture toughness in silicon nanocomponents is 0.95 ± 0.07 MPa√m and is independent of the dimension of materials and therefore inherent. Quantum mechanics/atomistic modeling explains and provides insight into these experimental results. This work therefore provides a fundamental understanding of fracture criterion and fracture properties in brittle nanomaterials