Threshold crack speed in dynamic fracture of silicon

We report a study of dynamic cracking of a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett., 2006). Here we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We find that the underlying reason for this behavior is formation of a 5-7-double ring defect at the tip of the crack, effectively hindering nucleation of the crack at the Griffith load. We develop a simple continuum model that explains the qualitative behavior of the fracture dynamics.