Ideal Brittle Fracture of Silicon Studied with Molecular Dynamics

Silicon is very brittle and a wafer dropped on the floor easily shatters. A clue to explaining why comes from static cracks. Even at room temperature, static cracks in silicon can have tips that are atomically sharp [1], and there is every reason to believe that crystals can be severed very efficiently by the propagation of such sharp cracks. Relations between crack speed and energy consumption have been measured, mainly in brittle plastics [2], but have never realistically been calculated. The only full characterization of how things break at the atomic level has been obtained in an ideal brittle crystal, which is a lattice of atoms in which forces between nearest neighbors rise linearly with separation up to a critical distance, after which they fall immediately to zero. That is, nearby atoms attract each other according to Hooke’s law, until they separate too far, at which point the bond between them instantly snaps. Slepyan [3,4] first showed that cracks in crystals of this type can completely be described analytically. A summary of some of the most important results [5,6] is as follows: (i) Moving cracks can naturally evolve to steady states in which patterns of atomic motion repeat indefinitely, and the crack leaves behind atomically flat surfaces. (ii) Cracks in steady state emit surface phonons whose phase velocity equals the crack velocity [3]. (iii) When energy flux to the crack tip falls below a lower critical value, crack motion becomes impossible. This lower critical value is larger than the value one would deduce from considering energy conservation [7], and the minimum allowed crack speed is on the order of 20% of the transverse sound speed, rather than zero. (iv) If energy flux to the crack passes an upper critical value, the tip goes unstable, is no longer atomically sharp, and the system’s dynamical behavior rapidly becomes very complex. These qualitative findings have been limited to the very special models that could be solved by hand. There was no persuasive argument that cracks in real materials should behave similarly, no determination whether ideal brittle fracture is a pathological feature of an artificial model, or whether it is a broad universality class. We therefore decided to check how much of the scenario would be preserved in three-dimensional molecular dynamics simulations of silicon, employing realistic twoand three-