Multiparadigm Modeling of Dynamical Crack Propagation in Silicon Using a Reactive Force Field

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100 000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations.

Figure 1

The interpolation method for defining a mixed Hamiltonian in the transition region between two paradigms. As an alternative to the linear interpolation we have also implemented the smooth sinusoidal function.

Figure 2

Geometry used for simulating mode I fracture in silicon. The systems contain between 13 000 and 113 015 atoms with $L_x\approx 550\AA$ and $L_y\approx 910\AA$.We can treat up to 3000 atoms with ReaxFF in ${\Omega }_{\mathbf{r}\mathbf{x}}$.

Figure 3

Crack propagation with a pure Tersoff potential (a) and the hybrid ReaxFF-Tersoff model (b) along the $[110]$ direction (energy minimization scheme). The blue regions are Tersoff atoms, the red regions are reactive atoms. The systems contain 28 000 atoms with $L_x\approx 270\AA \times L_y\approx 460\AA$. Subplot (c) shows the difference in large-strain behavior between Tersoff and ReaxFF. Both descriptions coincide at small strain.

Figure 4

(a) Crack dynamics along the $[110]$ direction at finite temperature ($T\approx 300\mathrm{K}$), 10% strain applied. (b) The same crack orientation, but 20% strain applied. (c) Crack dynamics along the $[100]$ direction at finite temperature ($T\approx 300\mathrm{K}$, 10% strain applied). Shortly after nucleation of the primary crack two branches develop along $[110]$ directions. The systems contain about 64 000 atoms and $L_x\approx 350\AA \times L_y\approx 700\AA$.

Figure 5

Crack dynamics in silicon without  (a) and with ${\mathrm{O}}_2$ molecules (b). The gray regions are Tersoff atoms, whereas the colored regions correspond to ReaxFF atoms. The systems contain about 13 000 atoms, with $L_x\approx 160\AA \times L_y\approx 310\AA$.