Role of Surface Reconstructions in (111) Silicon Fracture

The (111) cleavage in crystalline silicon was investigated by hybrid quantum/classical atomistic simulations showing that its remarkable stability is largely due to asymmetric $\pi$-bonded reconstructions of the cleavage surfaces created by the advancing crack front. Further simulations show that the same reconstructions can induce an asymmetric dynamical response to added shear stress components. This explains why $[2\overline{1}\overline{1}]$ upward steps are much more common than $[\overline{2}11]$ downward steps on (111) cleavage surfaces, while “zigzag” cleavage with alternated (111) and $(11\overline{1})$ facets will still occur in crystal samples fractured under [110] uniaxial loading.

Figure 1

Shear stress field plotted in the $(0\overline{1}1)$ plane for the $\mathrm{Si}(111)[\overline{2}11]$ cracks at the onset of propagation (see text). The color indicates regions of positive (red), and negative (blue) shear stress. Values out of the range [$-0.005\mathrm{MPa}$, $+0.005\mathrm{MPa}$] are plotted in saturated blue (negative) and red (positive) colors. (a) Mode I loading: the arrows in the insets define positive and negative shear stresses. (b) and (c) Mixed mode I-II loading with positive and negative shear, long arrows indicate the directions of the displacements applied on the boundaries.

Figure 2

(a) Snapshot of the transient regime configuration under mode I: U and L identify inequivalent surfaces, arrows indicate the direction of the shear stress in the surface vicinity; (b) and (c) (111) surface reconstructions in the transient regime on the U and L surfaces respectively: bulk terminated structures are on the left, reconstructed surfaces on the right. The arrows indicate the main atomic displacement direction; (d),(e),(f) Snapshots of the second propagation regime in mode I at $G=7.4\mathrm{J}/{\mathrm{m}}^2$; (g),(h),(i) Snapshots of the $[2\overline{1}\overline{1}]$ step formation in the $\mathrm{Si}(111)[\overline{2}11]$ crack system under mixed mode I-II loading ($G=7.6\mathrm{J}/{\mathrm{m}}^2$): the large arrows indicate the displacement corresponding to the applied (negative) shear strain boundary conditions. Inset: view of the L surface reconstructions in the $(1\overline{1}0)$ plane revealing the presence of a $\pi$-bonded chain structure along the $[1\overline{1}0]$ direction. The yellow (light grey) atoms in this picture belong to the classical region.