Dissociative Chemisorption of ${\mathrm{O}}_2$ Inducing Stress Corrosion Cracking in Silicon Crystals

Fracture experiments to evaluate the cleavage energy of the $(110)[1\overline{1}0]$ and $(111)[11\overline{2}]$ cleavage systems in silicon at room temperature and humidity give $\text{2}.\text{7}\pm 0.\text{3}$ and $2.2\pm 0.2\mathrm{J}/{\mathrm{m}}^2$, respectively, lower than any previous measurement and inconsistent with density functional theory (DFT) surface energy calculations of 3.46 and $2.88\mathrm{J}/{\mathrm{m}}^2$. However, in an inert gas environment, we measure values of $3.5\pm 0.2$ and $2.9\pm 0.2\mathrm{J}/{\mathrm{m}}^2$, consistent with DFT, that suggest a previously undetected stress corrosion cracking scenario for Si crack initiation in room conditions. This is fully confirmed by hybrid quantum-mechanics–molecular-mechanics calculations.

Figure 1

Experimental fracture: (a) Optical photograph showing the assembly containing the Si specimen glued by epoxy resin to an aluminum loading frame. Confocal microscopy images showing examples of misalignment steps due to (b) offset or (c) tilted precracks. The effect of precrack or physical crack misalignment on the fracture surface of the $(110)[1\overline{1}0]$ system and the energy consumption in cleavage of silicon is demonstrated for well-aligned precrack, where (d) ${\Gamma }_0=2.7\mathrm{J}/{\mathrm{m}}^2$, while for poorly aligned cracks, (e) ${\Gamma }_0=4\mathrm{J}/{\mathrm{m}}^2$. For cracks initiating on the $(111)[11\overline{2}]$ system: a well-aligned precrack, where (f) ${\Gamma }_0=2.2\mathrm{J}/{\mathrm{m}}^2$ and a poorly aligned precrack (g) ${\Gamma }_0=3.9\mathrm{J}/{\mathrm{m}}^2$.

Figure 2

The cleavage energy ${\Gamma }_0$ vs parallel and straight misalignment step height for $(110)[1\overline{1}0]$ [blue (dark gray) marks] and $(111)[11\overline{2}]$ [red (light gray) marks] crack systems of silicon under room conditions (solid circles, labeled $R$) and atmospheric pressure of Ar (solid squares, Ar). The error of ${\Gamma }_0$ was defined by the error in temperature measurements of $\pm 0.1\hspace{0.17em}°\mathrm{C}$ during cleavage, which was used by abaqus to evaluate the range of the ${\Gamma }_0$.

Figure 3

Stress corrosion cracking in the $\mathrm{Si}(110)[1\overline{1}0]$ cleavage system. (a) Model system, colored by principal stress, with red (light gray) regions corresponding to high tensile stress and dark blue (dark gray) regions to zero; the black rectangle shows the region shown in subsequent panels. Crack tip structures obtained by QM-MM geometry optimization with (b) a sharp crack tip and (c) a lower energy blunt crack tip, related to the sharp tip by rotation of bonds $X/X^{\prime }$ and $Y/Y^{\prime }$. Dark blue (dark gray) atoms are treated at the QM level. (d)–(i) Snapshots from QM-MM dynamics showing dissociative chemisorption of two ${\mathrm{O}}_2$ molecules and the resulting crack advance (see the text). Bonds shown are based on time-averaged atomic positions.

Figure 4

Stress corrosion cracking in the $\mathrm{Si}(111)[11\overline{2}]$ fracture system. As in Fig. 3, panels show only the near tip region, treated with QM accuracy. An ${\mathrm{O}}_2$ molecule [red (dark gray) spheres] inserted $1.5\AA$ behind the crack tip (a) immediately dissociates, (b) in this case, forming an ${\mathrm{OH}}^{-}$ radical, and (c) subsequently chemisorbs, leading to crack advance via cleavage of the Si-Si bond labeled (1) at the crack tip. (d) After 0.2 ps, both oxygen atoms are incorporated in stable Si-O-Si bridges.

Figure 5

Analysis of bond breaking and stress concentration in the (a) Si(111) and (b) Si(110) cleavage systems. Red (light gray) and magenta (mid dark gray) lines: O-O distances, increasing during dissociation. Blue (very dark gray) and cyan (very light gray) lines: Si-Si bonds cleaved during crack advance. Green (mid gray) lines: horizontal crack advance, measured by fitting the atom-resolved stress field to the Irwin near-field solution. Advance of the stress field can occur either (a) at the same time as or (b) before Si-Si bond rupture (see the text). Vertical dashed lines correspond to the labeled snapshots illustrated in Figs. 3 and 4.