Dynamic stress corrosion cracking in silicon crystal

Abstract

We investigated, experimentally, the stress corrosion cracking (SCC) phenomenon in dynamic cracks propagating on two low energy cleavage systems (LECSs) of silicon crystal, (111)[$11\,\bar{{2}}$] and (110)[$1\,\bar{{1}}\,0$], under air and under Ar at atmospheric pressure. We used our high resolution Coefficients of Thermal Expansion Mismatch (CTEM) method to initiate and propagate the cracks. An important variable in this investigation was the gradient of the energy release rate (ERR) flow to the crack front for unit length of crack advance, $dG_{0}/da$, denoted $\varTheta$, in units of $\hbox {J}/\hbox {m}^{2}/\hbox {mm}$. The CTEM method is capable of manipulating the value of $\varTheta$. When loaded by low ERR gradient, e.g., when $\varTheta <0.5\hbox { J}/\hbox {m}^{2}/\hbox {mm}$, in air, a complex and diverse SCC behavior was revealed; the cleavage energy strongly depends on $\varTheta$, the environment and crystallographic structure. For higher $\varTheta$, the cleavage energy is higher than that at vacuum and remains constant during crack propagation. We further show that at $\varTheta \,0.5\hbox { J}/\hbox {m}^{2}/\hbox {mm}$, the SCC mechanisms vanish for both LECSs, and the cracks initiate and propagate at cleavage energy higher than that in vacuum, or the Griffith barrier of $2\gamma _{\mathrm{s}}$, twice the free surface energy of the cleavage plane. This investigation suggests that the large scatter existing in the literature for the experimental cleavage energies of the current LECSs of silicon crystal and the still existing debate regarding the susceptibility of silicon crystal to SCC, is caused by the different value of $\varTheta$ in the various past experiments. We further suggest that $\varTheta$ should be stated when discussing the quasi static and dynamic cleavage energy of brittle crystals.

Appendix A—The rotated stiffness tensor

{110}<110> cleavage system

The rotated coordinate system for this cleavage system

$$\begin{aligned} x'=[1\bar{{1}}0];\hbox { }y'=[110];\hbox { }z'=[001] \end{aligned}$$

The stiffness tensor obtained from the rotation is,

$$\begin{aligned}&C_{\left( {110} \right) \left[ {1\,\bar{{1}}\,0} \right] } \\&\ =\left[ {{\begin{array}{llllll} {\hbox { }\frac{\hbox {C}_{{11}} \hbox {+C}_{{12}} }{2}\hbox {+C}_{{44}} \hbox { }}&{} {\frac{\hbox {C}_{{11}} +\hbox {C}_{{12}} }{2}-\hbox {C}_{{44}} }&{} {\hbox {C}_{{12}} }&{} {\hbox {0}}&{} \hbox {0}&{} \hbox {0} \\ &{} {\frac{\hbox {C}_{{11}} \hbox {+C}_{{12}} }{2}\hbox {+C}_{{44}} }&{} {\hbox {C}_{{12}} }&{} \hbox {0}&{} \hbox {0}&{} \hbox {0} \\ &{} &{} {\hbox { C}_{{11}} }&{} {\hbox { 0}}&{} \hbox {0}&{} \hbox {0} \\ &{} &{} &{} {\hbox {C}_{{44}} }&{} \hbox {0}&{} \hbox {0} \\ &{} &{} &{} &{} {\hbox {C}_{{44}} }&{} 0 \\ &{} &{} &{} &{} &{} {\frac{\hbox {C}_{{11}} -\hbox {C}_{{12}} }{2}} \\ \end{array} }} \right] \end{aligned}$$

{111}<112> cleavage system

The rotated coordinate system for this cleavage system

$$\begin{aligned} x'=[11\bar{{2}}];y'=[111];z'=[\bar{{1}}10] \end{aligned}$$

The stiffness tensor obtained from the rotation is,

$$\begin{aligned} C_{(111)[11\bar{2}] }= \left[ {{\begin{array}{llllll} {\frac{C_{11} +C_{12} +2\hbox {C}_{{44}} }{2}}&{} {\frac{C_{11} +2C_{12} -2\hbox {C}_{{44}} }{3}}&{} {\frac{C_{11} +5C_{12} -2\hbox {C}_{{44}} }{6}}&{} {\hbox { 0}}&{} {0}&{} {\sqrt{{2}}\frac{C_{11} -C_{12} -2\hbox {C}_{{44}} }{6}} \\ &{} {\frac{C_{11} +2C_{12} +4\hbox {C}_{{44}} }{3}}&{} {\frac{C_{11} +2C_{12} -2\hbox {C}_{{44}} }{3}}&{} {0}&{} {0}&{} {0} \\ &{} &{} {\frac{C_{11} +C_{12} +2\hbox {C}_{{44}} }{2}}&{} {\hbox { 0}}&{} {0}&{} {-\sqrt{{2}}\frac{C_{11} -C_{12} -2\hbox {C}_{{44}} }{6}} \\ &{} &{} &{} {\frac{C_{11} -C_{12} +\hbox {C}_{{44}} }{3}}&{} {-\sqrt{{2}}\frac{C_{11} -C_{12} -2\hbox {C}_{{44}} }{6}}&{} {0} \\ &{} &{} &{} &{} {\frac{C_{11} -C_{12} +2\hbox {C}_{{44}} }{6}}&{} 0 \\ &{} &{} &{} &{} &{} {\frac{C_{11} -C_{12} +\hbox {C}_{{44}} }{3}} \\ \end{array} }} \right] \end{aligned}$$