Atomically Smooth Stress-Corrosion Cleavage of a Hydrogen-Implanted Crystal

We present a quantum-accurate multiscale study of how hydrogen-filled discoidal “platelet” defects grow inside a silicon crystal. Dynamical simulations of a 10-nm-diameter platelet reveal that ${\mathrm{H}}_2$ molecules form at its internal surfaces, diffuse, and dissociate at its perimeter, where they both induce and stabilize the breaking up of highly stressed silicon bonds. A buildup of ${\mathrm{H}}_2$ internal pressure is neither needed for nor allowed by this stress-corrosion growth mechanism, at odds with previous models. Slow platelet growth up to micrometric sizes is predicted as a consequence, making atomically smooth crystal cleavage possible in implantation experiments.

Figure 1

(a) Atomistic model of a (100) HIP at the center of a $35\times 35{\mathrm{nm}}^2$ bulk Si model system. One Si cubic primitive cell is repeated along the periodic boundary condition (PBC) $z$ direction (either [001] or $[10\overline{1}]$). The surfaces perpendicular to $x$ and $y$ are instead unconstrained. The LOTF QM region comprises the Si atoms depicted in red and all H atoms. (b) Enlarged picture of a HIP’s left edge. (c) Distribution of the ${\sigma }_{yy}$ component of the atom-resolved stress tensor for the relaxed HIP system. The color palette ranges from red (tension) to blue (compression) and is limited to the stress value interval $-4.0\mathrm{GPa}\le {\sigma }_{yy}\le 4.0\mathrm{GPa}$. (d) Cross sections of ${\sigma }_{yy}$ near the HIP edge for different platelet configurations and orientations. Si-2H and Si-H refer to the dihydride and monohydride HIP surfaces, respectively. V indicates the HIP model obtained by coalescence of hydrogenated vacancies.

Figure 2

Formation of ${\mathrm{H}}_2$ during the dihydride-to-monohydride reconstruction of the HIP surfaces. An unsaturated Si-H group approaches an adjacent doubly hydrogenated Si atom (a), producing an intermediate H-Si-Si-2H structure (b). Later, one of the two H atoms bound to the overcoordinated Si atom desorbs and binds to a H atom of a neighboring Si-2H group, producing a stable H-Si-Si-H dimer, a free ${\mathrm{H}}_2$ molecule, and a novel unsaturated Si-H group (c).

Figure 3

Stress-corrosion mechanism for the HIP’s growth. (a)–(d) Snapshots of the bond-breaking reaction from an 800 K LOTF MD simulation (colors explained in the text). (e) Time evolution of the distance between the Si atoms pictured in red in (a)–(d) (black line). The time axis zero is set to the moment the bond length exceeds 2.8 Å just before bond breaking. The red and green lines refer to additional simulations, where the ${\mathrm{H}}_2$ molecule [blue in (a)–(c)] is removed from the system 180 fs before and 20 fs after the bond-breaking event, respectively. The blue line represents the bond length evolution obtained if the ${\mathrm{H}}_2$ molecule is not removed, but the transfer of the H atom colored in green in (a)–(b) is prevented. (f) Evolution of the density $\rho$ of ${\mathrm{H}}_2$ molecules formed inside the HIP, displayed as a function of the platelet radius $r$ during platelet growth. The horizontal solid line indicates the initial value of the ${\mathrm{H}}_2$ density ${\rho }_0$. The right-hand vertical axis coordinate is scaled so that the HIP radial velocity for $\xi ={10}^9\mathrm{Hz}$, in $\mathrm{m}{\mathrm{s}}^{-1}$ units, is represented by its corresponding curve.