Solid-Phase Silicon Homoepitaxy via Shear-Induced Amorphization and Recrystallization

We study mechanically induced phase transitions at tribological interfaces between silicon crystals using reactive molecular dynamics. The simulations reveal that the interplay between shear-driven amorphization and recrystallization results in an amorphous shear interface with constant thickness. Different shear elastic responses of the two anisotropic crystals can lead to the migration of the amorphous interface normal to the sliding plane, causing the crystal with lowest elastic energy density to grow at the expense of the other one. This triboepitaxial growth can be achieved by crystal misorientation or exploiting elastic finite-size effects, enabling the direct deposition of homoepitaxial silicon nanofilms by a crystalline tip rubbing against a substrate.

Figure 1

Two diamond-cubic Si(110) crystals in relative motion. (a) Interface under normal load $P_n$ before sliding along the $[1\overline{1}0]$ direction with $v=10{\mathrm{ms}}^{-1}$. (b) After shearing at $P_n=8\mathrm{GPa}$ for a sliding distance $s=300\mathrm{nm}$. Blue and gray spheres represent Si atoms in the crystalline and amorphous regions, respectively. (c) $a$-Si thickness $\mathrm{\Delta }h(s,P_n)$ as a function of $s$ for different $P_n$ (dotted line, $P_n=0$). The blue line shows $\mathrm{\Delta }h(s)$ when the initial $P_n^{\text{high}}=9\mathrm{GPa}$ is reduced to $P_n^{\text{low}}=5\mathrm{GPa}$ at $s=200\mathrm{nm}$. (d) Vertical positions $h_1(s)$ and $h_2(s)$ of the two amorphous-crystal interfaces for $P_n=5\mathrm{GPa}$. Amorphous and crystalline regions are gray and blue, respectively. (e) Shearing of differently oriented crystals: The upper crystal slides along the $[1\overline{1}0]$ and the lower crystal (in red) along the [001] direction. (f) $h_1(s)$ and $h_2(s)$ for the system in (e) with $P_n=0$.

Figure 2

Triboepitaxial growth mechanism. (a) Running average of shear stress $\tau$ (black) during the MD simulation in Fig. 1, showing stick-slip instabilities. The horizontal dashed line represents $⟨\tau ⟩$. The green line is the $z$ coordinate of an atom (green sphere) that is transferred from the upper to the lower crystal as a result of triboepitaxy. (b) Potential energy per atom $E$ as a function of $z$ for applied shear stress ${\tau }_q=0$ and ${\tau }_q>0$. (c) Enlargement with vertical dashed lines highlighting the energy levels of the crystals. (d) Elastic energy differences per atom $\mathrm{\Delta }{E}_{\mathrm{el}}$ (green) between the upper and lower crystal when the original sliding direction [Fig. 1] is rotated by an angle α (inset). $\mathrm{\Delta }{E}_{\mathrm{el}}$ is determined by quasistatically shearing either the tribosystem (squares) or two single crystals (circles) and by linear elasticity (diamonds). Black triangles show the time-averaged growth rate of the lower crystal $⟨\xi ⟩$ measured in MD simulations (see definition in the main text).

Figure 3

Triboepitaxy with a finite tip. (a),(b) Snapshots of sliding simulations with tip sizes $l\approx 151\AA$ and $l\approx 53\AA$ at $s\approx 600\mathrm{nm}$ along [001] of the tip and $[1\overline{1}0]$ of the substrate. The horizontal dashed lines indicate the initial position of the interface between tip (blue) and substrate (red). (c) Effective shear modulus $G^{*}(l)$ of the tips. The tip’s width $l$ is shown in the inset along with the surface thickness $b$, which is the thickness of the tip’s surface region in which the elastic response differs from the bulk elastic response, i.e., the response of the infinite tip ($l=\infty$). Black squares denote $G^{*}$ from quasistatic shear deformation. Dashed horizontal lines indicate $G^{*}$ of an infinite substrate ($G_{\text{substrate}}^{*}$) and tip [$G^{*}(\infty )$] and of a tip whose elastic response is completely determined by its surface [$G^{*}(2b)$]. The solid curve shows the interpolation Eq. (1) between bulk and surface modulus. The best fit to the data points is obtained using $b\approx 19.68\AA$ (Supplemental Material [20]). (d) Scheme for an experiment to deposit silicon nanostructures on (110) silicon substrates using (110) tips. High-frequency oscillations with velocity ${\overrightarrow{v}}_{\text{osc}}$ along $[1\overline{1}0]$ of the tip and [001] of the substrate induce triboepitaxial growth. For writing, the tip is slowly translated with a velocity ${\overrightarrow{v}}_{\text{trans}}(t)$ along arbitrary directions, leaving behind a nanocrystalline line with width $w=l+w_{\text{osc}}$, where $w_{\text{osc}}$ is the magnitude of tip oscillation at the contact. Besides the oscillation direction ${\widehat{v}}_{\text{osc}}$, also surface orientation, $l$, and $P_n$ influence triboepitaxial growth (Supplemental Material [20]).