Geometrical Frustration in Nanowire Growth

Idealized nanowire geometries assume stable sidewalls at right angles to the growth front. Here we report growth simulations that include a mix of nonorthogonal facet orientations, as for Au-catalyzed Si. We compare these with in situ microscopy observations, finding striking correspondences. In both experiments and simulations, there are distinct growth modes that accommodate the lack of right angles in different ways—one through sawtooth-textured sidewalls, the other through a growth front at an angle to the growth axis. Small changes in conditions can reversibly switch the growth between modes. The fundamental differences between these modes have important implications for control of nanowire growth.

Figure 1

(a),(b) Wulff construction of the 2D equilibrium crystal shapes used in simulations. (a) ${\gamma }_{3,\mathrm{vs}}=1.25{\gamma }_{6,\mathrm{vs}}$; 6 thermodynamically stable facet orientations are available, (b) ${\gamma }_{3,\mathrm{vs}}=1.15{\gamma }_{6,\mathrm{vs}}$; 9 stable facets. (c) Simulation with ${\gamma }_{3,\mathrm{vs}}$ as in (a), giving angled wires. (d) Simulation with ${\gamma }_{3,\mathrm{vs}}$ as in (b), giving sawtooth wires. (e) 47 nm-diameter Si nanowire imaged during growth at $645°\mathrm{C}$ and $1.2\times {10}^{-6}\mathrm{Torr}\mathrm{\text{disilane}}+1\times {10}^{-7}\mathrm{Torr}$ oxygen. (f) 220 nm-diameter Si nanowire imaged during growth at $600°\mathrm{C}$ and $2\times {10}^{-6}\mathrm{Torr}$ disilane, adapted from 2. The sawtooth structure is not well resolved on the left sidewall, giving a misleading impression that it is smooth as in (d). Both nanowires are viewed in the $[1\overline{1}0]$ direction.

Figure 2

(a) Reversible switching using ${\mathrm{O}}_2$ of a 30 nm-diameter Si nanowire imaged at $700°\mathrm{C}$ and $2\times {10}^{-6}\mathrm{Torr}$ disilane with $2\times {10}^{-7}\mathrm{Torr}$ oxygen added at the times indicated (in minutes; arbitrary zero). Growth changes direction by $\sim 33°$, consistent with switching between $⟨110⟩$ and $⟨111⟩$ directions. The small features on the sidewall are polycrystalline Si that grows on the oxidized surfaces of the wire. (b) Simulation of reversible switching by changing ${\gamma }_{3,\mathrm{vs}}$ between the two values used in Fig. 1.

Figure 3

(a) Simulation of $⟨111⟩$-like wire as in Fig. 1d, but with gradual Au loss. (b) Si nanowire imaged after growth at $575°\mathrm{C}$ and $1\times {10}^{-6}\mathrm{Torr}$ disilane. (c) Simulation of angled wire as in Fig. 1c, with gradual Au loss. Arrows indicate the discrete jogs. (d) Si nanowire imaged during growth at $575°\mathrm{C}$ and $1\times {10}^{-6}\mathrm{Torr}\mathrm{\text{disilane}}+1\times {10}^{-7}\mathrm{Torr}$ oxygen. (e) Simulation of angled wire with gradual Au gain. Arrows indicate the discrete jogs. (f) Si nanowire imaged during growth under the same conditions as (d). The dark bands are extended defects consistent with multiple twinning.

Figure 4

(a),(b) Final shape of a $⟨111⟩$ wire whose catalyst has shrunk away due to Au diffusion during growth. Growth conditions in simulation (a) and experiment (b) are as in Figs. 3a, 3b respectively. Arrows highlight the last three “sawteeth” before the extended $\{111\}$ facet. (c),(d) Final shape of a $⟨111⟩$ wire in simulation (c) and experiment (d), where growth was stopped without changing temperature, so Au continued to diffuse away. In (c), the top surface appears smooth but is composed of tiny facets from the allowed set.