Alloy-assisted deposition of three-dimensional arrays of atomic gold catalyst for crystal growth studies

Large-scale assembly of individual atoms over smooth surfaces is difficult to achieve. A configuration of an atom reservoir, in which individual atoms can be readily extracted, may successfully address this challenge. In this work, we demonstrate that a liquid gold–silicon alloy established in classical vapor–liquid–solid growth can deposit ordered and three-dimensional rings of isolated gold atoms over silicon nanowire sidewalls. We perform ab initio molecular dynamics simulation and unveil a surprising single atomic gold-catalyzed chemical etching of silicon. Experimental verification of this catalytic process in silicon nanowires yields dopant-dependent, massive and ordered 3D grooves with spacing down to ~5 nm. Finally, we use these grooves as self-labeled and ex situ markers to resolve several complex silicon growths, including the formation of nodes, kinks, scale-like interfaces, and curved backbones.


Supplementary Discussion
• Analysis of atomic gold deposition.

Overview
The formation of the parallel line pattern on silicon (Si) nanowires can be explained by a combination of a stick-slip motion that positions the liquid alloy droplet edge and a chemical potential variation that delivers Au.

Stick-slip motion
During the growth of an n-type Si nanowire, the dopant gas phosphine (PH3) decomposes into phosphorus (P) which bonds strongly to Si 1-4 . Additionally, P also interacts robustly with Au species 5 , leading to pinning of the droplet and an energy barrier for unpinning (U). During the nanowire growth, the alloy droplet contact angle is constantly decreasing because the triplephase boundary (TPB) contact line is pinned at the equilibrium or quasi-equilibrium position. During the nanowire growth, the alloy droplet contact angle (θ) is initially decreasing because the TPB is pinned at the sidewall (i.e., 'Stick'). When θ reaches its minimum (θmin), the potential barrier U can subsequently be overcome by the gain in Gibbs free energy (ΔG) upon snapping the TPB to the next equilibrium/quasi-equilibrium position with a contact angle θ0 (i.e., 'Slip'). Because the Si chemical potential near the TPB is proportional to the contact angle, a reduction of θ upon nanowire elongation causes a local drop of μSi,l, and correspondingly a local elevation of Au concentration and Au atom deposition near the TPB. However, unlike traditional droplet stick-slip motions due to either evaporation-induced droplet shrinking or directional droplet movement by external manipulation, the driving force for the current TPB dynamics is the elongation of Si nanowire through a VLS mechanism.
Detailed analysis of the stick-slip motion 6 can be performed based on an interfacial energy consideration. In most of the existing literature on VLS surface energetics, alloy droplet wetting over semiconductor sidewalls were not considered. However, our work revealed that this situation could occur. Specifically, when the TPB randomly shifts leftward and touches the solid sidewall, the droplet may get pinned if there is a strong 'retention' due to the presence of chemical species (in our case, phosphorus, P) over the semiconductor sidewalls (Phase I, Supplementary Fig. 11a).
At any given contact angle θ, the interfacial Gibbs free energy of the Au/Si alloy droplet can be described as lv lv sl sl sl sv where where θ0 is the equilibrium contact angle. Combining Supplementary Eqs. 1 and 2, the Gibbs free energy could be rewritten as lv lv sl lv 0 During nanowire growth, the TPB contact line is assumed to become pinned at its equilibrium/quasi-equilibrium position starting from a certain time point. When the nanowire continues to elongate for an extra length of L, this newly grown segment would cause an increase of the solid/liquid interfacial area by L×d, where d is a geometrical factor at the TPB. The corresponding contact angle of the alloy droplet decreases from θ0 to θ (Phase II, Supplementary Fig. 11b).
The excess Gibbs free energy under the non-equilibrium state is Besides θ, Alv is also a function of d from the geometrical analysis of the alloy droplet shape.
When the excess Gibbs free energy reaches its maximum.
, (5) where U is the pinning energy due to the interaction between Au/Si liquid alloy and solid ntype Si nanowire sidewall, the droplet has enough driving force to overcome the pinning potential barrier so the TPB contact line can jump to its next equilibrium/quasi-equilibrium position (Phase III, Supplementary Fig. 11c) 7 . In general, U should be highly dependent on the chemical environment during the VLS growth. In our case, the higher the PH3 feeding concentration, the higher the amplitude of U as it is related to the interaction between P and Au/Si.

Chemical potential variation
During the above stick-slip motion, Au atoms would be deposited on the Si nanowire sidewall due to contact-angle-dependent Au delivery. This process can be understood by a chemical potential argument.
In a typical Si nanowire growth process, the Gibbs free energy change during the process of Si deposition at TPB can be described as 8 Si where μSi,s and μSi,l are the chemical potentials of Si in the solid nanowire and liquid alloy, respectively, δ is a positive constant that is relevant to the geometry and energy at TPB and displaces a property of a δ-function, θ is the alloy droplet contact angle, NSi is the total number of Si under consideration. The contact angle dependence is introduced due to a force normal to the solid-liquid interface that induced a stress on the nanowire sidewall 8 .
Since the nanowire has a uniform diameter, i.e., there is no radial deposition of Si atoms, therefore ΔGSi=0. Supplementary Eq. 6 can be reorganized to 8 Si,l Si,s sin µ µ δ θ − = .
Within a single oscillation cycle, the contact angle is constantly decreasing from the initial pinning time point, due to the stretching of the liquid alloy droplet by the newly elongated segment. From Supplementary Eq. 7, the chemical potential difference of Si at TPB reaches its maximum at the minimum contact angle, which triggers Au deposition at the solid Si nanowire surface to counterbalance the change of . The extraction of Au atoms from the alloy droplet and their deposition at the TPB may also be facilitated by the strong interaction between P and Au. Finally, since such a chemical potential variation follows a δ-function around the TPB, we therefore only expect Au deposition in the form of lines, instead of patches.