Atomistic Mechanism Underlying the $\mathrm{Si}(111)\text{−}(7\times 7)$ Surface Reconstruction Revealed by Artificial Neural-Network Potential

The $7\times 7$ reconstruction of the Si(111) surface represents arguably the most fascinating surface reconstruction so far observed in nature. Yet, the atomistic mechanism underpinning its formation remains unclear after it was discovered sixty years ago. Experimentally, it is observed post priori so that analysis of its formation mechanism can only be carried out in analogy with archaeology. Theoretically, density-functional theory (DFT) correctly predicts the $\mathrm{Si}(111)\text{−}(7\times 7)$ ground state but is impractical to simulate its formation process; while empirical potentials failed to produce it as the ground state. Developing an artificial neural-network potential of DFT quality, we carried out accurate large-scale simulations to unravel the formation of the $\mathrm{Si}(111)\text{−}(7\times 7)$ surface. We reveal a possible step-mediated atom-pop rate-limiting process that triggers massive nonconserved atomic rearrangements, most remarkably, a critical process of collective vacancy diffusion that mediates a sequence of selective dimer, corner-hole, stacking-fault, and dimer-line pattern formation, to fulfill the $7\times 7$ reconstruction. Our findings may not only solve the long-standing mystery of this famous surface reconstruction but they also illustrate the power of machine learning in studying complex structures.

Figure 1

(a) Top (upper panel) and side views (lower panel) of $\mathrm{Si}(111)\text{−}(7\times 7)$ surface unit cell (black-dashed line). Red, yellow, and purple balls represent dimers, adatoms, and rest atoms, respectively. (b) Calculated surface energies of the Si(111) surfaces with a series of DAS reconstructions, in comparison with results of DFT and other potentials, and the latter are extracted from Ref. [19]. The inset is an enlarged plot to better show the comparison between DFT, ANN, and GAP potentials. (c) Illustration of the two main kinetic processes proposed for ($7\times 7$) reconstruction. Process I: step-mediated atom-pop process (indicated by two cyan arrows), which leaves behind a row of vacancies (small blue circles) next to the step. Process II: collective vacancy diffusion (indicated by six purple arrows) toward the center of terrace, converting the surface into the ($7\times 7$) reconstruction consisting of faulted (labeled “F”) and unfaulted (“U”) half unit cells.

Figure 2

(a) and (c) Atom-pop pathways around different steps. Cyan, purple, and wine balls represent the second-layer, third-layer atoms of $1\times 1$ (upper and lower) terrace and the surface-layer atoms of $7\times 7$ upper terrace, respectively. Arrows indicate directions of atom popping or diffusing. Purple arrows indicate the dimerization process. (b) and (d) Energy barriers for the kinetic processes shown by arrows in (a) and (c), respectively, in corresponding colors. Insets show local structures of initial, transition, and final states.

Figure 3

(a) and (b) First and second steps of vacancy diffusion in FHUC, respectively. Black circles indicate the original vacancy positions. Black arrows indicate vacancy diffusion directions and green arrows illustrate surface atoms relaxing to new positions after exchanging with vacancies. VR1(2) and AR1(2) indicate the first (second) row of vacancies and surface atoms next to the step, respectively. Red and blue areas mark the eight-atom and double-five-atom rings, respectively. Purple arrows depict dimerization. (c) Structure resulting from the first and second steps of collective vacancy diffusion. Red and blue trapezoidal frames display the areas within which the vacancies diffused in two steps. Green, brown, and yellow areas mark the corner hole, eight-atom, and double-five-atom rings along the diagonal directions (orange arrow), respectively. (d) Final structure of FHUC. Dark-green area marks the twelve-atom ring forming a corner hole. The inset shows the transition state and energy barrier for vacancy diffusion indicated by arrows in (a), (b).

Figure 4

(a) Vacancy diffusion in UHUC. Gray and yellow areas mark the UHUC and FHUC, respectively. Black circles, black arrows, and green arrows are the same labels as Fig. 3. VR1(2, 3, and 8) and AR1(2 and 7) represent the first (second, third, and eighth) row of vacancies and first (second and seventh) row of atoms next to the step, respectively. The large green arrow indicates the sequential vacancy diffusion processes leading to VR8. (b) Final structure of UHUC. VR8 becomes the “VR1” for the next round of diffusion.