Atomistic Mechanism Underlying the Si(111)-(7\times7) Surface Reconstruction Revealed by Artificial Neural-network Potential

The 7\times7 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 Si(111)-(7\times7) 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 Si(111)-(7\times7) surface. We reveal a possible step-mediated atom-pop rate-limiting process that triggers massive non-conserved 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\times7 reconstruction. Our findings may not only solve the long-standing mystery of this famous surface reconstruction but also illustrate the power of machine learning in studying complex structures.