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The 7\times7 reconstruction of the Si(111) surface represents arguably themost fascinating surface reconstruction so far observed in nature. Yet, theatomistic mechanism underpinning its formation remains unclear after it wasdiscovered sixty years ago. Experimentally, it is observed post priori so thatanalysis of its formation mechanism can only be carried out in analogy witharchaeology. Theoretically, density-functional-theory (DFT) correctly predictsthe Si(111)-(7\times7) ground state but is impractical to simulate itsformation process; while empirical potentials failed to produce it as theground state. Developing an artificial neural-network potential of DFT quality,we carried out accurate large-scale simulations to unravel the formation of theSi(111)-(7\times7) surface. We reveal a possible step-mediated atom-poprate-limiting process that triggers massive non-conserved atomicrearrangements, most remarkably, a critical process of collective vacancydiffusion that mediates a sequence of selective dimer, corner-hole, stackingfault and dimer-line pattern formation, to fulfill the 7\times7 reconstruction.Our findings may not only solve the long-standing mystery of this famoussurface reconstruction but also illustrate the power of machine learning instudying complex structures.

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