The $\mathrm{Sn}/\mathrm{Si}\left(111\right)-(\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ surface, a 2D Mott insulator, has long been predicted and then found experimentally to metallize and even turn superconducting upon boron doping. To clarify the structural, spectroscopic, and theoretical details of that evolution, here we present angle resolved photoemission spectra data supplementing morphology and scanning tunneling measurements. These combined experimental results are compared with predictions from a variety of electronic structure approaches, mostly density functional $\mathrm{DFT}+U$, but not neglecting Mott-Hubbard models, both ordered and disordered. These theoretical pictures address different spectroscopic aspects, including the 2D Fermi surface, the Hubbard bands, etc. While no single picture accounts for all observations at once, the emergent hypothesis compatible with all data is that metallization arises from sub-subsurface boron doping, alternatively to the main standard subsurface boron geometry that would leave the surface insulating. These results advance the indispensable frame for the further understanding of this fascinating system.

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• Antiferromagnetism
• Doping effects
• Electronic structure
• First-principles calculations
• Monolayer films
• Surfaces
• Angle-resolved photoemission spectroscopy
• Density functional calculations
• Extended Hubbard model
• Mean field theory
• Scanning tunneling microscopy
• Scanning tunneling spectroscopy
• Tight-binding model
• X-ray photoelectron spectroscopy