The Role of Holes in Borophenes: An Ab Initio Study of Their Structure and Stability with and without Metal Templates.

An electron-counting strategy starting from magnesium boride was used to show the inevitability of hexagonal holes in 2D borophene. The number (hole density, HD) and distribution of the hexagonal holes determine the binding energy per boron atom in monolayer borophenes. The relationship between binding energy and HD changes dramatically when the borophene is placed on a Ag(111) surface. The distribution of holes in borophenes on Ag(111) surfaces depends on the temperature. DFT calculations show that aside from the previously reported S1 and S2 borophene phases, other polymorphs may also be competitive. Plots of the electron density distribution of the boron sheets suggest that the observed STM image of an S2 phase corresponds to a sheet with a HD of 2/15 instead of a sheet with a HD of 1/5. The hole density and the hole distribution echo the distribution of vacancies and extra occupancies in complex β-rhombohedral boron.