Atomic and electronic structure of diamond (111) surfaces II. (2 × 1) and (√3 × √3) reconstructions of the clean and hydrogen-covered three dangling-bond surfaces

We present ab-initio local-density functional calculations of the atomic reconstruction of clean and hydrogen-covered three dangling-bond (3db) diamond (111) surfaces, extending our earlier work on the one dangling-bond surface. The calculations are based on a finite-temperature local-density approximation, optimized ultrasoft pseudopotentials, and an exact calculation of the electronic ground state and Hellmann-Feynman forces before any step in the geometrical optimization of the surface. For the bulk-terminated surfaces we predict a difference of 1.90 eV per atom in the cleavage energies of the 1db and 3db surfaces (also referred to as shuffle- and glide-plane cleavage), i.e. considerably less than expected from a simple bond-scission argument. This difference is further reduced by reconstruction. We find that the clean 3db-C(111) surface reconstructs in a (2 × 1) geometry with symmetric, buckled π-bonded chains (Seiwatz chains) and a pronounced buckling in some of the deeper layers. However, a (√3 × √3) reconstruction with the surface atoms forming slightly buckled trimers is energetically less favourable by only 0.13 eV per atom. Hydrogenation of the surface stabilizes the (2 × 1) geometry of the surface relative to the (√3 × √3) geometry. Deposition of a monolayer of hydrogen reduces the buckling at the surface but does not change the single-chain topology. A hydrogen coverage of two H atoms per surface C atom leads to the formation of parallel rows of C2H4 units arranged again in a (2 × 1) geometry. A coverage of three H atoms per C atom leads to a complete de-reconstruction and stabilizes the 3db-C(111)-(1 × 1) surface (which is identical to a 1db-C(111)-(1 × 1) surface covered with CH3 groups). Our calculations show that at larger values of the hydrogen chemical potential, the strongly hydrogenated 3db surfaces are stabilized over the 1db surface.