Atomic and electronic structure of diamond(111) surfaces .2. (2x1) and (root 3x root 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 bused 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 rye 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 (2x1) geometry with symmetric, buckled pi-bonded chains (Seiwatz chains) and a pronounced buckling in some of the deeper layers. However, a (root 3x root 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 (2x1) geometry of the surface relative to the (root 3x root 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 (2x1) geometry. A coverage of three H atoms per C atom leads to a complete de-reconstruction and stabilizes the 3db-C(111)-(1x1) surface (which is identical to a 1db-C(111)-(1x1) 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.