Series of $(n\times 2)$ Si-rich reconstructions of β-SiC(001):  A prospective atomic wire

We perform ab initio plane wave supercell density-functional calculations on three candidate models of the $(3\mathrm{}\times 2)$ reconstruction of the β-SiC(001) surface. We find that the two-adatom-layer asymmetric-dimer model (TAADM) is unambiguously favored for all reasonable values of the Si chemical potential. We then use structures derived from the TAADM parent to model the silicon lines that are observed when the $(3\mathrm{}\times 2)$ reconstruction is annealed [the $(n\times 2)$ series of reconstructions], using a density-functional tight-binding method. Two stable structures are observed to form, a ground state structure with buckled ad-dimers and a metastable structure with flat ad-dimers. For the $(n\times 2)$ series with $n>~3,$ we find that as we increase n, and so separate the lines, a structural transition for the metastable structure occurs in which the top ad-dimer of the line flattens. We also find that associated with the separation of the lines for the metastable structure is a large decrease in the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO-LUMO) gap, and that the HOMO state becomes quasi-one-dimensional. These properties are qualititatively and quantitatively different from the electronic properties of the original $(3\mathrm{}\times 2)$ reconstruction.