A self-consistent multicenter local-orbital formalism is used to investigate the total energy and atomic equilibrium positions of several structural models suggested for the $\mathrm{Si}\left(001\right)\mathrm{}$ surface covered by half a monolayer of boron. Density-functional calculations based on the Harris functional approximation for the total energy are performed within the local-density approximation and the pseudopotential method. Localized atomiclike orbitals are used for the expansion of the electronic wave functions, together with the slab supercell description for the surface. We focus on the identification of the structural subunits which form the ordered $c(4\mathrm{}\times 4)$ reconstruction patterns recently observed by scanning-tunneling microscopy (STM). Our calculations favor a structural model which is different than previously proposed geometries. Moreover, the local density of surface states determined for the lowest-energy configuration agrees very well with the corrugation, lateral distribution, and orientation of the protrusions seen in the STM topographs.

• Received 21 August 1997

DOI:https://doi.org/10.1103/PhysRevB.57.9745