Density functional theory study of the geometry, energetics, and reconstruction process of Si(111) surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3 × 3 to 9 × 9 dimer-adatom-stacking fault (DAS) structures. These calculations used the Perdew-Burke-Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7 × 7 structure, with a surface energy of 1.044 eV/1 × 1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1 × 1 structure. We obtain an energy barrier at the 2 × 2 cell size and confirm that the 7 × 7 regular stage of the SSC model (corresponding to the DAS 7 × 7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si(111) 1 × 1 surface.