Bond-order potential for silicon

The tight-binding description of covalent bonding is used to propose a four-level, bond-order potential for elemental silicon. The potential addresses both the $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ bonding and the valence of this $sp$-valent element. The interatomic potential is parametrized using ab initio and experimental data for the diamond cubic, simple cubic, face-centered-cubic, and body-centered-cubic phases of silicon. The bond-order potential for silicon is assessed by comparing the predicted values with other estimates of the cohesive energy, atomic volume, and bulk modulus for the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Sn}$, bc8, st12, and 46 clathrate structures. The potential predicts a melting temperature of $1650\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in good agreement with the experimental value of $1687\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The energetics of various high-symmetry point defect structures and the structure and energetics of small silicon clusters are investigated. The potential also provides a robust description of surface reconstructions; it notably predicts with high fidelity the surface formation energy of the (111) $7\ifmmode\times\else\texttimes\fi{}7$ dimer adatom stacking fault configuration.