Displacement-threshold energies in Si calculated by molecular dynamics

Molecular-dynamics calculations of simple defect production in bulk Si are reported. The Tersoff three-body potential-energy function is used to provide a realistic lattice-atom interaction potential. The displacement-threshold energy ${\mathit{E}}_{\mathit{d}}$ is calculated as a function of the initial primary knock-on momentum direction, and the formation energies for resulting defect structures are obtained. In addition, we determine the effect of the vacancy-interstitial separation on the anisotropy in ${\mathit{E}}_{\mathit{d}}$, where the criterion for stable Frenkel-pair defect formation is assumed to require a certain minimum separation. The resultant angular dependent ${\mathit{E}}_{\mathit{d}}$ versus (θ,φ) is compared with that proposed by Hemment and Stevens (HS) to account for the magnitude and anisotropy of the observed energetic electron-induced radiation damage in Si. The anisotropy of our ${\mathit{E}}_{\mathit{d}}$ surface is consistent with that of HS provided a lower limit of 4 Å is placed on the initial Frenkel-pair separation for the production of long-lived damage. The relatively large formation energy of 8.4 eV which we obtain for such widely separated vacancy-interstitial pairs indicates that the individual point defects are essentially isolated (i.e., noninteracting). More closely spaced vacancy-interstitial complexes are also identified, which have lower formation energies. While it is argued that these complexes are relatively short lived, they may be relevant to dynamical processes such as beam-enhanced molecular-beam epitaxy, atomic mixing at interfaces, and ‘‘subthreshold’’ damage production.