It was recalled that the ion implantation of Si introduced excess point defects that quickly recombined during annealing to leave net interstitial and vacancy populations. After higher-energy implantation, the separation between interstitials and vacancies was larger. This led to a vacancy-rich region near to the surface and an interstitial-rich region deeper into the bulk. The high supersaturation of vacancies in the near-surface region could lead to their aggregation into vacancy clusters or voids. A continuum model for vacancy clusters was developed here, using discrete cluster sizes. The results of previous atomistic calculations were exploited with regard to the energetics of cluster growth and dissolution. The model was compared with published data for Au in-diffusion after high-energy Si implants. It was found there was good agreement with experimental data, without any tuning of the parameters. However, the model was too complex and computationally expensive to be effectively incorporated into continuum process simulations. The system of discrete rate equations was therefore reduced to a 2-moment model by carefully considering the behavior of the full model under a range of conditions. The parameters of the moment-based model followed from the full model which, in turn, was based upon atomistic calculations. The resultant simple model was found to reproduce Au labelling experiments accurately.

Modelling of Vacancy Cluster Formation in Ion-Implanted Silicon. S.Chakravarthi, S.T.Dunham: Journal of Applied Physics, 2001, 89[9], 4758-63