Diffusion–influenced nucleation: a case study of oxygen precipitation in silicon

The classical theory of homogeneous nucleation is an interface–limited theory and does not strictly apply for transformations where long–range diffusion is dominant. A new approach that takes account of the coupled stochastic fluxes of interface attachment and long–range diffusion is presented. Steady–state nucleation rates can be orders of magnitude smaller and the induction times for time–dependent nucleation correspondingly larger than expected from the classical theory. In solute precipitation, the regions of the parent phase near subcritical precipitate clusters are enriched (rather than depleted) in solute. Oxygen precipitation in silicon is chosen to illustrate these features. Measured precipitate densities following multi–step anneals show better agreement with predictions from the coupled–flux model than with those from the classical theory. The kinetics of formation for small oxide clusters and the dependence of their population density on the initial oxygen concentration agree well with data for thermal donor defects.