Precipitate strain relief via point defect interaction: models for SiO 2 in silicon

Abstract

Precipitation in the solid state is often accompanied by a volume mismatch, creating strain which inhibits precipitation. For the SiO 2 Si system, this strain, if unrelieved, is large enough to prevent precipitation altogether. The strain is usually assumed to be relieved via emission or absorption of point defects. Here, we suggest a model in which only one species of point defect is involved and the emission/absorption relieves the strain only partially. We generate a Gibbs free energy equation in two variables and by monitoring the atom movements during precipitation, are able to derive two relationships: an expression for the critical radius and, more importantly, a direct correlation between strain and point defect supersaturations. We use this approach to study three systems: SiO 2 strain relief via interstitial emission, vacancy absorption and carbon absorption. Finally, the importance of the strain/supersaturation relationship is emphasized by noting its impact upon nucleation rates. Even small point defect supersaturations can eliminate nucleation and must therefore be considered carefully in studies of precipitation.