Interstitial oxygen precipitates in silicon during thermal treatment. The amount precipitated increases in an S-shaped fashion as a function of increasing initial interstitial oxygen concentration. A likely hypothesis for this behavior is that the number of nucleation sites that develop into precipitates (successful sites) varies with the initial interstitial oxygen concentration as well as with the precipitation rate at each site. In this paper, a deterministic precipitate growth model is first used to show that a fit to the present data requires the precipitate density to increase by more than a factor of 10 when the oxygen concentration goes from 24 to 40 ppma.
Three-dimensional Monte Carlo calculations are then used to show how the nucleation site survival probability depends on the initial number of oxygen atoms at the site and the oxygen concentration. The program treats oxygen diffusion, growth at nucleation sites by the addition of oxygen atoms, and loss at nucleation sites by the escape of oxygen atoms.