| Experimental data for oxygen precipitation densities in Czochralski-grown silicon following multistep annealing treatments are compared with predictions from both the classical theory and a new coupled-flux model for time-dependent nucleation. For the classical theory, quantitative agreement is obtained between the measured and calculated densities of oxygen precipitates for nucleation temperatures above 650°C, but fails for lower temperatures. Further, the classical theory does not approach the correct form for the diffusion-limited growth of large clusters. The coupled-flux model is a more correct model for diffusion-controlled nucleation processes since it directly links the two stochastic fluxes of interfacial attachment and long-range diffusion, and goes to the correct limit for large clusters. Quantitative agreement with predictions from the coupled-flux model is again obtained between the measured and calculated densities for nucleation temperatures greater than 650°C. When the effects of an enhanced oxygen diffusion coefficient and the ejection of Si-interstitials to relieve strain are taken into account, quantitative agreement is also obtained for lower temperatures. The justification for a vacancy-enhanced oxygen diffusion coefficient is provided and further confirmed by initial calculation results. |
