Coupled-flux nucleation modeling of oxygen precipitation in silicon

Experimental data for oxygen precipitation densities in Czochralski-grown s ilicon following multistep annealing treatments are compared with predictio ns from a coupled-flux model for time-dependent nucleation. This is a more correct model for diffusion-controlled nucleation processes than is the cla ssical theory of nucleation since it directly couples the two stochastic fl uxes of interfacial attachment and long-range diffusion. Quantitative agree ment is obtained between the measured and calculated densities for nucleati on temperatures greater than 650 degrees C. Good agreement is obtained for lower temperatures if the oxygen diffusion rate is taken to be larger than is predicted from high-temperature diffusion data. The fit values for the d iffusion coefficient from the nucleation data are in good agreement with re cent results from dislocation-unlocking experiments. The oxygen loss calcul ated by coupled-flux nucleation and diffusion-limited growth agrees with th e experimental observations. Classical theory nucleation calculations predi ct a much greater oxygen loss, signaling the failure of the theory to corre ctly treat nucleation when long-range diffusion is important, true in most solid-state precipitation processes. (C) 2000 American Institute of Physics . [S0021-8979(00)00921-X].