Oxygen precipitation in silicon: Experimental studies and theoretical investigations within the classical theory of nucleation

Quantitative measurements of the oxygen precipitate rate as a function of annealing were made in Czochralski-grown silicon wafers that contained different initial concentrations of oxygen. All wafers were annealed at 1000 °C for 15 min to ensure that the initial cluster-size distributions were identical in all samples of the same composition prior to the multi-step annealing treatments used for the precipitation studies. The experimental data are compared with numerical predictions for time-dependent nucleation within the classical theory of nucleation. Quantitative agreement is obtained between the measured and calculated densities of oxygen precipitates for nucleation temperatures greater than 600 °C, but only over a narrow range of oxygen composition. Below 600 °C, the measured density for all samples is orders of magnitude larger than is predicted from the model. Further, the measured data show an anomalously small temperature dependence for the induction time for nucleation that does not scale with the diffusion coefficient, as expected from the classical theory of nucleation. Fundamentally, the classical theory of nucleation cannot explain the time-dependent nucleation of oxygen precipitates for temperatures below 650 °C. A possible reason is given.