A model has been developed that simulates oxygen precipitation in silicon wafers during high temperature device processing. The approach used to calculate the nucleation and growth of oxygen precipitates is radically different from other approaches presented in the literature. A discrete rate equation representation of nucleation and growth has been transformed into a continuum representation in the form of a partial differential equation. This partial differential equation describing both the statistical clustering of oxygen during nucleation and the diffusion driven transport during precipitate growth is solved continuously starting from crystal growth through any arbitrary time-dependent temperature process.

A new method for the nucleation of oxygen precipitates in Czochralski silicon is described. The temperature is ramped at approximately 100°C/hr from a very low value, near 400°C, to the highest temperature used for subsequent process steps. The technique generates a larger precipitate number density and a greater volume fraction of precipitated oxygen than standard isothermal nucleation anneals. The morphology of the precipitates changes from 0.lum sizéd (100) platelets to small particles unresovable by TEM. The new temperature ramping technique can reduce the time needed for precipitate nucleation by at least a factor of three. The details of oxygen precipitation can be totally controlled by adjusting the temperature ramp rate as a function of time.