An effective nucleation rate for oxide precipitation in Czochralski silicon and a simple framework for multi-step anneal calculations

• New nucleation rate expression using experimentally observed plate morphology of oxygen precipitates in silicon.
• Separate treatments of surface and edge interface energy terms in nucleation rate.
• Simple computational framework and comparison against experimental results.

A simple and physically consistent quantitative model of oxide precipitate nucleation in Czochralski-Silicon (Cz-Si) can significantly improve predictions of wafer characteristics during fabrications of semiconductor devices or solar cells. Towards that end, a classical nucleation theory based nucleation rate expression is developed for oxide precipitation in Cz-Si wafers in which vacancy supersaturation is not high. The precipitate morphology is assumed to be thin flat plates. The estimates of critical cluster sizes from new model corroborate the theory that thermal donors or some other embryonic form of oxygen clusters can be precursors of oxide precipitates. The new model predicts effective nucleation rates which are in agreement with previously reported data. The nucleation rates predictions from the new model and diffusion limited growth of precipitate plates of constant thickness are used in a simple framework to calculate precipitate densities after multi-step anneals reported previously in literature. The modeled precipitate densities are found to be in reasonable agreement with corresponding experimental values.