On the other hand, process modeling of oxygen precipitation in Czochralski-grown (CZ) crystals has been more challenging due to the inherent complexity of oxygen precipitation and its strong coupling to the point defect distributions (e.g. ref. ). Oxygen precipitation is a critically important process because bulk oxide precipitates provide essential gettering, or trapping, sites for metallic atoms that are introduced during wafer processing. It is therefore essential to ensure that these precipitates are present in a wafer before metallic elements are introduced, but also that they are not located at the device-active surface region.
We present a comprehensive continuum model, based on a hybrid Master-Fokker Planck equation formulation, of coupled vacancy aggregation and oxide precipitation. This model is an extension of a recently developed model for vacancy aggregation, which has been demonstrated to provide a quantitatively accurate picture of void formation under a wide range of operating conditions during both crystal growth and wafer annealing . The coupling physics between the oxide precipitation and vacancy aggregation behavior is probed in detail and the model results compared to experimental measurements in both crystal growth and wafer thermal annealing environments. Several model descriptions for oxide precipitation are compared and contrasted.
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