Growth/dissolution model for oxygen precipitation based on the kinetics of phase transformations

A model is presented for the growth and dissolution of oxygen precipitates in Czochralski silicon during heat treatment. Growth and dissolution rates are newly derived and inserted into a set of chemical rate equations and a Fokker–Planck equation. It can calculate the size distribution of the oxygen precipitates and oxygen concentration profile without calculation of the interfacial concentrations at the interface of Si matrix and precipitates. It accounts for the oxidizing ambient effect, the solubility enhancement effect of oxygen, and the surface recombination and generation of point defects. The formation of stacking faults is also taken into account. This approach allows one to calculate more accurately the residual oxygen depth profile and the density distribution of oxygen precipitates which can be measured experimentally. By comparing the simulated results with experimental ones, it is proved that this model can be used to estimate the depth profile and the defect densities under inert conditions and oxidation conditions.