The incorporation of intrinsic point defects into a growing crystal is affected by the presence of impurities that can react with vacancies and self-interstitials. The critical value of the ratio of the growth rate, V, to the axial temperature gradient, G, ͑V/G ratio͒ that separates the interstitial growth mode from the vacancy growth mode, is shifted by impurities, and this effect can be described by simple analytical expressions. Some impurities, such as oxygen, nitrogen, and hydrogen, trap vacancies and cause a downward shift in the critical V/G ratio ͑and also a fast increase in the fraction of trapped vacancies, on lowering T͒. Other impurities, like carbon, trap self-interstitials, and cause an upward shift in the critical V/G ratio ͑and also an increase in the fraction of impurity interstitials, on lowering T͒. The impurities affect both the incorporation and agglomeration stages of microdefect production.
Most common microdefects in Czochralski silicon, voids and dislocation loops, are formed by agglomeration of point defects, vacancies, and self-interstitials, respectively. Dynamics of formation and growth of the microdefects along with the entire crystal pulling process is simulated. The Frenkel reaction, the transport and nucleation of the point defects, and the growth of the microdefects are considered to occur simultaneously. The nucleation is modeled using the classical nucleation theory. The microdefects are approximated as spherical clusters, which grow by a diffusion-limited kinetics. The microdefect distribution at any given location is captured on the basis of the formation and path histories of the clusters. The microdefect type and size distributions in crystals grown under various steady states as well as unsteady states are predicted. The developed one-dimensional model captures the salient features of defect dynamics and reveals significant differences between the steady-state defect dynamics and the unsteady-state defect dynamics. The model predictions agree very well with the experimental observations. Various predictions of the model are presented, and results are discussed.
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