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.

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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.

Injection-dependent minority carrier lifetime measurements are a valuable characterisation method for semiconductor materials, particularly those for photovoltaic applications. For a sample containing defects which obey Shockley-Read-Hall statistics, it is possible to use such measurements to determine (i) the location of energy levels within the band-gap and (ii) the ratios of the capture coefficients for electrons and holes. In this paper, we discuss a convenient methodology for determining these parameters from lifetime data. Minority carrier lifetime is expressed as a linear function of the ratio of the total electron concentration to the total hole concentration for p-type (or vice versa for n-type) material. When this is plotted on linear scales, a single-level Shockley-Read-Hall centre manifests itself as a straight line. The gradient and intercepts of such a plot can be used to determine recombination parameters. The formulation is particularly instructive when multiple states are recombination-active in a sample. To illustrate this, we consider oxide precipitates in silicon as a case study and analyse lifetime data for a wide variety of p-type and n-type samples as a function of temperature. We fit the data using both a single two-level defect and two independent single-level defects and find the latter can fit the lifetime curves in all cases studied. The first defect is at E V þ 0.22 eV and has a capture coefficient for electrons $157 times greater than that for holes at room temperature. The second defect is at E C À 0.08 eV and has a capture coefficient for holes $1200 times greater than that for electrons at room temperature. We find that the presence of dislocations and stacking faults around the precipitates acts to increase the density of both states without introducing new levels. Using the analysis method described, we present a parameterisation of the minority carrier lifetime in silicon containing oxide precipitates. V