Dynamics of point defects and formation of microdefects in Czochralski crystal growth: Modeling, simulation and experiments

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 the 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 diffusion-limited growth of the nucleated precipitates is assumed. The microdefect distribution at any given location is captured on the basis of the formation history of nuclei. The microdefect type and size distributions in crystals grown under steady state as well as unsteady state are predicted. The surface energies for voids and interstitial clusters are determined using experimental results. The model predictions agree very well with the experimental results. Various predictions of the model are presented and the results are discussed.