Point defect and microdefect dynamics in Czochralski-grown silicon: Simulations and analysis of self-consistent models

Silicon single-crystals grown by the Czochralski method contain distributions of microdefects that adversely affect device performance. The research presented here is aimed at demonstrating that observed microdefect distributions and their response to crystal growth operating conditions can be explained with self-consistent, quantitative models of point defect transport, recombination and aggregation during crystal growth. A particularly useful microdefect system for the verification of our approach is the prediction of the Oxidation-Induced Stacking Fault Ring as a function of crystal growth rate and thermal conditions. In careful experiments, Dornberger and von Ammon [1] have shown that the radial position of the OSF-Ring, R-OSF correlates well to a constant value of the ratio of the crystal growth rate, V, to the axial temperature gradient at the melt-solid interface, G(R-OSF), as V/G(R-OSF) = 1.34 x 10(-3) cm(2)/minK at the radial location of the OSF-ring. The model presented here reproduces experimental results and provides a closed form expression for V/G(R-OSF) as a function of point defect thermophysical properties at the melting temperature. The estimate for V/G(R-OSF) presented here is in quantitative agreement with the empirical value in [1].