Numerical analysis for the dynamics of the oxidation-induced stacking fault in Czochralski-grown silicon crystals

The continuum model of point defect dynamics to predict the concentration of interstitial and vacancy is established by estimating expressions for the thermophysical properties of point defects and the point defect distribution in a silicon crystal and the position of oxidation-induced stacking fault ring (R-OiSF) created during the cooling of crystals in Czochralski silicon growth process are calculated by using the finite element analysis. Temperature distributions in the silicon crystal in an industrial Czochralski growth configuration are measured and compared with finite volume simulation results. These temperature fields obtained from finite volume analysis are used as input data for the calculation of point defect distribution and R-OiSF position. Calculations of continuum point defect distributions predict the transition between vacancy and interstitial dominated precipitations of microdefects as a function of crystal pull rate (V). The dependence of the radius of R-OiSF (R-Oisf) on the crystal length with fixed growth rate for a given hot zone configuration is examined. The R-OiSF is increased with the increase of crystal length. These predictions from point defect dynamics are well agreed with experiments and empirical V/G correlation qualitatively, where G is the axial temperature gradient at the melt/crystal interface.