Modeling microdefect formation in Czochralski silicon

An internally consistent model is presented for the dynamic formation of mi crodefects in single-crystal silicon. The model is built on the dynamics of point defects, vacancies and self-interstitials, and is extended to includ e the growth of clusters of these point defects into microdefects. A hybrid finite-element/finite-difference numerical method is used to solve the cou pled system of partial differential equations, which includes sets of discr ete rate equations for small clusters and Fokker-Planck equations for large r ones. As described previously by a point defect dynamics model [J. Electr ochem. Sec., 145, 303 (1998)],(1) the oxidation-induced stacking fault (OSF )-ring position delineates the vacancy-rich region inside from the external interstitial-rich crystal. In Czochralski silicon, the radial position of the OSF-ring correlates well with the expression V/G (R-OSF) = 1.34 X 10(-3 ) cm(2) min(-1) K-1. Simulations are used to explore the formation of voids in the vacancy-rich region inside the OSF-ring. Predictions of the total c oncentration of observable voids and the dependence of this concentration o n the cooling rate agree with experiments and point to the importance of th e axial temperature profile in the crystal from the melting point (1685 K) down to about 1150 K in setting the number and size of voids. The total num ber of voids correlates with V < G > where < G > is a measure of the temper ature gradient in the temperature range 1173 K less than or equal to T less than or equal to 1685 K. The appearance of the OSF-ring is explained quali tatively in terms of the residual vacancy concentration remaining in the cr ystal after aggregation has ceased. (C) 1999 The Electrochemical Society. S 0013-4651(98)07-034-7. All rights reserved.