Modeling Microdefect Formation in Czochralski Silicon

Abstract

An internally consistent model is presented for the dynamic formation of microdefects in single‐crystal silicon. The model is built on the dynamics of point defects, vacancies and self‐interstitials, and is extended to include the growth of clusters of these point defects into microdefects. A hybrid finite‐element/finite‐difference numerical method is used to solve the coupled system of partial differential equations, which includes sets of discrete rate equations for small clusters and Fokker‐Planck equations for larger ones. As described previously by a point defect dynamics model [J. Electrochem. Soc., 145, 303 (1998)], 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 . Simulations are used to explore the formation of voids in the vacancy‐rich region inside the OSF‐ring. Predictions of the total concentration of observable voids and the dependence of this concentration on the cooling rate agree with experiments and point to the importance of the 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 number of voids correlates with V 〈G〉 where 〈G〉 is a measure of the temperature gradient in the temperature range 1173 K ≤ T ≤ 1685 K. The appearance of the OSF‐ring is explained qualitatively in terms of the residual vacancy concentration remaining in the crystal after aggregation has ceased. © 1999 The Electrochemical Society. All rights reserved.