Modeling of point defect formation and dynamics in silicon monocrystal

Vasily A. Zabelin (zabelin-AT-softimpact-DOT-ru.gif), V. V. Kalaev
Soft-Impact Ltd., 27 33 Engelsa st, Saint-Petersburg, 194156, Russia.

High quality monocrystalline silicon now is the main semiconductor for producing integrated circuits. In recent years, crystal homogeneity and microstructure properties have become very important with respect to the improvement of technological process. Transition of the chip integration level to less then 0.13 scale makes crystal lattice defects critical for chip yield. Numerical model of crystal growth by the Czochralski technique has been developed[1]. For crystals grown by the CZ method, the primary imperfections are point defects (voids and oxygen precipitates), which form during crystal growth and further thermal treatment. Crystal growth is very complex process and fine prediction of thermal field and impurity concentration is needed for investigating defect interaction in the crystal during growth. The model of initial defect (vacancy, self-interstitial and impurity atoms) incorporation over the melt/crystal interface has been developed, providing spatial distribution of initial defect concentrations. Initial defect supersaturation during crystal cooling leads to formation of void and oxygen precipitate nucleus in the vacancy-reach zone of the crystal and growth of existing clusters[2,3]. We present the physical and numerical model of point defect clusterization and growth kinetics. This model based on homogeneous nucleation theory and diffusion limited growth described by the Fokker-Planck equation. Point defect concentration and size distribution function for different crystal growth conditions have been obtained. These models can be used for the prediction of point defect properties and optimization of growth process for producing crystals with specified quality.

References:
  1. V. V. Kalaev, V. A. Zabelin, Solid State Phenomena, vol. 82-84, p.41 (2002).
  2. V. V. Voronkov R. Falster, J. Cryst. Growth, vol. 194 p.76 (1998).
  3. T. Sinno, R. Brown, J. Elecrochem. Soc, vol. 146 p.2300 (1999).