**2. Classification of grown-in microdefects**

Currently, there are three classifications of grown-in microdefects: experimental classification, technological classification and physical classification.

Experimental classification of grown-in microdefects is based on the use of methods of selective etching, X-ray topography and transmission electron microscopy (Kock, 1970; Petroff & Kock, 1975; Foll & Kolbesen, 1975; Veselovskaya et al., 1977; Sitnikova et al., 1984; Sitnikova at al., 1985). A.J.R. de Kock entered the name of A-microdefects and Bmicrodefects, whereas Е.G. Sheikhet entered the name C-microdefects, D-microdefects. We are entered the name (I+V)-microdefects (V.I.Talanin et al., 2002a, 2002b). These research allowed to establish the physical nature of A-microdefects, B-microdefects, C-microdefects, D-microdefects and (I+V)-microdefects. Experimental results indicated the identity of the processes of defect formation in crystals of FZ-Si and CZ-Si (Kock et al., 1979; V.I. Talanin & I.E. Talanin, 2003). This means that the classifications of grown-in microdefects in both types of crystals should also be identical (V.I. Talanin & I.E. Talanin, 2004).

Technological classification is used for large-scale crystals. The larger the diameter of the growing crystal, the lower growth rate, at which the same type of grown-in microdefects is formed. This occurs by reducing the axial temperature gradient in the crystal (Ammon et al., 1999). This leads to the appearance of a new type of grown-in microdefects (microvoids) and dislocation-free crystal growth in a narrow range of growth rates (Voronkov & Falster, 1998). In large crystals of interstitial dislocation loops and microvoids are considered as major grown-in microdefects in dislocation-free silicon crystals (Kulkarni et al., 2004).

Analysis of the experimental results of investigations of grown-in microdefects indicates that there are only three types of grown-in microdefects: precipitates of impurities ((I+V) microdefects, D(C)-microdefects, B-microdefects), dislocation loops (A-microdefects) and microvoids (V.I. Talanin et. al., 2011b). We established that the basic elements of defect formation are primary oxygen-vacancy and carbon-interstitial agglomerates, which are formed at impurity centers near the crystallization front (V.I. Talanin & I.E. Talanin, 2006a).

The Diffusion Model of Grown-In Microdefects Formation

During Crystallization of Dislocation-Free Silicon Single Crystals 623

supersaturated solid solution of point defects; and (viii) the consequence of this symmetry is the formation of vacancy and interstitial grown-in microdefects of the same type and, correspondingly, the growth of dislocation-free Si single crystals in the same vacancy– interstitial mode (V.I. Talanin & I.E. Talanin, 2006b). It was revealed that the growth parameter *Vg*/*G* = ξcrit describes the conditions under which the (111) face appears on the crystallization front (V.I. Talanin & I.E. Talanin, 2006a). On the basis of physical model and concepts of primary and secondary grown-in microdefects we developed of physical

A detailed description of the heterogeneous mechanism formation of grown-in microdefects and its correspondence to the results of experimental researches are presented in the articles

The calculation of the precipitation is carried out within the framework of the classical theory of nucleation, growth and coalescence of precipitates. For the calculation of formation and growth of precipitates are used analytic and approximate calculations. In the case of analytical calculations applied solution of differential equations of the dissociative diffusion (Talanin et al., 2007b, 2008). In the case of approximate calculations, the solution is sought in the form of systems of interconnected discrete differential equations of quasi-chemical reactions to describe the initial stages of nucleation of new phases and a similar system of continuous

The solution is sought within the model of dissociative diffusion–migration of impurities (Bulyarskii & Fistul', 1997). In this case, the difference from the decomposition phenomenon

classification of the grown-in microdefects (V.I. Talanin & I.E. Talanin, 2006a).

Fig. 1. Diffusion model of grown-in microdefects formation

(V.I. Talanin & I.E. Talanin, 2004; V.I. Talanin & I.E. Talanin, 2006a).

differential equations of the Fokker-Planck (V.I. Talanin & I.E. Talanin, 2010a).

**4.1 Model of formation complex "impurity + intrinsic point defect"** 

**4. Diffusion kinetic of high-temperature precipitation** 

An excess concentration of intrinsic point defects (vacancies or silicon self-interstitials) arises when the crystal is cooled under certain thermal conditions (Cho et al., 2006). This process leads to the formation of secondary grown-in microdefects (А-microdefects or microvoids) (V.I. Talanin & I.E. Talanin, 2004). We have proposed the physical classification of grown-in microdefects. It is based on the differences in the physical nature of the formation of primary and secondary grown-in microdefects (V.I. Talanin & I.E. Talanin, 2006a).
