About the simulation of primary grown-in microdefects in dislocation-free silicon single-crystal formation

Abstract

A mathematical model of primary grown-in microdefects formation is proposed. The model is built on the basis of the dissociative process of diffusion. Here, we study the interaction patterns between oxygen-vacancy (O + V) and carbon-interstitial (C + I) near the crystallization front in dislocation-free silicon monocrystals grown by float-zone and Czochralski methods. As shown here, the approximate analysis formulas obtained tally with the heterogeneous mechanism of grown-in microdefects formation.Résumé : Nous proposons un modèle mathématique pour la formation des microdéfauts internes primaires. Le modèle se base sur le processus dissociatif de la diffusion. Nous étudions ici les patrons d'interaction entre une lacune d'oxygène (O + V) et le carbone interstitiel (C + I) près du front de cristalisation dans un monocristal de Si sans dislocation croissant par méthodes de flottaison ou de Czochralski. Comme nous le montrons ici, les formules approximatives d'analyse obtenues agréent avec le mécanisme hétérogène de formation des microdéfauts internes.[Traduit par la Rédaction]

Advances in Crystallization Processes

“…For the vacancy and interstitial mechanisms, we consider, respectively, the oxygen+vacancy (O+V) and carbon+interstitial (C +I) interactions. The calculations performed in the framework of approximation of strong complex formation have demonstrated that the edge of the reaction front of the formation of a complex (i.e., the "oxygen+vacancy" and "carbon + self-interstitials" complex) is located at a distance of ~ 3•10 -4 mm from the crystallization front (Talanin et al, 2007b). We have shown that complex formation occurs near the crystallization front.…”

“…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 vacancyinterstitial mode (V.I. Talanin & I.E. Talanin, 2006b).…”

“…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(Talanin et al, , 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 differential equations of the Fokker-Planck (V.I.…”

“…Vas'kin & Uskov are considered the problem of successive diffusion of a component A into a sample singly doped with a component B, taking into account the complex formation at the initial and boundary conditions (Vas'kin & Uskov, 1968). We are conducted similar consideration for our conditions (Talanin et al, 2007b;. Under physical-model conditions (heterogeneous mechanism of grown-in microdefect formation), we assume that the component A is the background impurity (oxygen O or carbon C) and the component B is intrinsic point defects (vacancies V or interstitials I).…”

On the problem of the consistency of the high-temperature precipitation model with the classical nucleation theory

“…Excess intrinsic point defects disappear at sinks whose role in this process is played by uncontrollable (back ground) impurities of oxygen and carbon [1,3]. The calculations performed in the framework of the model of dissociative diffusion-migration of impurities showed that the edge of the reaction front of the for mation of a complex (oxygen-vacancy and carboninterstitial silicon atom) is located at a distance of ~3 × 10 -4 mm from the crystallization front [22]. The results of calculations of the Fokker-Planck partial differential equations confirm that the processes of nucleation occur very rapidly in the vicinity of the crystallization front [8].…”