Simplistic approach for 2D grown‐in microdefect modeling

Prostomolotov, A. I.; Verezub, N. A.

doi:10.1002/pssc.200881439

Cited by 4 publications

(5 citation statements)

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“…The computer model takes into account the vacancy -selfinterstitial recombination, diffusion and vacancy cluster formation. Our two-dimensional formulation [8,10] was elaborated with the use of one-dimensional approach [11]. The analysis of axial temperature profiles in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…In the present work the two-dimensional model of the vacancyinterstitial kinetics [10] was considered by taking into account the vacancy cluster formation [8]. The solution was obtained by calculating time-spatial change of C v and C i concentrations, vacancy cluster density N v and its average radius oR v 4 .…”

Section: Numerical Approachmentioning

confidence: 99%

“…Therefore in the current study, this model was applied with Robbin's boundary conditions. Moreover, the model was updated, taking into account the vacancy cluster formation [8]. A defect structure of Si wafers subjected to RTA and subsequent multistep thermal annealing was investigated experimentally.…”

Section: Introductionmentioning

confidence: 99%

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Thermal optimization of CZ bulk growth and wafer annealing for crystalline dislocation-free silicon

Prostomolotov

Verezub

Mezhennii

et al. 2011

Journal of Crystal Growth

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Approachmentioning

confidence: 99%

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Thermal optimization of CZ bulk growth and wafer annealing for crystalline dislocation-free silicon

Prostomolotov

Verezub

Mezhennii

et al. 2011

Journal of Crystal Growth

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“…al., 2001;Wang & Brown, 2001;Kulkarni et. al., 2004;Kulkarni, 2005;Prostomolotov & Verezub, 2009). The rigorous model requires the solution to integrodifferential equations for point defect concentration fields, and the distribution of grown-in microdefects in this model is a function of the coordinates, the time, and the time of evolution of the size distribution of microdefects.…”

Section: Introductionmentioning

confidence: 99%

Advances in Crystallization Processes

2012

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He obtained his B.Sc in physical chemistry from Bar-Ilan University in 1989 and received his PhD from the Weizmann Institute of Science with Prof. Gary Hodes on nanomaterials synthesis (1999). He then went to the Max Planck institute of colloids and interfaces for 3 years, as postdoctoral fellow to work with Prof. M. Antonietti and Prof. H Cölfen on biomimetic chemistry and chiral polymers. In 2003 joined the staff of the chemistry department at Bar-Ilan University, where he is currently a Professor at the institute of nanotechnology at Bar-Ilan University leading the nano chirality laboratory. Prof. Mastai's earlier interests included nanomaterials synthesis and characterization. His current research is focused on the synthesis and analysis of chiral nanosurfaces, chiral self-assembled monolayers and polymeric chiral nanoparticles. Mastai has published more than 100 scientific articles and book chapters on various aspects of nanomaterials and chirality at the nanoscale.XIV Contents I wish to thank all the authors for their contributions for this book and it is my pleasure to acknowledge the assistance of Ms Vana Persen for her assistance during the write-up of this book and is preparation in final format.Finally I would like to acknowledge my family who has supported me through all the years of doing science. To my wife Dina von Schwarze and to our children Michael, Reut and Noa for their patience and support.

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confidence: 99%

The Diffusion Model of Grown-In Microdefects Formation During Crystallization of Dislocation-Free Silicon Single Crystals

Talanin¹,

Talanin²

2012

Advances in Crystallization Processes

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Advances in Crystallization Processes 612 microvoids as a result of aggregation of vacancies (Goethem et al., 2008;Kulkarni, 2008a). In this physical model, the interaction between the impurities and intrinsic point defects is not considered (Kulkarni et. al., 2004). R e c e n t v e r s i o n s o f t h i s m o d e l h a v e s u g g e s t e d t h a t p a r t o f t h e v a c a n c i e s ( v ) i n t h e temperature range 1683 ... 1373 K, due to the interaction with oxygen (O) and nitrogen (N) impurities, are bound into complexes of the vO, vO 2 , and vN types (Kulkarni 2007;2008b). After the formation of microvoids, the aforementioned complexes grow and take up vacancies. This model has ignored the growth of the complexes by means of the injection of intrinsic interstitial silicon atoms and the interaction of an impurity with intrinsic interstitial silicon atoms (Kulkarni 2007;2008b).In the general case recombination-diffusion model assumes that the process of defect formation in dislocation-free silicon single crystals occurs in four stages: (i) fast recombination of intrinsic point defects near the crystallization front; (ii) the formation in the narrow temperature range 1423...1223 K depending on the value of V g /G microvoids or interstitial dislocation loops; (iii) the formation of oxygen clusters in the temperature range 1223...1023 K; (iv) growth of precipitates as a result of subsequent heat treatments.Recombination-diffusion model is the physical basis for models of the dynamics of point defects. The mathematical model of point defect dynamics in silicon quantitatively explains the homogeneous mechanism of formation of microvoids and dislocation loops. It should be noted that, in the general case, the model of point defect dynamics includes three approximations: rigorous, simplified, and discrete-continuum approaches (Sinno, 1999;Dornberger et. al., 2001;Wang & Brown, 2001;Kulkarni et. al., 2004;Kulkarni, 2005;Prostomolotov & Verezub, 2009). The rigorous model requires the solution to integrodifferential equations for point defect concentration fields, and the distribution of grown-in microdefects in this model is a function of the coordinates, the time, and the time of evolution of the size distribution of microdefects. A high consumption of time and cost for the performance of calculations required the development of a simplified model in which the average defect radius is approximated by the square root of the average defect area. This approximation is taken into account in the additional variable, which is proportional to the total area of the defect surface. The simplified model is effective for calculating the twodimensional distribution of grown-in microdefects. Both models use the classical nucleation theory and suggest the calculation of the formation of stable nuclei and the kinetics of diffusion-limited growth of defects. The discrete-continuum approximation suggests a complex approach: the solution to discrete equations for the smallest defects and the solution to the Fokker-Planck equation for...

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Simplistic approach for 2D grown‐in microdefect modeling

Cited by 4 publications

References 2 publications

Thermal optimization of CZ bulk growth and wafer annealing for crystalline dislocation-free silicon

Thermal optimization of CZ bulk growth and wafer annealing for crystalline dislocation-free silicon

Advances in Crystallization Processes

The Diffusion Model of Grown-In Microdefects Formation During Crystallization of Dislocation-Free Silicon Single Crystals

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