The coarsening and annihilation kinetics of dislocation loop

Burton, B.; Speight, M.V.

doi:10.1080/01418618608242839

Cited by 71 publications

(84 citation statements)

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“…critical radius. The dislocation loops with a radius of crit R R > become bigger in size at the coalescence stage, while small dislocation loops with a radius of crit R R < will dissolve [28,29]. The growth of dislocation loop in course of consequent as grown silicon crystal' cooling occurs both due to the dissolution of small loops with the sizes less than critical, and the oversaturation of silicon self-interstitials.…”

Section: Algorithm For the Formation Of Dislocation Loopsmentioning

confidence: 99%

“…We have shown earlier that at the stage of growth and coalescence of precipitates their concentration is the function of the crystal cooling time [18]. Then, the loop concentration depends on the crystal cooling time [29]:…”

Section: Algorithm For the Formation Of Dislocation Loopsmentioning

confidence: 99%

“…Increase in the radius of interstitial dislocation loop can be defined by the formula depending on the crystal cooling time [29]:…”

Section: Algorithm For the Formation Of Dislocation Loopsmentioning

confidence: 99%

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Algorithm for Calculating the Initial Defect Structure of Semiconductor Silicon

Talanin¹

2017

EAS

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An algorithm for calculating the defect structure of semiconductor silicon crystals was proposed. The proposed approach makes it possible to calculate the sizes, distribution densities of grown-in microdefects at any point of the crystal. Calculations are performed by using and analyzing the thermal conditions of crystal growth in the temperature range from 1683 K to 300 K. The algorithm flowchart is given.

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Section: Algorithm For the Formation Of Dislocation Loopsmentioning

confidence: 99%

Section: Algorithm For the Formation Of Dislocation Loopsmentioning

confidence: 99%

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Algorithm for Calculating the Initial Defect Structure of Semiconductor Silicon

Talanin¹

2017

EAS

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“…The dislocation loops with a radius of crit RR > become bigger in size at the coalescence stage, while small dislocation loops with a radius of crit RR < will dissolve (Bonafos et al, 1998;Burton & Speight, 1985). The growth of dislocation loops during cooling after the growth of single crystal silicon occurs as due to dissolution of small loops with sizes less than critical, and as a result supersaturation for intrinsic interstitial silicon atoms.…”

Section: ≥+mentioning

confidence: 99%

“…In conditions of cooling the crystal after being grown, we presume that the diffusion processes play a core role. The model (Burton & Speight, 1985) is further used in the calculations for evolution in size-dependant distribution of loops and for evolution in loop density.…”

Section: ≥+mentioning

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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