Analysis of the geometry of the growth ridges and correlation to the thermal gradient during growth of silicon crystals by the Czochralski-method

Stockmeier, L.; Kranert, C.; Fischer, Peter; Epelbaum, Boris M.; Reimann, C.; Friеdrich, J.; Raming, G.; Miller, Alfred

doi:10.1016/j.jcrysgro.2019.03.009

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…Based on the measurement results, Voronkovs’ theory of the shape of the growth ridge could be verified. By extending his theory it was possible to calculate the temperature gradient at the growth ridge from its geometrical parameters . Therefore, the measurement of the growth ridge geometry gives an easy, direct experimental access to the thermal conditions, both qualitative and quantitative, at the solid–liquid interface during the Cz but also FZ growth process.…”

Section: Development Of Industrial Singe Crystal Melt Growth Technolomentioning

confidence: 99%

Erlangen—An Important Center of Crystal Growth and Epitaxy: Major Scientific Results and Technological Solutions of the Last Four Decades

Friеdrich

Müller

2019

Crystal Research and Technology

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This article describes the historic development of the Erlangen Crystal GrowthLaboratory CGL from its beginnings in 1974 at the chair of Materials of Electrical Engineering (Department of Material Science) of the University of Erlangen-Nuremberg until its current status as a large department "Materials" of the Erlangen Fraunhofer-Institute for Integrated Systems and Device Technology. Essential developments and scientific achievements in the various fields of crystal growth and epitaxy are presented from the early period until today.

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Section: Development Of Industrial Singe Crystal Melt Growth Technolomentioning

confidence: 99%

Erlangen—An Important Center of Crystal Growth and Epitaxy: Major Scientific Results and Technological Solutions of the Last Four Decades

Friеdrich

Müller

2019

Crystal Research and Technology

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“…The solidification interface makes an angle θ with the free surface. In the case of a faceted growth, θ can be a fixed angle [15,16,17]. The unit normal is uniquely defined everywhere on the interface except at the triple point.…”

Section: Introductionmentioning

confidence: 99%

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces

Noronha¹,

Ydstie²

2021

Preprint

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Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to singularities. To address this problem, we propose a simulation model based on the weak formulation of the Stefan problem. Numerical solutions of the weak Stefan formulation are obtained using the finite volume method. This approach provides an energy conserving discretization scheme that accurately evaluates heat transfer around non-smooth interfaces. We apply the weak formulation to numerically simulate the solidification of silicon in the horizontal ribbon growth process. Results exhibit a limitation on the ribbon's pull speed, which previous classical Stefan models have failed to demonstrate. A comparison of heat transfer between radiation and gas cooling shows that gas cooling increases the pull speed limit for the same amount of heat removed.

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Facet growth and geometry of the growth ridge during dynamic Czochralski processes

Kranert

Raming²,

Miller³

et al. 2021

Journal of Crystal Growth

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Analysis of the geometry of the growth ridges and correlation to the thermal gradient during growth of silicon crystals by the Czochralski-method

Cited by 5 publications

References 9 publications

Erlangen—An Important Center of Crystal Growth and Epitaxy: Major Scientific Results and Technological Solutions of the Last Four Decades

Erlangen—An Important Center of Crystal Growth and Epitaxy: Major Scientific Results and Technological Solutions of the Last Four Decades

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces

Facet growth and geometry of the growth ridge during dynamic Czochralski processes

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