Three-dimensional phase field modelling of twin nucleation during directional solidification of multi-crystalline silicon

Jhang, J. W.; Lan, C.W.

doi:10.1016/j.jcrysgro.2019.05.018

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…Other approaches that track the interface evolution implicitly, like phase field models, are also used to model crystal growth [10]. However, they are better suited to model phase transition at the microscopic level based on thermodynamic considerations, like dendrite growth and phase boundaries [11,12].…”

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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Section: Introductionmentioning

confidence: 99%

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

Noronha¹,

Ydstie²

2021

Preprint

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“…Various numerical methods have been used to model polycrystalline silicon growth during directional solidification. Lan and co-authors [16,17] have performed three-dimensional (3D) phase field computations considering highly anisotropic interfacial energy and kinetic coefficients. They evidenced the formation of {111} faceted interfaces at the grain boundaries during growth as commonly observed experimentally.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional cellular automaton modeling of silicon crystallization with grains in twin relationships

et al. 2020

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A three-dimensional model is proposed to simulate the grain structure in directionally solidified silicon. This includes the nucleation and growth of grains in twin relationship whose formation is very frequent during silicon solidification. Based on analyses of in-situ and real-time observations of the crystallization front, a three-dimensional cellular automaton method is developed to model the dynamic of {111} facets, groove formation at grain boundaries, nucleation and growth of grains in twin relationship. The model is applied to well-characterized experiments assuming the frozen temperature approximation. A comparison of solidification sequences, crystallographic orientation maps, and coincidence site lattice maps in both experiment and simulation results is achieved. Results demonstrate that the model could be applied to optimize crystallization processes for both polycrystalline and cast-mono silicon fabrication processes.

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The role of crystal orientation and grain boundaries in the cavitation resistance of EN 1.4301 austenitic stainless steel: An EBSD study

Stella

Pohl

2021

Wear

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Three-dimensional phase field modelling of twin nucleation during directional solidification of multi-crystalline silicon

Cited by 3 publications

References 25 publications

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

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

Three-dimensional cellular automaton modeling of silicon crystallization with grains in twin relationships

The role of crystal orientation and grain boundaries in the cavitation resistance of EN 1.4301 austenitic stainless steel: An EBSD study

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