Dynamic three-dimensional simulation of facet formation and segregation in Bridgman crystal growth

Lan, C.W.; Chen, C.J.

doi:10.1016/j.jcrysgro.2006.11.333

Cited by 11 publications

(6 citation statements)

References 20 publications

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“…Successful modeling of facetted interface shapes by 3D simulations was very recently reported at the 5 th Int. Workshop on Modeling in Crystal growth (2006) by Lan et al [19].…”

Section: Facetted Growth Interfacementioning

confidence: 99%

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

Müller

2007

Cryst. Res. Technol.

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The Czochralski method, i.e. pulling a crystal from the melt, became the most important technology for the production of large semiconductor (Si, GaAs, InP, GaP …) and optical crystals (oxides, CaF 2 …). The present status is achieved by a profound analysis of the mechanisms of heat and species transport which are relevant for the stability of the Czochralski growth process and the performance of the growing crystal. It was clearly demonstrated in the last few years that modeling by numerical simulation is an indispensable tool to analyze the Czochralski process and to understand the governing mechanisms. The contribution presents examples of this kind of modeling the Czochralski technique in correlation with experimental investigations in order to illustrate the present status of understanding relevant processing phenomena. Furthermore, it is shown what problems need still to be solved in the future in order to further improve the yield and quality of Czochralski-grown crystals.

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“…Successful modeling of facetted interface shapes by 3D simulations was very recently reported at the 5 th Int. Workshop on Modeling in Crystal growth (2006) by Lan et al [19].…”

Section: Facetted Growth Interfacementioning

confidence: 99%

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

Müller

2007

Cryst. Res. Technol.

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“…Facet formation has an adverse effects on the stress distribution and the dopant segregation near the singular edges, which reduces the crystal quality. To predict and control the facet formation, many numerical models have been proposed . These models can be classified as geometrical and kinetic model approach.…”

Section: Introductionmentioning

confidence: 99%

“…Both transient and quasi‐steady‐state simulations on oxide crystal of facet formation have been studied. Only Lan et al . studied dopant segregation at the facets.…”

Section: Introductionmentioning

confidence: 99%

Transient Simulation of Dopant Segregation at Facets During Growth of Nd:YAG Crystal

2017

Crystal Research and Technology

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Numerical simulation of faceting and dopant segregation for vertical Bridgman growth of Nd:YAG is presented. The numerical scheme for the interface tracking considers the coupling between kinetic model and thermal transport. Dopant distributes inhomogeneously at the radial direction of the crystal/melt interface and piles up in front of the interface near the crucible. The dopant concentration of faceted portions of the crystal/melt interface is higher than that of unfaceted surface. Effect of natural convection on dopant segregation at facets is studied. The dopant boundary layer thickness decreases with the enhancement of the natural convection. The scaling analysis of the dopant boundary layer thickness for facet surface is obtained. Conflict of InterestThe author has declared no conflict of interest.

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“…Measures to improve performance were either ineffective, such as reordering the equations, or too expensive, notably increasing the size of the Krylov space used in GMRES. We note that other researchers attempting to solve such Stefan-like problems in three dimensions have also resorted to a decoupled solution strategy [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A Schur complement formulation for solving free-boundary, Stefan problems of phase change

Lun

Yeckel

Derby

2010

Journal of Computational Physics

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Dynamic three-dimensional simulation of facet formation and segregation in Bridgman crystal growth

Cited by 11 publications

References 20 publications

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

Transient Simulation of Dopant Segregation at Facets During Growth of Nd:YAG Crystal

A Schur complement formulation for solving free-boundary, Stefan problems of phase change

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