Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of Si crystals

Evstratov, I. Yu.; Kalaev, V.V.; Zhmakin, Alexander I.; Makarov, Yu.N.; Абрамов, А. Г.; Ivanov, Nikolay; Смирнов, Е. М.; Dornberger, E.; Virbulis, J.; Tomzig, E.; Ammon, Wilfried von

doi:10.1016/s0022-0248(01)01314-8

Cited by 47 publications

(18 citation statements)

References 9 publications

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“…where ef f ¼ þ SGS and l ef f ¼ l þ SGS = SGS , SGS are the turbulence Prandtle numbers, and SGS is calculated using the dynamic Smagorinsky sub-grid scale model [23] …”

Section: Les For the Melt Flow With A Large Volumementioning

confidence: 99%

Computer modeling of crystal growth of silicon for solar cells

Liu

et al. 2011

Front. Energy

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A computer simulator with a global model of heat transfer during crystal growth of Si for solar cells is developed. The convective, conductive, and radiative heat transfers in the furnace are solved together in a coupled manner using the finite volume method. A three-dimensional (3D) global heat transfer model with 3D features is especially made suitable for any crystal growth, while the requirement for computer resources is kept permissible for engineering applications. A structured/unstructured combined mesh scheme is proposed to improve the efficiency and accuracy of the simulation. A dynamic model for the melt-crystal (mc) interface is developed to predict the phase interface behavior in a crystal growth process. Dynamic models for impurities and precipitates are also incorporated into the simulator.Applications of the computer simulator to Czochralski (CZ) growth processes and directional solidification processes of Si crystals for solar cells are introduced. Some typical results, including the turbulent melt flow in a large-scale crucible of a CZ-Si process, the dynamic behaviors of the mc interface, and the transport and distributions of impurities and precipitates, such as oxygen, carbon, and SiC particles, are presented and discussed. The findings show the importance of computer modeling as an effective tool in the analysis and improvement of crystal growth processes and furnace designs for solar Si material.

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“…where ef f ¼ þ SGS and l ef f ¼ l þ SGS = SGS , SGS are the turbulence Prandtle numbers, and SGS is calculated using the dynamic Smagorinsky sub-grid scale model [23] …”

Section: Les For the Melt Flow With A Large Volumementioning

confidence: 99%

Computer modeling of crystal growth of silicon for solar cells

Liu

et al. 2011

Front. Energy

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show abstract

“…Refs. [2][3][4]. Our model simply uses the large velocity in the center, to derive a representation of the enhanced heat transfer due to the real spatial and time variations of that jet.…”

Section: Model Approachmentioning

confidence: 99%

“…Particularly in the center of the melt, large vertical velocity components form a locally fixed jet in 2D axisymmetric simulations. However, as known from DNS, LES and experiments [2][3][4], there is a strong mixing in the subcrystal region, caused by time and spatial fluctuations of the jet. Recent experimental results from a CZ model facility described in Ref.…”

Section: Introductionmentioning

confidence: 95%

Prediction of the growth interface shape in industrial 300mm CZ Si crystal growth

Wetzel¹,

Virbulis

Muižnieks

et al. 2004

Journal of Crystal Growth

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“…LES turbulence modeling for the melt flow in CZ crystal growth systems has been intensively investigated in the last years, and, in calculations, different variations of the Smagorinsky LES model were applied. In [6], a Smagorinsky LES model with wall-function boundary treatment for velocity, temperature, and dopant concentration and a damping function for turbulent viscosity was used. Ref.…”

Section: Introductionmentioning

confidence: 99%