Advanced approach for oxygen transport and crystallization front calculation in Cz silicon crystal growth

Borisov, Dmitriy; Artemyev, Vladimir; Kalaev, V.V.; Smirnov, Andrey; Kuliev, A.T.; Zobel, Frank; Kunert, R.; Turan, Raşit; Aydin, O. Isil; Kabaçelik, Ismail

doi:10.1016/j.jcrysgro.2021.126493

Cited by 10 publications

(6 citation statements)

References 16 publications

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“…This model was applied for the calculation of turbulent heat and mass transport in the silicon melt during growth of 200 mm diameter crystals in an EKZ-3500 furnace. [25] We obtained a good agreement of the oxygen concentration level with the experimental data from ref. [25].…”

Section: Introductionsupporting

confidence: 84%

“…[25] We obtained a good agreement of the oxygen concentration level with the experimental data from ref. [25]. However, it was necessary to perform model constants adjustment for different melt heights to obtain the oxygen concentration decrease with the body length of the crystal, which was observed experimentally.…”

Section: Introductionsupporting

confidence: 84%

“…The task formulation can be found in. [ 25 ] The convective terms were approximated with the third‐order accuracy for the momentum and temperature transport equations and with the first‐order accuracy for the turbulence kinetic energy and dissipation rate transport equations. Approximation of diffusive terms was performed using the second‐order accuracy for momentum, temperature as well as turbulence quantities transport equations.…”

Section: Str K‐ε Model and Its Application For Prediction Of Cz Silic...mentioning

confidence: 99%

“…In the present work, we have also adjusted and validated the STR k-𝜖 model using the ILES data of turbulent melt convection during Cz Si crystal growth [11] as well as experimental data on the oxygen concentration during Cz growth of 100 and 200 mm diameter crystals. [25][26][27] The results were compared to the results obtained with the low Reynolds number Chien k-𝜖 model [14] extended by the buoyancy generation term.…”

Section: Introductionmentioning

confidence: 99%

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Extended Hypothesis for Reynolds Stress Tensor and Turbulent Heat Flux Modeling Within a Novel K‐ε Model for Prediction of Crystal Growth from the Melt

Kalaev,

Borisov

2023

Cryst. Res. Technol.

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The major technique of manufacturing silicon monocrystals is Czochralski (Cz) method. To obtain high‐quality crystals, it is necessary to control the melt flow that is turbulent. The most cost‐effective approach for modeling turbulence nowadays is RANS (Reynolds Averaged Navier‐Stokes) that allows for providing steady axisymmetric computations using reasonable grids. However, conventional eddy‐viscosity RANS models usually fail to predict spatial details of turbulence characteristics of the melt flow. To overcome the limitations of the eddy‐viscosity approach the Stress Tensor Reconstruction (STR) approach is developed that is aimed at the reproduction of anisotropy of the Reynolds stresses. The Generalized Gradient Diffusion Hypothesis (GGDH) in combination with the STR approach successfully takes into account the anisotropy of turbulent fluxes in a melt flow. Relying upon the STR/GGDH approach a novel RANS STR k‐ε model is developed. The model is validated using the ILES (Implicit Large Eddy Simulation) data of turbulent melt convection during Cz Si crystal growth, as well, as the experimental data of oxygen concentration in 100 and 200 mm diameter Cz crystals. The results are compared to the results obtained with the conventional low Reynolds number Chien k‐ε model extended by the buoyancy generation term.

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Section: Introductionsupporting

confidence: 84%

Section: Introductionsupporting

confidence: 84%

Section: Str K‐ε Model and Its Application For Prediction Of Cz Silic...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended Hypothesis for Reynolds Stress Tensor and Turbulent Heat Flux Modeling Within a Novel K‐ε Model for Prediction of Crystal Growth from the Melt

Kalaev,

Borisov

2023

Cryst. Res. Technol.

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“…Threedimensional transient simulations have shown that different ZGP positions can cause thermal waves to travel around the melt free surface, potentially leading to temperature oscillations at the interface [3,9]. Furthermore, it has been discovered that the large eddy simulation (LES) method can effectively reproduce temperature fluctuations in turbulent melts, making it a popular tool for turbulence modeling in CZ-Si simulation and other engineering applications [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields

Cen,

Guo

2023

Crystals

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The application of magnetic fields has become a standard control technique in the CZ-Si growth industry. To investigate the impact of cusp-shaped magnetic fields (CMF) on heat and mass transfer in the melt, a series of transient three-dimensional simulations were conducted for the growth of a 100 mm CZ-Si crystal with a cylindrical crucible. The turbulent melt motion was modeled using the large eddy simulation (LES) method. Six configurations of CMF with various zero-Gaussian plane (ZGP) positions were examined and numerically compared. The computed results showed that different ZGP positions resulted in distinct types of melt convection, buoyant plumes, and thermal waves. Additionally, it was observed that the studied CMF configurations effectively reduced oxygen dissolution from the crucible wall along with oxygen impurity incorporation into the crystal. These findings demonstrate the potential for precise control of the heat and mass transfer process in CZ-Si growth through the application of suitable CMF.

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Evaluating cooling tube effects on defect formation and distribution in Czochralski crystal growth

Huang,

Dezfoli

2024

J Mater Sci: Mater Electron

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Advanced approach for oxygen transport and crystallization front calculation in Cz silicon crystal growth

Cited by 10 publications

References 16 publications

Extended Hypothesis for Reynolds Stress Tensor and Turbulent Heat Flux Modeling Within a Novel K‐ε Model for Prediction of Crystal Growth from the Melt

Extended Hypothesis for Reynolds Stress Tensor and Turbulent Heat Flux Modeling Within a Novel K‐ε Model for Prediction of Crystal Growth from the Melt

Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields

Evaluating cooling tube effects on defect formation and distribution in Czochralski crystal growth

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