ILES of melt turbulent convection with conjugated heat transfer in the crucible and gas flow for Czochralski silicon crystal growth system

Borisov, Dmitry V.; Kalaev, V.V.

doi:10.1016/j.jcrysgro.2021.126305

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…We adopted the 2D-3D combination method reported by Kalaev, Borisov and Smirnov. 26,27 The external boundary conditions of the 3D local model are provided by the 2D global axisymmetric model. To ensure the rationality of the axisymmetric boundary conditions, the graphite crucible, quartz crucible, melt, crystal and local argon were included in this model, as shown in Fig.…”

Section: Geometric Modelmentioning

confidence: 99%

“…2) Another way is that T f is fixed as the melting point and V f is calculated. 26 The growth-rate at the triple point V tri is modified to the pulling speed V ps by the PID control system.…”

Section: Crystengcomm Papermentioning

confidence: 99%

“…However, these articles do not explicitly state whether the corrected interface is axisymmetric or not, and whether a special method is used in the interface correction process. 26,27,33,34 This lack of information makes it difficult to make comparisons. Fig.…”

Section: Crystengcomm Papermentioning

confidence: 99%

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Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

et al. 2023

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Section: Geometric Modelmentioning

confidence: 99%

Section: Crystengcomm Papermentioning

confidence: 99%

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Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

et al. 2023

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“…Our simulation was conducted on a cylindrical CZ-Si geometry using a Leybold EKZ 1300 crucible. This crucible is commonly used for the growth of 100 mm silicon crystals, and has been extensively studied in previous research [18,[20][21][22][23][24][25][26][27]. In this study, we used a cylinder-like crucible with a diameter of 340 mm and a height of 85 mm (Figure 1).…”

Section: Physical Parametersmentioning

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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“…[3][4][5][6] Despite the achieved progress some of the key characteristics in particular the crystallization front shape and the oxygen concentration in the crystal were not reproduced within the RANS approach. [7][8][9] Based on the simulation results of turbulent silicon melt convection during Cz Si crystal growth obtained within ILES (Implicit Large Eddy Simulation) approach, [10,11] in our previous research we have studied the applicability of the Boussinesq eddy viscosity assumption as well as Standard Gradient Diffusion Hypothesis (SGDH) which are widely used in RANS turbulence models for modeling Reynolds stresses and turbulent heat flux respectively. The investigation revealed that the strong anisotropy of Reynolds stresses and heat fluxes is observed near the crucible wall, melt-crystal interface as well as near the melt-free surface, which cannot be predicted by the eddy-viscosity approach.…”

Section: Introductionmentioning

confidence: 99%

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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ILES of melt turbulent convection with conjugated heat transfer in the crucible and gas flow for Czochralski silicon crystal growth system

Cited by 8 publications

References 21 publications

Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

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

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

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