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

Wetzel, Th.; Virbulis, J.; Muižnieks, A.; Ammon, Wilfried von; Tomzig, E.; Raming, G.; Weber, M.

doi:10.1016/j.jcrysgro.2004.02.027

Cited by 14 publications

(7 citation statements)

References 7 publications

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“…Hence low Reynolds number turbulence model of Launder and Sharma (11) is used for this case. [5] [ ]…”

Section: Modeling Of Turbulencementioning

confidence: 99%

“…Time dependent 3D simulations are more computationally demanding (2,3,4). Although 2D axisymmetric model does not the replicate the actual flow, these models are useful for preliminary analysis and parametric sensitivity studies (3,5).…”

Section: Introductionmentioning

confidence: 99%

“…For process optimization, simulated results with wide range of operating conditions are required which is still lacking in the literature. Wetzel et al (5) has carried out 2D axisymmetric simulations for 300mm crystal growth. This study was focused on relating non-symmetric enhanced mixing by modifying effective turbulent viscosity.…”

Section: Introductionmentioning

confidence: 99%

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Melt Flow Simulations of Czochralski Crystal Growth Process of Silicon for Large Crystals

Gunjal¹,

Kulkarni²,

Ramachandran³

2006

ECS Trans.

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Czochralski Growth of Silicon Crystal (Cz) is extensively used for single crystal manufacturing and most of the Silicon wafers are manufactured by this process. Melt flow in large crucibles, used for growth of large diameter (300mm) crystal, is turbulent in nature. In this study, we present a model for simulating Czochralski crystal growth process for 300mm crystal. This study is mainly focused on effect of crucible rotation on flow and temperature profiles in the melt. Two-dimensional axisymmetric model was used for this purpose which accounts for generated turbulence, heat/ mass transfer with phase change. Investigations show that flow pattern in co-rotation below the crystal is totally opposite that of counter-rotation. Centrifugal force is dominant due to crystal and crucible rotation, which creates vertical upwards or downward flow below the crystal, depending upon the co-rotation or counter rotation. With increase in pull rate, depth of the predicted interface in the melt was also found to be increased. Simulated results will be helpful for optimization of process parameters to achieve better quality of crystals.

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“…Hence low Reynolds number turbulence model of Launder and Sharma (11) is used for this case. [5] [ ]…”

Section: Modeling Of Turbulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Melt Flow Simulations of Czochralski Crystal Growth Process of Silicon for Large Crystals

Gunjal¹,

Kulkarni²,

Ramachandran³

2006

ECS Trans.

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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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“…In a given hot zone, increasing the crystal growth rate without limits will lead melt surface crystallization, crystal distortion, and dislocations. In order to optimize hot zone design, the computer simulation [3][4][5][6][7] is used for analyzing temperature distributions with different hot zone configurations [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Simulation aided hot zone design for faster growth of CZ silicon mono crystals

et al. 2011

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

Cited by 14 publications

References 7 publications

Melt Flow Simulations of Czochralski Crystal Growth Process of Silicon for Large Crystals

Melt Flow Simulations of Czochralski Crystal Growth Process of Silicon for Large Crystals

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

Simulation aided hot zone design for faster growth of CZ silicon mono crystals

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