Numerical Study of the Effect of Magnetic Fields on Melt-Crystal Interface-Deflection in Czochralski Crystal Growth

2003 ◽  
Author(s):  
Lijun Liu ◽  
Koichi Kakimoto
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Numerical Study ◽  
Silicon Crystal ◽  
Czochralski Growth ◽  
Thermal Flow ◽  
Interface Shape ◽  
Convective Thermal ◽  
And Control ◽  
Crystal Interface

In order to control the impurity distribution and remove defects in a crystal grown in Czochralski growth for high quality crystals of silicon, it is necessary to study and control the melt-crystal interface shape, which plays an important role in control of the crystal quality. The melt-crystal interface interacts with and is determined by the convective thermal flow of the melt in the crucible. Application of magnetic field in the Czochralski system is an effective tool to control the convective thermal flow in the crucible. Therefore, the shape of the melt-crystal interface can be modified accordingly. Numerical study is performed in this paper to understand the effect of magnetic field on the interface deflection in Czochralski system. Comparisons have been carried out by computations for four arrangements of the magnetic field: without magnetic field, a vertical magnetic field and two types of cusp-shaped magnetic field. The velocity, pressure, thermal and electromagnetic fields are solved with adaptation of the mesh to the iteratively modified interface shape. The multi-block technique is applied to discretize the melt field in the crucible and the solid field of silicon crystal. The unknown shape of the melt-crystal interface is achieved by an iterative procedure. The computation results show that the magnetic fields have obvious effects on both the pattern and strength of the convective flow and the interface shape. Applying magnetic field in the Czochralski system, therefore, is an effective tool to control the quality of bulk crystal in Czochralski growth process.

Effect of the pulling, crystal and crucible rotation rate on the thermal stress and the melt–crystal interface in the Czochralski growth of germanium crystals

CrystEngComm ◽  
2021 ◽  
Vol 23 (39) ◽  
pp. 6967-6976
Author(s):  
Mahboobeh Saadatirad ◽  
Mohammad Hossein Tavakoli ◽  
Hossein Khodamoradi ◽  
Seyedeh Razieh Masharian
Keyword(s):  
Thermal Stress ◽  
Rotation Rate ◽  
Czochralski Growth ◽  
Interface Shape ◽  
Crucible Rotation ◽  
Crystal Interface

The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.

A numerical study of a bubble pair rising side by side in external magnetic fields

2021 ◽  
Vol 926 ◽  
Author(s):  
Jie Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Transverse Field ◽  
Asymmetric Distribution ◽  
Streamwise Vortices ◽  
Horizontal Magnetic Field

The motion of a pair of bubbles rising side by side under the influence of external magnetic fields is numerically examined. Through solving the fully three-dimensional Navier–Stokes equations, the results reveal that the bubble interactions are rather sensitive to the field direction and strength. At first, we identify that, in a hydrodynamic flow, whether the two bubbles will bounce or coalesce depends on the developments of the counter-rotating streamwise vortices during the collision. In particular, for an originally bouncing bubble pair, a streamwise magnetic field tends to promote their coalescence by weakening the strengths of the standing streamwise vortices, and such a weakening effect is caused by the asymmetric distribution of the Lorentz force in the presence of another bubble such that a torque is induced to offset the original streamwise vortices. Under a horizontal magnetic field, on the other hand, the influences are highly dependent on the angle between the bubble centroid line and the field: a transverse field or a moderate spanwise field always leads the bubble pair to coalescence while a strong spanwise field has the opposite effect. This anisotropic effect comes from the Lorentz force induced flow diffusion along the magnetic field, which not only produces two pairs of streamwise vortices at the bubble rear, but also homogenizes the pressure along the magnetic lines. As the competition between the two mechanisms varies with the magnetic direction and strength, the interaction between the bubble pair also changes. We show that the external magnetic fields control the bubble interaction through reconstructing the vortex structures, and hence the core mechanisms are identified.

Particle assembling induced by non-homogeneous magnetic field at transformer oil-based ferrofluid/silicon crystal interface by neutron reflectometry

2019 ◽  
Vol 473 ◽  
pp. 912-917 ◽  
Author(s):  
Anatolii Nagornyi ◽  
Viktor I. Petrenko ◽  
Michal Rajnak ◽  
Igor V. Gapon ◽  
Mikhail V. Avdeev ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Silicon Crystal ◽  
Homogeneous Magnetic Field ◽  
Neutron Reflectometry ◽  
Transformer Oil ◽  
Crystal Interface

scholarly journals Influence of Crucible Thermal Conductivity on Crystal Growth in an Industrial Directional Solidification Process for Silicon Ingots

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Zaoyang Li ◽  
Lijun Liu ◽  
Yunfeng Zhang ◽  
Genshu Zhou
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Crystal Growth ◽  
Directional Solidification ◽  
Silicon Crystal ◽  
Solidification Process ◽  
Interface Shape ◽  
Directional Solidification Process ◽  
Reasonable Range ◽  
Crystal Interface

We carried out transient global simulations of heating, melting, growing, annealing, and cooling stages for an industrial directional solidification (DS) process for silicon ingots. The crucible thermal conductivity is varied in a reasonable range to investigate its influence on the global heat transfer and silicon crystal growth. It is found that the crucible plays an important role in heat transfer, and therefore its thermal conductivity can influence the crystal growth significantly in the entire DS process. Increasing the crucible thermal conductivity can shorten the time for melting of silicon feedstock and growing of silicon crystal significantly, and therefore large thermal conductivity is helpful in saving both production time and power energy. However, the high temperature gradient in the silicon ingots and the locally concave melt-crystal interface shape for large crucible thermal conductivity indicate that high thermal stress and dislocation propagation are likely to occur during both growing and annealing stages. Based on the numerical simulations, some discussions on designing and choosing the crucible thermal conductivity are presented.

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