• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.4
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• pp.155-159
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• 2004

Numerical analysis which is based on finite element techniques, implicit Euler method and frontal solving algorithm was performed to study the effects of the crucible shape on the temperature of sapphire crystal and the shape of the melt/crystal interface in heat exchanger method. The computer simulation described here and effective to solving the heat transport phenomena with the transition of the interface shape from hemispherical to planar. In the work, various crucibles with differently shaped corners at their bottom are considered to improve the deflection of the melt/crystal interface. The shape of the crucible should be considered as one of the variables for the process optimization.

• Current Photovoltaic Research
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• v.8 no.1
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• pp.17-26
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• 2020

It is clear that monocrystalline Silicon (Si) ingots are the key raw material for semiconductors devices. In the present industries markets, most of monocrystalline Silicon (Si) ingots are made by Czochralski Process due to their advantages with low production cost and the big crystal diameters in comparison with other manufacturing process such as Float-Zone technique. However, the disadvantage of Czochralski Process is the presence of impurities such as oxygen or carbon from the quartz and graphite crucible which later will resulted in defects and then lowering the efficiency of Si wafer. The heat transfer plays an important role in the formation of Si ingots. However, the heat transfer generates convection in Si molten state which induces the defects in Si crystal. In this study, a crystal growth simulation software was used to optimize the Si crystal growth process. The furnace and system design were modified. The results showed the melt-crystal interface shape can affect the Si crystal growth rate and defect points. In this study, the defect points and desired interface shape were controlled by specific crystal growth rate condition.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.5
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• pp.1308-1318
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• 1995

The influence of varying rotation speed of both crystal and crucible was numerically investigated for the Czochralski silicon-crystal growth. Based on a simplified model assuming flatness of free surfrae, the Navier-Stokes Boussinesq equations were employed to identify the flow pattern, temperature distribution as well as the shape of the melt/crystal interface. The present results showed that the interface shape was relatively convex with respect to the melt at lower pulling rate and tended to be concave as the pulling rate increased. In particular, the experimentally observed gull-winged shape of the interface was qualitatively in agreement with the predicted shape. The rotation of crystal alone little affected the growth system. When the rotation speed of the crucible was increased, there occurred inversion of the interface shape from convex to concave pattern. At rapid rotation of the crucible, an interesting channel formation was predictied primarily due to the assumption of laminar flow.

• Journal of the Korean Ceramic Society
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• v.43 no.11 s.294
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• pp.728-733
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• 2006

The equilibrium or growth shape of ceramic materials is classified largely into two categories according to the thermodynamic conditions imposed. One is a polyhedral shape where the surface free energy is anisotropic, and the other a spherical shape where the surface free energy is isotropic. In the case of grains with a polyhedral shape of anisotropic surface free energy, socalled abnormal grain growth usually takes place due to a significant energy barrier for a growth unit to be attached to the crystal surface. In the case of grains with a spherical shape of isotropic surface free energy, however, normal grain growth with a uniform size distribution takes place. In this contribution, the state-of-the-art of our current understanding of the relationship between the crystal shape and the microstructure evolution during the sintering of ceramic materials in the presence of a liquid phase was discussed.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.18 no.4
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• pp.140-145
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• 2008

Silicon single crystals are grown by Czochralski (CZ) method in different growing conditions. The different shapes of the crystal-melt interface are obtained with various magnetic fields. Effects of zero-Gauss plane (ZGP) shape and magnetic intensity (MI) on the crystal-melt interface in the crystal experimentally are investigated. The shape of ZGP is not only flat but also parabolic, which is due to magnetic ratio (MR) of the lower to upper current densities in the configurations of the cusp-magnetic fields. As the MR increases, the crystal-melt interface becomes more concave. It means that the hot melt can be easily transported to the crystal-melt interface with increasing the MR. Effective shape of the crystal-melt interface is found to depend on the magnetic field in cusp-magnetic CZ method. The experimental results are compared with other studies and discussed.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.5
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• pp.454-458
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• 1999

Hydrodynamic Thermal Capilary Model developed previously has been modified to study the transport phenomena in the Czochralski process. Our analysis is focused on the heat transfer in the system, convection in the melt phase, and the meniscus and interface shape. Four major forces drive melt flow in the crucible, which include thermal buoyancy force in the melt, thermocapillary force along the curved meniscus, crucible rotation and crystal rotation. Individual flow mechanism due to each driving force has been examined to determine its interaction with the meniscus and interface shape. A nominal 4-inch-diameter silicon crystal growth process is chosen as a subject for analysis. Heater temperature profile for constant diameter crystal is also present as a function of crystal height or fraction solidified.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.7 no.1
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• pp.41-46
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• 1997

The change of flow field and the effects of convective heat transfer on the shape and location of melt/crystal interface has been studied during the crystal growth by the heat exchanger method. Although the thermal structure is stable in the crucible, the flow due to the natural convection driven by radial temperature gradient is significant, because the thermal stability is broken by the hemispherical melt/crystal interface shape. The maximum interface deflection with convection is smaller than without and the convective heat transfer should be considered to simulate the heat transfer process of heat exchanger method rigorously.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.2
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• pp.58-62
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• 2004

The shape evolution of the interface void of copper metallization for intergrated circuits under electromigration stress is modeled. A 2-dimensional finite-difference numerical method is employed for computing time evolution of the void shape driven by surface diffusion, and the electrostatic problem is solved by boundary element method. When the diffusion coefficient is isotropic, the numerical results agree well with the known case of wedge-shape void evolution. The numerical results for the anisotropic diffusion coefficient show that the initially circular void evolves to become a fatal slitlike shape when the electron wind force is large, while the shape becomes non-fatal and circular as the electron wind force decreases. The results indicate that the open circuit failure caused by slit-like void shape is far less probable to be observed for copper metallization under a normal electromigration stress condition.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.10
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• pp.3322-3333
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• 1996

A numerical analysis has been conducted to investigate a modified floating-zone crystal growth process in which most of the melt surface is covered with a heated ring. The crystal rod is not only pulled downward but rotated around its axisymmetric line during crystal growth process in order to produce the flat interface of crystal growth and the single crystal growth of NaNO3 is considered in 6mm diameter. The present study is made from a full-equation-based analysis considering a pulling velocity in all of solid and liquid domains and both of solid-liquid interfaces are tracked simultaneously with a governing equation in each domain. Numerical results are mainly presented for the comparison of the surface shape of rotational crystal rod with that of no-rotational crystal rod and the effects of revolution speeds of the crystal rod. Results show that the rotation of crystal rod produces more its flat surface. In addition, the shape of crystal growth near the centerline is more concaved with the increase in the revolution speed of crystal rod. The flow pattern and temperature distribution is analyzed and presented in each case. As the pulling velocity of crystal rod is increasing, the free surface of the melt below the heated ring is enlarged due to the crystal interface migrating downward.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.23 no.2
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• pp.67-75
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• 2013

In order to improve osseo-integration of a dental implant with bone crystal we studied an implant with holes inside its body to deliver bioactive materials based on a proposed patent. After bioactive material is absorbed, bone crystal can grow into holes to increase implant bonding in addition to surface integration. The larger cross section area of outlet holes showed the less values of the maximum stress, and the stress concentrations near the uppermost outlet holes were also reduced with an increasing number of outlet holes. The conclusion, that the uppermost outlet design improvement was most effective to reduce the stress concentration and improve the growth rate of bone crystal, could be drawn. After the design optimizations, Type 6-C had provided the best results in this study. The overall shape optimization studies on the shape, location, number, and so on, of the outlet holes, should be carried out further.