• Journal of computational fluids engineering
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• v.3 no.1
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• pp.100-107
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• 1998

A numerical analysis of thermal stress over temperature variations near the crystal-melt interface is carried out for a floating-zone growth of Cadmium Telluride (CdTe). Thermocapillary convection determines crystal-melt interfacial shape and signature of temperature in the crystal. Large temperature gradients near the crystal-melt interface yield excessive thermal stresses in a crystal, which affect the dislocations of the crystal. Based on the assumption that the crystal is elastic and isotropic, thermal stresses in a crystal are computed and the effects of operating conditions are investigated. The results show that the extreme thermal stresses are concentrated near the interface of a crystal and the radial and the tangential stresses are the dominant ones. Concentrated heating profile increases the stresses within the crystal, otherwise, the pulling rate decreases the stresses.

• 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.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.

• 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.

• 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.

• 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 Crystal Growth and Crystal Technology
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• v.5 no.4
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• pp.306-317
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• 1995

Abstract Gallium arsenide crystal is usually grown from the melt by the horizontal Bridgman method. We constructed pseudo - steady - state model for crystal growth of GaAs which inclue melt, crystal and the free interface. Mathematical equations of the model were solved for flow, temperature, and concentration field in the melt and temperature field in the crystal. The location and shape of the interface were also solved simultaneously. In 2 - dimensional model, the shape of the interface is flat with adiabatic thermal boundary condition, but it becomes curved with completely conducting thermal boundary condition. In 3 - dimensional model, the interface is less curved than 2 - dimensional case and the flow intensity is similar to that of 2 - dimensional case. With the increase of flow intensity vertical segregation shows maximum value in both 2 - and 3 - D model. However, the maximum value occurs in lower flow intensity in 2 - D model because the interface is more curved for the same flow intensity.

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.12
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• pp.1667-1675
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• 2001

Numerical simulations are carried out for the liquid encapsulant Czochralski(LEC) by imposing a magnetic field. The use of a magnetic field to the crystal growth is to suppress melt convection and to improve the homogeneity of the crystal. In the present numerical investigation, we focus on the range of 0-0.3Tesla strength for the axial and cusped magnetic field and the effect of the magnetic field on the melt-crystal interface, flow field and temperature distribution which are the major factors to determine the quality of the single crystal are of particular interest. For both axial and cusped magnetic field, increase of the magnetic field strength causes a more convex interface to the crystal. In general, the flow is weakened by the application of magnetic field so that the shape of the melt-crystal interface and the transport phenomena are affected by the change of the flow and temperature field.

• Coupled systems mechanics
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• v.5 no.4
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• pp.341-353
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• 2016

Manufactures of multi-crystalline silicon ingots by means of the directional solidification system (DSS) is important to the solar photovoltaic (PV) cell industry. The quality of the ingots, including the grain size and morphology, is highly related to the shape of the crystal-melt interface during the crystal growth process. We performed numerical simulations to analyze the thermo-fluid field and the shape of the crystal-melt interface both for steady conditions and transient processes. The steady simulations are first validated and then applied to improve the hot zone design in the furnace. The numerical results reveal that, an additional guiding plate weakens the strength of vortex and improves the desired profile of the crystal-melt interface. Based on the steady solutions at an early stage, detailed transient processes of crystal growth can be simulated. Accuracy of the results is supported by comparing the evolutions of crystal heights with the experimental measurements. The excellent agreements demonstrate the applicability of the present numerical methods in simulating a practical and complex system of directional solidification system.