• 한국전산유체공학회지
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• 제3권1호
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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.

• 한국결정성장학회지
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• 제18권4호
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• pp.140-145
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• 2008

Cz법을 이용하여 다양한 성장 조건하에서 실리콘 단결정이 성장되었따. 고액 계면 형상의 차이는 다양한 자기장 분포를 통하여 구현되었으며 결정의 고액 계면에 있어 ZGP(zero-Gauss plane) 형태와 자기장 세기(MI)의 효과가 실험적으로 연구되었따. ZGP의 형태는 커습 자기장에 있어 상부 및 하부 코일에 인가되는 자기장의 비율(MR)로 인하여 평평하거나 포물선의 형태를 갖게 된다. MR이 증가함에 따라 고액 계면은 더욱 음각(more concave)의 형태가 되고 이는 MR 증가에 따른 고액 계면으로의 뜨거운 융액이 쉽게 유입될 수 있음을 의미한다. 고액 계면의 효과적인 형상은 자기장 분포에 의존됨을 발견하였으며 실험결과는 다른 연구와 비교하였다.

• 한국결정성장학회지
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• 제7권1호
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• pp.41-46
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• 1997

열교환법에 의한 결정 성장에서 용융액 내에서의 유동장의 변화와 대류 열전달이 고/액 계면의 형태와 위치에 미치는 영향에 대해 고찰하였다. 비록 도가니 내의 온도분포가 안정한 구조라도 고/액 계면이 반구형태를 가지기 때문에 안정화가 깨어지게 되고, 반경방향 온도 기울기에 의한 용응액 내에서의 자연대류 흐름이 무시할 수 없을 정도로 발생한다. 대류 열전달이 존재하는 경우에 최대 휨도는 대류 열전달이 존재하지 않은 경우에 비해 감소하며, 열교환법에서의 정확한 열전달 공정모사를 위해 대류 열전달이 고려되어야 한다.

• Current Photovoltaic Research
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• 제8권1호
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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.

• 한국결정성장학회지
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• 제14권4호
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• pp.155-159
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• 2004

열교환법을 활용한 사파이어 단결정 성장 공정에서 도가니 형상 변화가 결정 온도와 고/액 계면 형태에 미치는 영향에 관해 고찰하기 위해 유한요소법, implicit Euler법, frontal 해석 연산을 활용한 수치해석을 수행하였다. 개발된 컴퓨터 시뮬레이션 기법은 고/액 계면의 형상이 반구 형상에서 평면 형상으로 전환되는 열전달 현상 해석에 효율적이다. 본 연구에서는 고/액 계면의 휨도를 개선하기 위해, 도가니 밑면의 다양한 형상을 고려하였으며, 도가니 형상은 공정 최적화 변수로 고려되어야 한다.

• 대한기계학회논문집
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• 제19권5호
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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.

• 한국결정성장학회지
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• 제5권4호
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• pp.306-317
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• 1995

수평 브릿지만법은 갈륨 비소 반도체 결정을 성장시키는데 많이 사용된다. 수평 브릿지만 법에 의하여 성장된 단결정 내에서 불순물 분포를 알아보기 위하여 성장 과정 중의 액상에서 열전달, 물질전달, 유체흐름과 고상에서 열전달을 의사 정상상태를 가정하여 2차원 및 3차원 모델을 세우고 유한요소법에 의하여 수치모사하였다. 이때 고-액 계면의 위치와 형태도해의 일부분으로 다른 해들과 동시에 구하였다. 2차원 단열 경계조건에서는 3차원의 계면이 2차원의 경우보다 덜 휘어졌고, 대류 강도는 비슷하였다. 대류강도의 증가에 따라 수직 편석은 최대값을 보였으나 계면이 2차원에서 더 휘어져 최대값은 2차원에서 대류 강도가 더 작을 때 나타났다.

• 한국결정성장학회지
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• 제9권5호
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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.

• 대한기계학회논문집B
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• 제25권12호
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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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• 제5권4호
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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.