• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권1호
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• pp.121-131
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• 2000

Melt flow, heat and mass transfer of oxygen have been analyzed numerically in the process of Czochralski single crystal growth of silicon under the influence of misaligned cusp magnetic fields. Since the silicon melt in a crucible for crystal growth is of high temperature and of highly electrical-conducting, experimentation method has difficulty in analyzing the behavior of the melt flow. A set of simultaneous nonlinear equations including Navier-Stokes and Maxwell equations has been used for the modelling of the melt flow which can be regarded as a liquid metal. Together with the melt flow which forms the Marangoni convection, a flow circulation is observed near the comer close both to the crucible wall and the free surface. The melt flow tends to follow the magnetic lines instead of traversing the lines. These flow characteristics helps the flow circulation exist. Mass transfer characteristics influenced by the melt flow has been analyzed and the oxygen absorption rate to the crystal has been calculated and turned out to be rather uniform than in the case of an aligned magnetic field.

• 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.

• 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.

• 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.

• 한국결정성장학회지
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• 제19권5호
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• pp.215-222
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• 2009

Many concepts of external magnetic field applications in crystal growth processes have been developed to control melt convection, impurity content and growing interface shape. Especially, travelling magnetic fields (TMF) are of certain advantages. However, strong shielding effects appear when the TMF coils are placed outside the growth vessel. To achieve a solution of industrial relevance within the framework of the $KRISTMAG^{(R)}$ project inner heater-magnet modules(HMM) for simultaneous generation of temperature and magnetic field have been developed. At the same time, as the temperature is controlled as usual, e.g. by DC, the characteristics of the magnetic field can be adjusted via frequency, phase shift of the alternating current (AC) and by changing the amplitude via the AC/DC ratio. Global modelling and dummy measurements were used to optimize and validate the HMM configuration and process parameters. GaAs and Ge single crystals with improved parameters were grown in HMM-equipped industrial liquid encapsulated Czochralski (LEC) puller and commercial vertical gradient freeze (VGF) furnace, respectively. The vapour pressure controlled Czochralski (VCz) variant without boric oxide encapsulation was used to study the movement of floating particles by the TMF-driven vortices.

• 대한기계학회논문집B
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• 제20권3호
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• pp.988-1004
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• 1996

The characteristics of flow and oxygen concentration are numerically studied in Czochralski 8" silicon crystal growing process considering radiative heat transfer. The analysis of net radiative heat flux on all relevant surfaces shows growing crystal affects the heater power. Furthermore, the variation of the radiative heat flux along the crystal surface in the growing direction is confirmed and should be a cause of thermal stress and defect of the crystal. The calculated distributions of temperature and, heat flux along the wall boundaries including melt/crystal interface, free surface and crucible wall indicate that the frequently used assumption of the thermal boundary conditions of insulated crucible bottom and constant temperature at crucible side wall is not suitable to meet the real physical boundary conditions. It is necessary, therefore, to calculate radiative heat transfer simultaneously with the melt flow in order to simulate the real CZ crystal growth. If only natural convection is considered, the oxygen concentration on the melt/crystal interface decreases and becomes uniform by the application of a cusp magnetic filed. The heater power needed also increases with increasing the magnetic field. For the case of counter rotation of the crystal and crucible, the magnetic field suppresses azimutal flow produced by the crucible rotation, which results in the higher oxygen concentration near the interface.

• 한국결정성장학회지
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• 제7권1호
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• pp.108-116
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• 1997

초크랄스키 대류에서의 동적 천이과정에 대한 실험 및 수치해석 연구가 수행되었다. 결정의 회전에 의한 강제대류와 결정/용융 경계면과 도가니 외벽간의 온도차에 의한 자연대류의 상호작용에 의해서 결정되어지는 유동구조와 천이현상을 해석하기 위해 도가니 내의 온도진동 특성을 시간주기($t_p$)와 진동크기($Delta\theta$)에 의해 검토하였다. 혼합대류인자에 따른 천이현상의 체계적인 연구가 수행되었으며($0.134\le Ra/PrRe^2 \le3.804$), 천이현상에 대한 Pr수의 영향을 조사하였다. 천이 메카니즘을 이해하기 위해, 자오면상의 온도장과 중심축에서의 축방향 속도에 대한 해석이 부가되었다.

• 한국결정성장학회지
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• 제10권5호
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• pp.356-361
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• 2000

The radial position of OiSF-ring has been meaningful data in industry. Thus it's position was calculated by application of (V/G)/sub crit/ = 0.138 ㎟/minK and point defect dynamics for industrial scale grower with various pull rates. After the calculation, compared with experimental result. OiSF-ring diameters expected with calculation were good agreement with experimental results. In order to show validity of the predicted temperature distribution using STHAMAS which is one of the global simulator for Cz crystal growing, temperature was measured along the axis of crystal using thermocouples, and compared with the calculated temperature. We found the effective thermal conductivity K/sub m/ (r) which gives in accordance with the temperature distribution at the axis of crystal and crystal/melt interface shape between experimental and computational results. Therefore, effective thermal conductivity K/sub m/ (r) was applied instead of solving melt convection problem.

• 한국결정성장학회지
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• 제10권3호
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• pp.177-184
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• 2000

약한 cusp 자장이 가하여진 Czochralski실리콘 단결정 성장에서 유동장의 종횡비에 따라 부력과 열모세관 현상이 용융물질의 유동과 물질(산소)전달에 미치는 영향이 수치적인 방법으로 연구되었다. 실리콘 단결정 성장이 진행됨에 따라 도가니안의 용융물질의 깊이가 즐어들어 유동장의 종횡비가 감소하고, 이에 따라 현존하는 유동장에 작용하는 자장의 상대적인 형태가 변화하므로 유동의 형태가 계속 변화한다. 유동장 내부에서 자유표면으로 접근하여 Marangoni 대류를 구성하는 용융물질의 흐름(열모세관 현상)과 함께 도가니 벽 근처의 자유표면 바로 아래에서 순환류가 발생하는데, 이 순환류의 존재로 인하여 부력의 효과가 “전반적으로”나타나지 않고 도리어 “국소적으로”나타나는 특성을 갖는다. 종횡비가 작아질수록 유동장의 대부분에서 자장의 반경방향 성분이 축방향 성분보다 우세하여 용융물질의 유동은 횡방향 성분(수평성분)이 현저해지므로 자오면에서의 온도분포는 점차 반경방향에 의존하는 특성을 갖게 된다 종횡비가 작아질수록 결정의 가장자리에서 온도구배가 작아지며 따라서 열모세관 현상포 약화된다 또 이때 결정주위의 산소의 농도가 작아지며 따라서 흡수되는 산소의 양도 작아진다.

• 한국재료학회지
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• 제22권12호
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• pp.711-716
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• 2012

Tungsten bronze structure $Sr_{1-x}Ba_xNb_2O_6$ (SBN) single crystals were grown primarily using the Czochralski method, in which several difficulties were encountered: striation formation and diameter control. Striation formation occurred mainly because of crystal rotation in an asymmetric thermal field and unsteady melt convection driven by thermal buoyancy forces. To optimize the growth conditions, bulk SBN crystals were grown in a furnace with resistance heating elements. The zone of $O_2$ atmosphere for crystal growth is 9.0 cm and the difference of temperature between the melt and the top is $70^{\circ}C$. According to the growth conditions of the rotation rate, grown SBN became either polycrystalline or composed of single crystals. In the case of as-grown $Sr_{1-x}Ba_xNb_2O_6$ (x = 0.4; 60SBN) single crystals, the color of the crystals was transparent yellowish and the growth axis was the c-axis. The facets of the crystals were of various shapes. The length and diameter of the single crystals was 50~70 mm and 5~10 mm, respectively. Tungsten bronze SBN growth is affected by the temperature profile and the atmosphere of the growing zone. The thermal expansion coefficients on heating and on cooling of the grown SBN single crystals were not matched. These coefficients were thought to influence the phase transition phenomena of SBN.