• Journal of Mechanical Science and Technology
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• v.15 no.12
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• pp.1876-1881
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• 2001

We present the numerical analysis of the growth of a silicon (Si) single crystal. In the MCZ (Magnetic-field-applied Czochralski) method, two magnetic fields that stand opposite to each other generate a cusp magnetic field. In this work, the three cusp magnetic fields used for the analysis are an extern magnetic field, a surface magnetic field and an internal magnetic field. Each case was evaluated mainly as to the degree of stirring, shaft symmetry and the stability of the flow. As a result, the cusp magnetic field that yielded to best conditions was the internal magneic field.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.6 no.1
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• pp.1-10
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• 1996

A numerical study was conducted on the effects of the cusp magnetic field in 8" silicon single crystal grwoth by Czochralski method. For a damping effects simulation by magnetic field, low reynolds number ${\kappa} - {\varepsilon}$ model was adopted. Symmetrci cusp magnetic field has a effect of damping streamline crystal, is lowerd with the increasing cusp magnetic field intensity. The uniformity of the oxygen concentration was improved. The asymmetirc cusp magnetic field increased the oxygen concentration however, oxygen concentration distribution in the radial direction was remained uniform. Suitable combination of symmetric and asymmetric cusp magnetic fields could give uniform and low oxygen concentration in the axial direction.tion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.3
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• pp.388-397
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• 1999

Numerical simulations are carried out for the magnetic Czochralski single crystal growth system. It Is shown that a magnetic field significantly suppresses the convective flow and as the strength of magnetic field becomes to be stronger, the heat transfer in the melt is dominated by conduction rather than convection. By imposing a cusp magnetic field, the growth interface shape becomes convex toward the melt. When the axial magnetic field is imposed, there occurs an inversion of the interface shape with increase of the magnetic field strength. The oxygen concentration near the interface decreases with increasing cusp magnetic field strength while axial field causes an increase of an oxygen concentration at the central region and decrease of that at the edge of the crystal. The results show that the cusp magnetic field has advantages over an axial magnetic field In the radial uniformity of oxygen as well as in the additional degree of control.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.7 no.3
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• pp.406-417
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• 1997

A numerical study was conducted on the optimum magnetic field intensity and asymmetric factor for uniform axial oxygen concentration in 8 inch silicon single crystal growing process by magnetic Czochralski method. For constant shape of cusp field, a change of coil and crucible position were compared. In case of symmetric cusp field, magnetic field intensity variation shows concave downward with crystal growing for uniform, axial oxygen concentration. A numerical results show similar value of standard deviation of average oxygen concentration for uniform oxygen concentration between coil and crucible position change. In case of asymmetric cusp field. asymmetric factor is increased with crystal growing to have uniform oxygen concentration.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.15 no.4
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• pp.129-134
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• 2005

A numerical analysis was performed on magnetic field effects of silicon melt motion in Czochralski crystal puller. The turbulent modeling was used to simulate the transport phenomena in 18' single crystal growing process. For small crucible angular velocity, the natural convection is dominant. As the crucible angular velocity is increased, the forced convection is increased and the distribution of temperature profiles is broadened. The cusp magnetic field reduces effectively the natural and forced convection near the crucible and the temperature profiles of the silicon fluids is similar in the case of conduction.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.250.1-250.1
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• 2014

A multicusp ion source has been used widely in negative hydrogen cyclotrons mainly for radioisotope productions. The ion source is designed to have cusp geometries of magnetic field inside plasma chamber, where ions are confining and their mean lifetimes increase. The magnetic confinement produced a number of permanent magnetic poles helps to increase beam currents and reduce the emittance. Therefore optimizing the number of magnets confining more ions and increasing their mean lifetime in plasma has to be investigated in order to improve the performance of the ion source. In this work a numerical simulation of the magnetic flux density from a number of permanent magnets is carried to optimize the cusp geometries producing the highest plasma density, which is clearly indicated along the full-line cusp geometry. The effect of magnetic fields and a number of poles on the plasma structure are investigated by a computing tool. The electron confinement effect becomes stronger and the density increases with increasing the number of poles. On the contrary, the escape of electrons from the loss cone becomes more frequent as the pole number increases [1]. To understand above observation the electron and ion's trajectories along with different cusp geometries are simulated. The simulation has been shown that the optimized numbers of magnets can improve the ion density and uniformity.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.7 no.1
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• pp.27-40
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• 1997

The heat in Czochralski method is transfered by all transport mechanisms such as convection, conduction and radiation and convection is caused by the temperature difference in the molden pool, the rotations of crystal or crucible and the difference of surface tension. This study delvelops the simulation model of Czochralski growth by using the finite difference method with fixed grids combined with new latent heat treatment model. The radiative heat transfer occured in the surfce of the system is treated by calculating the view factors among surface elements. The model shows that the flow is turbulent, therefore, turbulent modeling must be used to simulate the transport phenomena in the real system applied to 8" Si single crystal growth process. The effects of a cusp magnetic field imposed on the Czochralski silicon melt are studied by numerical analysis. The cusp magnetic field reduces the natural and forced convection due to the rotation of crystal and crucible very effectively. It is shown that the oxygen concentration distribution on the melt/crystal interface is sensitively controlled by the change of the magnetic field intensity. This provides an interesting way to tune the desired O concentration in the crystal during the crystal growing.

• Proceedings of the Korean Vacuum Society Conference
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• 2005.08a
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• pp.138-138
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• 2005

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.435-435
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• 2010

A inclined slot-excited plasma source is newly designed and constructed for higher flux HNB(Hyperthermal Neutral Beam) generation. The present source is different from the vertical SLAN(SLot ANtenna) sources [1] in two aspects. One is that the slots are inclined, and the other is that the magnetic field is configured to a cusp type. These modifications are intended to make the source plasma operated in sub-milli-torr pressure regime and as thin as possible, both of which is to get higher HNB flux by decreasing the re-ionization rate of the reflected atoms from the neutralizer [2]. The plasma is generated in a quartz tube of internal diameter 170 mm enclosed in a aluminum application chamber of larger diameter 250 mm. The microwave power is fed to the plasma chamber by 8 inclined slots cut into the application chamber wall. The slots are coupled the chamber to a WR280 waveguide wound around it to form a ring resonator. In order to make two slots $\lambda_g/2$ apart in phase, the adjacent slots are rotated in opposite directions. The rotation angle of the slots are set to $60^{\circ}$ from the chamber axis. Between the quartz chamber and the aluminum cylindrical chamber 8 NdFeB magnets are equally spaced and fixed to form the cusp magnetic field confinement and ECR (Electron Cyclotron Resonance) field. In this presentation, the magnetic and electromagnetic simulations, and the measured plasma parameters are given for both the inclined and the vertical slot-excited plasma sources. We also discuss how the sources can be tailored to suit better-performing HNB sources.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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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.