• 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.

• 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 Korea Association of Crystal Growth Conference
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• 1997.10a
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• pp.117-121
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• 1997

It is shown theoretically that uniform axial dopant concentration distribution can be made throughout the crystal by continuous Czochralski process. Numerical simulation are performed for the transient two-dimensional convection-diffusion model. A typical value of the growth and system parameters for Czochralski growth of p-type, 4 inches silicon crystal was used in the numerical calculations. Using this model with proper model parameter, the axial segregation in batchwise Czochralski growth can be described. It is studied by comparing with the experimental data. With this model parameter, the uniform axial concentration distribution of dopant is predicted in continuous Czochralski process.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2397-2408
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• 1996

A numerical study was made of the control of transient oscillatory flow modes in Czochralski convection. The reduction of temperature oscillation was achieved by changing the rotation rate of crystal rod, .OMEGA.$_{S}$=.OMEG $A_{S0}$(1+ $A_{S}$sin(2.pi. $f_{S}$/ $t_{p}$t)). The temporal behavior of oscillation flow was scrutinized over broad ranges of two parameters, i.e., the rotation amplitude( $A_{S}$.leq.0.5) and the nondimensional frequency (0.9.leq. $f_{S}$.leq.1.5). The mixed convection parameter was ranged 0.225.leq.Ra/PrR $e^{2}$.leq.0.929, which encompassed the buoyancy-and forced-dominant convection regimes. Computational results revealed that the temperature oscillations could be reduced effectively by a proper adjustment of the control parameters. The uniformity of temperature distribution near the crystal rod was examined. The control of oscillatory flow modes was also made for a realistic, low value of Pr.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.4 no.1
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• pp.46-56
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• 1994

The characteristics of flows, temperatures, concentrations of the boron are numerically studied when uniform axial magnetic fields are applied in the Czechralski crucible. The to governing factors to the flow regimes are buoyancy, thermocapillarity, centrifugal forces, magnetic forces, diffusion coefficient and segregation coefficient of the boron. Since the concentration of the boron is so low that buoyancy effects are negligible, it cannot affect the flow and temperature fields. From the fact that the flow fields are rotationally symmetric, two velocity components in the meridional plane and the circumferential velocity are calculated together with the temperature in the steady state. Based on the known velocity and temperature distributions the unsteady concentration distributions of the boron are calculated. As the strength of the magnetic is increased, the flow velocities are decreased. Circumferential velocities are large near the crucible side-wall and in the region below the rotating crystal. Steep temperatures gradient near the edge of the rotating crystal causes the Marangoni convection. It has been found out that the convection characteristics affects the unsteady transport phenomena of the boron.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.4 no.3
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• pp.210-222
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• 1994

The characteristics of flows, temperatures, and concentrations of oxygen are numerically studies in the Czochralski furnace with a uniform axial magnetic field. Important governing factors to the flow fields include buoyancy, thermocapillarity, centrifugal force, magnetic force, diffusion and segregation coefficients of the oxygen, evaporation coefficient in the form of SiO, and ablation rate of crucible wall. With an assumption that the flow fields have reached the steady state, which means that two velocity components in the meridional plane and circumferential velocity, temperatures, electric current intensity become non-transient, then unsteady concentration field of oxygen has been analyzed with an initially uniform oxygen concentration. Oxygen transports due to convection and diffusion in the Czochralski flow field and oxygen flux through the growing crystal surface has been investigated.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.8 no.1
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• pp.18-28
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• 1998

A laboratory experiment was made of a control of temperature oscillation in Czochralski convection. Numerical computation was also made to delineate the control of temperature oscillation. The suppression of temperature oscillation was achieved by varying the rotation rate of crystal rod ($\Omega=\Omega_0(1+A sin 2{\pi}ft/t_p)$), where A denotes the amplitude of rotation rate and f the frequency factor. Based on the inherent dimesionless time period of temperature oscillation ($t_p$), the suppression rate of temperature oscillation was characterized by the mixed convection parameter ($0.217{\leq}Ra/PrRe^2{\leq}1.658$). The optimal values of A and f were also scrutinized. To understand the suppression mechanism of temperature oscillation, the controls of isotherm($\theta$) and equi-vorticity($\omega$) were investigated.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.2
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• pp.149-156
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• 1999

An experimental simulation on the flow in Czochralski melt using a cold model was carried out to obtain the velocities of fluid flow which affects the oxygen concentration of Czochralski crystal growing system. Low melting point Woods metal with similar Pr number to the silicon melt was adopted as a working fluid. Local flow velocities at numerous positions in the melt were simulataneously measured in three dimension using incorporated magnet probe. The measured velocity field showed a non-axisymmetric pattern dominated by natural convection. The analysis on the correlation between data set of temperatures simultaneously measured at two melt positions showed that the values of correlation coefficients were smaller than those of previous study on the small size of silicon melt and these phenomena are believed to occur because turbulent behavior becomes stronger in large size of the melt.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.28 no.4
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• pp.141-147
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• 2018

Solar energy has attracted big attentions as one of clean and unlimited renewable energy. Solar energy is transformed to electrical energy by solar cells which are comprised of multi-silicon wafer or mono-silicon wafer. Monosilicon wafers are fabricated from the Czochralski method. In order to decrease fabrication cost, increasing a poly-silicon charge size in one quartz crucible has been developed very much. When we increase a charge size, the temperature control of a Czochralski equipment becomes more difficult due to a strong melt convection. In this study, we simulated a Czochralski equipment temperature at 20 inch and 24 inch in quartz crucible diameter and various charge sizes (90 kg, 120 kg, 150 kg, 200 kg, 250 kg). The simulated temperature profiles are compared with real temperature profiles and analyzed. It turns out that the simulated temperature profiles and real temperature profiles are in good agreement. We can use a simulated profile for the optimization of real temperature profile in the case of increasing charge sizes.

• 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.