Buoyant convection during Czochralski silicon growth with a strong, non-uniform, axisymmetric magnetic field

Khine, Yu Yu; Walker, John S.

doi:10.1016/0022-0248(94)00732-2

Cited by 10 publications

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“…Since the thermocapillary convection and the centrifugal-pumping flow are confined to the top layer, they have no effect on the 0(1) temperature because any heat released by a radially inward flow is exactly balanced by the heat absorbed by the equal radially outward flow. Since the 0(1) temperature is continuous through the top layer, i.e., Tt(r, ) = T,(r, b) + O(Ha-'/2), the temperatures needed to compute the thermocapillary 8 or buoyant 9 ' 0 convection in the top layer are given by the core temperature at z = b. We used a Chebyshev Spectral Collocation method to solve for the coupled variables Bpo and T,.…”

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Melt‐Motion during the Czochralski Growth of Silicon Crystals with a Cusp Magnetic Field

Khine

Walker

1997

J. Electrochem. Soc.

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The relative importance of the three melt-motion components (thermocapillary convection, the buoyant convection, and centrifugal-pumping flow) during the Czochralski growth of silicon crystals with a cusp magnetic field is investigated by combining the separate asymptotic solutions. The top boundary layer, which is adjacent to the crystal-melt interface and to the free surface, is very important because the thermocapillary and centrifugal-pumping flows are confined to this layer, and because the flow here determines the radial distributions of oxygen and dopants in the crystal, as well as the rate of oxygen evaporation from the free surface. The buoyant convection is not confined to the top layer, extends over the entire melt, and is the only component of the melt motion which affects the melt temperature for 0(1) thermal Peclet numbers. The analysis of the thermal problem with convective heat transport is presented. The effects of varying the Hartmann number, the thermal P6clet number, and the angular velocity of the crystal on the balance between the three melt-motion components in the top layer are investigated.

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