Three-dimensional simulation of heat flow, segregation, and zone shape in floating-zone silicon growth under axial and transversal magnetic fields

Lan, C.W.; Yeh, B.C.

doi:10.1016/j.jcrysgro.2003.09.055

Cited by 18 publications

(11 citation statements)

References 20 publications

(37 reference statements)

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“…[3][4][5]8) in floating zone, and this convection pattern is blamed to result in a large radial segregation in crystal growth under axis magnetic field. [3][4][5][6][7][8] 4.2 The axisymmetric non-uniform magnetic field generated by single coil The axisymmetric non-uniform magnetic field generated by the single coil is considered. The size of coil is ignored for the computation of magnetic field, the circle coil and liquid Figs.…”

Section: Axial Uniform Magnetic Fieldmentioning

confidence: 99%

“…In floating zone model under axial magnetic field, Lan 6) reported that there was a steady solution with a four-fold symmetry before reaching an axisymmetric state with the increasing magnetic field strength, it hints the importance to adopt three-dimensional model even under axisymmetric magnetic field. Floating half-zone model, so called liquid bridge model, is simplified from floating zone, and is widely applied to investigate thermocapillary flow.…”

Section: Introductionmentioning

confidence: 99%

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Thermocapillary Convection of Liquid Bridge under Axisymmetric Magnetic Fields

2008

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Three-dimensional numerical simulation of thermocapillary flow in liquid bridge model is performed. The effects of the magnetic field, including both axial uniform magnetic field and axisymmetric non-uniform magnetic field generated by circle coil, on the thermocapillary flow of semiconductor melt are investigated. For a three-dimensional thermocapillary flow, the axial magnetic field and the axisymmetric nonuniform magnetic field suppress convection effectively, and the three-dimensional thermocapillary flow tends to become an axisymmetric one. Under axial magnetic field, the convection in central core region becomes very weak, and in the meantime, the energetic thermocapillary flow is squeezed toward free surface. While the axisymmetric non-uniform magnetic field generated by single coil is applied on the melt of liquid bridge, the convection structure is similar with that under axial magnetic field. By applying the axisymmetric CUSP magnetic field generated by two coils, convection structure depends on the symmetric plane position of two coils (SPPTC), the surface tension flow penetrates the whole liquid bridge and no stagnant core in the inner part of the melt is observed when SPPTC locates at z Ã ¼ 0:5, which is thought as a more favorable convection structure to alleviate radial dopant segregation in floating zone crystal growth.

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Section: Axial Uniform Magnetic Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermocapillary Convection of Liquid Bridge under Axisymmetric Magnetic Fields

2008

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“…As shown in figure 9, under the magnetic field generated by transversal four coils of different radiuses, the convection structures look like cellular eddies at x * =0, and thermocapillary flow pass across the whole liquid bridge longitudinally. Consequently, radial segregation in thermocapillary flow under axial uniform magnetic field could be avoided [1][2][3][4]9,13]. Figure 10 draws the curve that describes the relationships of the mean and maximum convection velocities to the coil radius under the magnetic fields generated by transversal four coils, when L t * =4.…”

Section: Governing Equationsmentioning

confidence: 99%

“…There is no doubt that both axial uniform magnetic field and transversal uniform magnetic field could suppress convection in crystal growth and alleviate the oscillation of convection; however, related work indicates that radial segregation occurs under axial uniform magnetic fields [1][2][3][4], which is unfavorable to the growth of high-quality crystal; the axisymmetry of crystal growing environment is broken by transversal uniform magnetic fields, causing asymmetrical growing interface [5,6]. Accordingly, it is of great value to study how to optimize convection control by nonuniform static magnetic field generated by coils.…”

Section: Introductionmentioning

confidence: 99%

Influence of transverse magnetic field on thermocapillary flow in liquid bridge

Zeng

Yao

et al. 2011

Cryst. Res. Technol.

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For exploring the optimizing convection control technique by external magnetic field in floating zone crystal growth of semiconductor under microgravity, thermocapillary flow in a floating half-zone model is simulated numerically, and the influences of both the transversal uniform magnetic field and the magnetic field generated by transversal four coils on thermocapillary flow are investigated. The results indicate that the transversal uniform magnetic field is likely to break the axisymmetrical structure of thermocapillary flow, which is unfavorable to the growth of high-quality crystal; under the magnetic field generated by transversal four coils, both the mean and the maximum velocities increase with the increment of the distance between coils or the decrement of coil radius; and the convection tends to be more axisymmetrical with increasing coil radius. Compared to the transversal uniform magnetic field, the magnetic field generated by transversal four coils of appropriate radius and relative distance may not only suppress convection, but also enhance the axisymmetry of convection at the same time, and finally, the better convection control can be achieved.

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“…The hydrodynamic and hydrothermal instability mechanisms of low and high-Pr liquid bridges, respectively, have been confirmed in [Chen et al 1997;Lappa 2005a;Bouizi et al 2007] and elsewhere. Lan and Yeh [2004; performed quite complete full-zone modeling involving three-dimensional radiation, a deformable free surface and melting interfaces, dopant distribution, and axial and transverse magnetic damping. Prange et al [1999] studied the half-zone instability with axial magnetic field stabilization up to Ha = 25.…”

Section: Introductionmentioning

confidence: 99%

Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

Huang¹,

Houchens²

2011

J. Mech. Mater. Struct.

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A full-zone model of a thermocapillary-driven liquid bridge exposed to a steady, axial magnetic field is investigated using a global spectral collocation method for low-Prandtl number (Pr) fluids. Flow instabilities are identified using normal-mode linear stability analyses. This work presents several numerical issues that commonly arise when using spectral collocation methods and linear stability analyses in the solution of a wide range of partial differential equations. In particular, effects such as discontinuous boundary condition regularization, identification of spurious eigenvalues, and the use of pseudospectra to investigate the robustness of the stability analysis are addressed. Physically, this work provides simulations in the practical range of experimentally utilized magnetic field stabilization in optically heated float-zone crystal growth. A second-order vorticity transport formulation enables modeling of the liquid bridge up to these intermediate magnetic field strength ranges, measured by the Hartmann number (Ha). The thermocapillary driving and magnetic stabilization effects are observed up to Ha = 500 for Pr = 0.001 and up to Ha = 300 for Pr = 0.02. Prandtl number effects on temperature and flow fields are investigated within Pr ∈ (10 −12 , 0.0667) and indicate that Pr = 0.001 is a good representation of the base state in the Pr → 0 limit, at least up to Ha = 300.

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Three-dimensional simulation of heat flow, segregation, and zone shape in floating-zone silicon growth under axial and transversal magnetic fields

Cited by 18 publications

References 20 publications

Thermocapillary Convection of Liquid Bridge under Axisymmetric Magnetic Fields

Thermocapillary Convection of Liquid Bridge under Axisymmetric Magnetic Fields

Influence of transverse magnetic field on thermocapillary flow in liquid bridge

Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

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