Finite-element simulation of Czochralski bulk flow

Crochet, Marcel; Wouters, Pascale; Geyling, F. T.; Jordan, As.

doi:10.1016/0022-0248(83)90048-9

Cited by 79 publications

(22 citation statements)

References 12 publications

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“…Z.Galazka and H.Wilke [11] have showed that during the growth of YAG, the interface convexity decreases when the crystal rotation rate increases, it becomes almost flat for high Reynolds number values. Crochet M J et al [12] studied numerically the effect of forced convection induced by rotation on the Czochralski crystal growth of GaAs in a cylindrical crucible for different Reynolds number values. Liu L and Kakimoto K [13] analysed the effect of crystal rotation on the growth interface shape in the presence of a transverse magnetic field, they found that the melt-crystal interface changes from an obvious 3D shape when the crystal is not rotating to an almost 2D shape with increase in rotation rate.…”

Section: Introductionmentioning

confidence: 99%

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

Mokhtari

Bouabdallah

Zizi

et al. 2010

J. Phys.: Conf. Ser.

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Abstract. In order to understand the influence of a semispherical crucible geometry combined with different convection modes as a thermocapillary convection, natural convection and forced convection, induced by crystal rotation, on melt flow pattern in silicon Czochralski crystal growth process, a set of numerical simulations are conducted using Fluent Software. We solve the system of equations of heat and momentum transfer in classical geometry as cylindrical and modified crystal growth process geometry as cylindro-spherical. In addition, we adopt hypothesis adapted to boundary conditions near the interface and calculations are executed to determine temperature, pressure and velocity fields versus Grashof and Reynolds numbers. The analysis of the obtained results led to conclude that there is advantage to modify geometry in comparison with the traditional one. The absence of the stagnation regions of fluid in the hemispherical crucible corner and the possibility to control the melt flow using the crystal rotation enhances the quality of the process comparatively to the cylindrical one. The pressure field is strongly related to the swirl velocity.

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Section: Introductionmentioning

confidence: 99%

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

Mokhtari

Bouabdallah

Zizi

et al. 2010

J. Phys.: Conf. Ser.

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“…There are many papers dealing with modelling of the Czochralski flow, e. g. [6], [15], [8], [2], [7], [11]. Usually the above introduced system (often without unknowns C and χ and their equations) is studied from the physical point of view, several discretization schemes and numerical experiments are introduced.…”

Section: ∂ω ∂Z For Unknown Functions S ω T C ψ χ (U = U(ψ) W = mentioning

confidence: 99%

Modelling of the Czochralski flow

Franc

1998

Abstract and Applied Analysis

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Abstract. The Czochralski method of the industrial production of a silicon single crystal consists of pulling up the single crystal from the silicon melt. The flow of the melt during the production is called the Czochralski flow. The mathematical description of the flow consists of a coupled system of six P.D.E. in cylindrical coordinates containing Navier-Stokes equations (with the stream function), heat convection-conduction equations, convection-diffusion equation for oxygen impurity and an equation describing magnetic field effect.This paper deals with the analysis of the system in the form used for numerical simulation. The weak formulation is derived and the existence of the weak solution to the stationary and the evolution problem is proved.

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“…Galazka and Wilke [10] have showed that during the growth of YAG, the interface convexity decreases when the crystal rotation rate increases, it becomes almost flat for high Reynolds number values. Crochet et al [11] studied numerically the effect of forced convection induced by rotation on the Czochralski crystal growth of GaAs in a cylindrical crucible for different Reynolds number values. Liu and Kakimoto [12] analyzed the effect of crystal rotation on the growth interface shape in the presence of a transverse magnetic field, they found that the melt-crystal interface changes from an obvious 3D shape when the crystal is not rotating to an almost 2D shape with increase in rotation rate.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Mixed Convection in Cylinrical Czochralski Configuration for Crystal Growth of Silicon

Atia¹,

Bouabdallah²,

Teggar³

et al. 2015

IJHT

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A numerical study of the mixed convection of liquid metal in Czochralski configuration for crystal growth was carried out. The finite volume method with SIMPLER Algorithm was used to solve the conservation equations of mass, momentum and energy. Due to computational constraints, the simulations were limited to axisymmetric geometries. The obtained results are compared to the experimental data of the literature. The effect of Richardson number on the flow structure and the thermal field has been presented and discussed for Ri = 0.1, 0.5, 1, 1.5 and 2. The effect of the aspect ratio of the cavity was also analysed. The results showed that increasing of Richardson number increases the velocity of the fluid in the cavity and reduces the rate of heat transfer. The aspect ratio had a significant effect on the velocity and thermal fields.

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Finite-element simulation of Czochralski bulk flow

Cited by 79 publications

References 12 publications

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

Modelling of the Czochralski flow

Numerical Study of Mixed Convection in Cylinrical Czochralski Configuration for Crystal Growth of Silicon

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