Crystal growth in floating zone with phase change and thermo-solutal convections

Xiong, Bin; Hu, Wenrui

doi:10.1016/0022-0248(92)90330-l

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…According to our previous conclusions [5], the results show that the thermocapillary convection may act as a strong mixer, and the dimensionless solutal concentrations in the liquid region are much larger than the dimensionless concentration value in the multi-crystal region C0 = 1. As the intensity of the thermocapillary convections is much larger than the intensity of the forced flow of pulling, the concentration values in the liquid bridge are always nearly uniform no matter how the gravity level is.…”

Section: Numerical Simulationsupporting

confidence: 75%

“…The Stefan conditions, together with other boundary conditions, are used to determine the shapes of interfaces. As usual, we introduced stream function i~' and vorticity 12, and the equations in the liquid bridge may then be expressed in relations of stream function-vorticity [4,5].…”

Section: )mentioning

confidence: 99%

“…The governing equations with appropriate boundary conditions are solved by the so-called "up-wind" finite element method [5,6]. A quadrilateral iso-parametric element is employed.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…The phase change interfaces are calculated by a "pseudo time-dependent" method [5].The numerical simulation is applied especially for the crystal growth of silicon, of which the thermophysical properties are given in refs. [5,8]. A diluted solute of small concentration is considered.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…However, it will be an interesting question whether this conclusion also holds for other crystal growth systems, and whether the gravity level can be tolerated for the dopant non-uniformity in the floating zone system. In our previous work [4,5],in which we have studied the thermal and solutal convection, diffusion and directional solidified interfacial shapes in the floating zone crystal growth process under zero gravity condition, we used the formulation in the following sections and the "up-wind" FEM method [6] to examine the extent of dopant non-uniformity in the model of the floating zone on gravity level from 0 to 1g 0. Comparisons are made between the results of the previous work [2,3] and those of the present paper.…”

Section: Introductionmentioning

confidence: 99%

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Influence of low-gravity level on crystal growth in floating zone

Xiong

1993

Journal of Crystal Growth

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The influence of low gravity level on crystal growth in the floating zone, which involves thermocapillary convection, phase change convection, thermal and solutal diffusion, is investigated numerically by a finite element method for the silicon crystal growth process. The velocity, temperature, concentration fields and phase change interfaces depending on heating temperature and growth rates are analyzed. The influence of low gravity level on the concentration is studied especially. The results show that the non-uniformities of concentration are about i0 3 for growth rate = 5.12x 10-8 m/s, 10-2 for = 5.12X i0~m/s and relatively larger for larger growth rate in the gravity level g = 0-9.8 rn/s2. The thermocapillary effect is strong in comparison with the Bridgman system, and the level of low gravity is relatively insensitive for lower growth rates.

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Section: Numerical Simulationsupporting

confidence: 75%

Section: )mentioning

confidence: 99%

“…The governing equations with appropriate boundary conditions are solved by the so-called "up-wind" finite element method [5,6]. A quadrilateral iso-parametric element is employed.…”

Section: Numerical Simulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of low-gravity level on crystal growth in floating zone

Xiong

1993

Journal of Crystal Growth

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Influence of curved interfaces of phase change on the radial segregation of crystal growth

1997

Chin. Sci. Bull.

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THE radial uniformity of components is an important parameter for crystal growth of a semiconductor of binary alloy. Radial segregation may be influenced by many factors, such as the convection"], curved solidification interfa~e[~-~]"), curved melting interface') and others. The influence of each factor is often interpreted by analytical solutions of simplified mode l~[ ' -~] " ) . However, the coupling process of more complete problems should be studied by the numerical method[59 61 .In this note, pure diffusion process is used to study the crystal growth process of binary alloy in the microgravity environment, and the influence of curved interfaces on solidification process in a cylindrical melting region with finite length and curved interfaces is investigated. The analytical solution was obtained by using the perturbation method and finite Hankel transform. The results show that the influence of curved melting interface on the radial segregation is smaller than that of curved solidification interface in general.Considering a melting region of radius a and length 1, the origin of the cylindrical coordinate system is located at the center of solidification interface and the z-axis is directed to the melting interface as shown in fig. 1. The equations and boundary conditions may be written as[2-41. 1)C ( r , x ) = C l ( r ) , z = W m ( r ) , (5 where C and CI are the concentrations in the melt and at the melting boundary respectively, V, D and k are the growth velocity, diffusion coefficient and effective segregation coefficient respectively, Ws( r ) and Wm( r ) are the functions of solidification interface and melting interface. In most cases, the studies have been completed for a plane melting interface Wm( r ) = 1) Xiong, B., Hu, W . R . , Crystal growth in floating zone with phase change and thermosolutal converction.

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