Finite Element Modeling of Silicon Transport into Germanium Using a Simplified Crystal Growth Technique

Mechighel, Farid; Ganaoui, Mohammed El; Pateyron, Bernard; Kadja, Mahfoud; Dost, S.

doi:10.4028/www.scientific.net/ddf.312-315.240

“…Vynnycky and Kimura [92] simulated the solidification and phase change in the presence of convection by using both numerical and analytical techniques. Mechighel et al [93] carried out a 2-D numerical simulation to study the velocity, temperature, and concentration distribution in the dissolution process of silicon into a germanium melt by utilizing the vertical Bridgman method. They showed that gravity has a strong effect on the shape of the interfaces and showed the transport becomes convection dominated when gravity is present.…”

Section: Solidificationmentioning

confidence: 99%

“…F. Mechighel et al [118] performed a numerical simulation to analyze the temperature and concentration behaviour in the separation process of silicon into molten germanium. They used a simplified arrangement similar to the materials arrangement used in the vertical Bridgman growth technique.…”

Section: Solidificationmentioning

confidence: 99%

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Jafar-Salehi¹

2021

Preprint

0

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The objective of this research was to study the solidification process of binary molten metals. This study was conducted in three phases. One was to estimate the thermodiffusion factor, two was to simulate the effect of natural convection and radiation on the velocity, temperature, and concentration distributions, and the third was to investigate the solidification process of binary molten metals using the proposed thermodiffusion factors. The proposed expression for the estimation of thermodiffusion factor was based on the physical properties of the mixture constituents. The estimated thermodiffusion factor was used to study thermosolutal convection in a quartz enclosure filled with molten Sn-Bi alloy. Two simulations were carried out: top heating and bottom heating. The sidewalls in both cases were exposed to convection and radiation. Numerical results show that in the case of top heating, the distribution of temperature and concentration are linear, but species segregation occurs due to the thermodiffusion effect. In the bottom heating case, boundary-driven convective flow develops with a large Rayleigh number (Ra) where an increase in the Ra number negates thermodiffusion due to the development of strong mixing. The results of these simulations showed that the effect of convection and radiation are negligible. In phase three, finite element method (FE) was employed to investigate the effect of thermodiffusion during vertical solidification of binary molten metal alloys with bottom cooling. The systems considered here are tin-bismuth (Sn-Bi), tin-cadmium (Sn-Cd), tin-zinc (Sn-Zn), tin-lead (Sn-Pb), tin-gallium (Sn-Ga), and bismuth-lead (Bi-Pb) binary molten metals. The geometry under study was a cylindrical cavity. The FE model was constructed using a 2D axisymmetric element to represent a 3D cyclindrical model. Two cases were studied: one without and one with the effect of thermodiffusion. The simulation including thermodiffusion showed slight variation from the simulation without thermodiffusion, in that thermodiffusion causes a slightly faster solidification and a more uniform concentration distribution if the thermodiffusion coefficient is greater than zero (DT > 0). The main object of this research is development of a more accurate thermodiffusion factor, and applying it in a numerical simulation to study its effects on radiation, natural convection, and solidification processes.

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“…Vynnycky and Kimura [92] simulated the solidification and phase change in the presence of convection by using both numerical and analytical techniques. Mechighel et al [93] carried out a 2-D numerical simulation to study the velocity, temperature, and concentration distribution in the dissolution process of silicon into a germanium melt by utilizing the vertical Bridgman method. They showed that gravity has a strong effect on the shape of the interfaces and showed the transport becomes convection dominated when gravity is present.…”

Section: Solidificationmentioning

confidence: 99%

“…F. Mechighel et al [118] performed a numerical simulation to analyze the temperature and concentration behaviour in the separation process of silicon into molten germanium. They used a simplified arrangement similar to the materials arrangement used in the vertical Bridgman growth technique.…”

Section: Solidificationmentioning

confidence: 99%

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Jafar-Salehi¹

2021

Preprint

0

View full text Add to dashboard Cite

The objective of this research was to study the solidification process of binary molten metals. This study was conducted in three phases. One was to estimate the thermodiffusion factor, two was to simulate the effect of natural convection and radiation on the velocity, temperature, and concentration distributions, and the third was to investigate the solidification process of binary molten metals using the proposed thermodiffusion factors. The proposed expression for the estimation of thermodiffusion factor was based on the physical properties of the mixture constituents. The estimated thermodiffusion factor was used to study thermosolutal convection in a quartz enclosure filled with molten Sn-Bi alloy. Two simulations were carried out: top heating and bottom heating. The sidewalls in both cases were exposed to convection and radiation. Numerical results show that in the case of top heating, the distribution of temperature and concentration are linear, but species segregation occurs due to the thermodiffusion effect. In the bottom heating case, boundary-driven convective flow develops with a large Rayleigh number (Ra) where an increase in the Ra number negates thermodiffusion due to the development of strong mixing. The results of these simulations showed that the effect of convection and radiation are negligible. In phase three, finite element method (FE) was employed to investigate the effect of thermodiffusion during vertical solidification of binary molten metal alloys with bottom cooling. The systems considered here are tin-bismuth (Sn-Bi), tin-cadmium (Sn-Cd), tin-zinc (Sn-Zn), tin-lead (Sn-Pb), tin-gallium (Sn-Ga), and bismuth-lead (Bi-Pb) binary molten metals. The geometry under study was a cylindrical cavity. The FE model was constructed using a 2D axisymmetric element to represent a 3D cyclindrical model. Two cases were studied: one without and one with the effect of thermodiffusion. The simulation including thermodiffusion showed slight variation from the simulation without thermodiffusion, in that thermodiffusion causes a slightly faster solidification and a more uniform concentration distribution if the thermodiffusion coefficient is greater than zero (DT > 0). The main object of this research is development of a more accurate thermodiffusion factor, and applying it in a numerical simulation to study its effects on radiation, natural convection, and solidification processes.

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“…Natural convection may be also present in some of the crystallisation processes, [20][21][22][23][24][25][26][27] which is the subject of our other work to be published separately. In solidification of binary molten alloys, all phenomena involved in heat transfer of a binary alloy without solidification is present as well as the solidification process, which is the last stage.…”

Section: Introductionmentioning

confidence: 99%

Estimation of molecular and thermodiffusion coefficients for non‐ideal molten metal alloys and its implication in solidification process

Jafar-Salehi

¹

,

Eslamian

²

,

Saghir

³

2014

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In this paper an expression is proposed for the estimation of thermodiffusion factor in liquid metal alloys. The expression can be readily used given that it requires properties that could be easily obtained from the physical properties of the mixture constituents, such as viscosity and molar volume. The predictive power of the proposed expression, as well as other pertinent models is examined against the experimental data. The estimated thermodiffusion factor is then used to study thermo‐solutal convection in an enclosure filled with molten Sn–Bi alloy by solving the transport equations numerically. Two simulations were carried out in a vertical rectangular cell encapsulated by a quartz container: top heating and bottom heating. The sidewalls in both cases were exposed to the external natural convection and surface radiation to the ambient. Numerical results show that in the top heating case, the distribution of temperature and concentration are linear, but species segregation occurs due to the thermodiffusion effect. In the bottom heating case, boundary‐driven convective flow develops with a large Rayleigh number (Ra) where an increase in the Ra number negates the thermodiffusion effect due to the development of strong mixing.

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Finite Element Modeling of Silicon Transport into Germanium Using a Simplified Crystal Growth Technique

Cited by 3 publications

References 17 publications

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

Estimation of molecular and thermodiffusion coefficients for non‐ideal molten metal alloys and its implication in solidification process

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