Dynamic simulation of impurity transport and chemical reactions in a Bridgman furnace for directional solidification of multi-crystalline silicon

Bellmann, M.P.; Panjwani, Balram; Syvertsen, Martin; Meese, Ernst A.

doi:10.1016/j.jcrysgro.2013.02.008

Cited by 18 publications

(10 citation statements)

References 22 publications

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“…Heat conservation equation (1) Heat conservation at the interface (2) Temperature continuity at the interface (3) Impurity concentration equation (4) Impurity conservation at the interface (5) Phase diagram relation (6) In these equations, is the thermal conductivity, is the thermal capacity, is the density, is the latent heat of fusion, and is the solutal diffusivity.…”

Section: Meyer's Original Methodsmentioning

confidence: 99%

“…The continuous development of computational resources and the need for a better understanding of the phenomena and for optimization of industrial processes have led to the development of several numerical modelling strategies in the last decades. Numerous efforts have been made to develop realistic 2D and 3D simulation tools using either an enthalpy approach featuring a diffuse interface computed on a fixed mesh [1][2][3][4][5] or resorting to adaptive meshing techniques to track the solidification front and insure its fine description with nodes located on the interface [6][7][8][9][10][11]. Combining coupled 2D and 3D simulations is now an established strategy to reduce computational cost in particular in the Czochralski configuration in which the front is nearly fixed in space [12,13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient 1D numerical model adapted to the study of transient convecto-diffusive heat and mass transfer in directional solidification

Tavernier

Millet

Henry

et al. 2017

International Journal of Heat and Mass Transfer

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International audienceWe combine an effective diffusivity model with a numerical approach initially proposed by Meyer (1981) to simulate transient heat and mass transfer phenomena in a directionally solidifying Sn-Bi rod. This particularly efficient 1D numerical model is light enough to be used within the frame of optimization methods at reasonable numerical cost. This approach is tested against reference in situ measurements obtained under microgravity conditions during the Mephisto program. We simulate the final homogenization transient of several experimental runs with different pulling velocities. The solid/liquid interface temperature evolution with time is extracted from the simulations and compared with that obtained by Seebeck in line measurements. After optimization of the model the observed discrepancy between the simulated and measured data is less than 1.5%. This validates both the proposed very efficient 1D numerical approach and the consistency of the set of thermophysical parameters values for dilute Sn-Bi alloys

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Section: Meyer's Original Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient 1D numerical model adapted to the study of transient convecto-diffusive heat and mass transfer in directional solidification

Tavernier

Millet

Henry

et al. 2017

International Journal of Heat and Mass Transfer

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show abstract

“…In some furnaces, the carbon solubility limit in the melt could be already exceeded during melting down resulting in significant SiC precipitates at the beginning [92]. Furthermore, the reaction of the silica crucible and the graphite susceptor could also occur [46], i.e., SiO 2ðsÞ þ C ðsÞ ¼ SiO ðgÞ þ CO ðgÞ :…”

Section: Control Of Impuritiesmentioning

confidence: 99%

Multicrystalline Silicon Crystal Growth for Photovoltaic Applications

Lan

Hsu

Nakajima

2015

Handbook of Crystal Growth

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“…To improve silicon ingot quality, the seeded DS process still needs considerable work. The impurities in the silicon ingots significantly influence the quality of the silicon ingots and the photoelectric conversion efficiency of solar cells [1,2]. Typically, oxygen and carbon are the main impurities in the DS furnace affecting solar cell wafers.…”

Section: Introductionmentioning

confidence: 99%

Effect of Argon Flow on Oxygen and Carbon Coupled Transport in an Industrial Directional Solidification Furnace for Crystalline Silicon Ingots

Xue

et al. 2021

Crystals

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Transient global simulations were carried out to investigate the effect of argon flow on oxygen and carbon coupled transport in an industrial directional solidification furnace for quasi-single crystalline silicon ingots. Global calculation of impurity transport in the argon gas and silicon melt was based on a fully coupled calculation of the thermal and flow fields. Numerical results show that the argon flow rate affects the flow intensity along the melt–gas surface, but has no significant effect on the flow patterns of silicon melt and argon gas above the melt–gas surface. It was found that the evaporation flux of SiO along the melt–gas surface decreases with the increasing argon flow rate during the solidification process. However, the net flux of oxygen atoms (SiO evaporation flux minus CO dissolution flux) away from the melt–gas surface increases with the increasing argon flow rate, leading to a decrease in the oxygen concentration in the grown ingot. The carbon concentration in the grown ingot shows an exponential decrease with the increase of the argon flow rate, owing to the fact that the dissolution flux of CO significantly decreases with the increasing argon flow rate. The numerical results agree well with the experimental measurements.

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Dynamic simulation of impurity transport and chemical reactions in a Bridgman furnace for directional solidification of multi-crystalline silicon

Cited by 18 publications

References 22 publications

An efficient 1D numerical model adapted to the study of transient convecto-diffusive heat and mass transfer in directional solidification

An efficient 1D numerical model adapted to the study of transient convecto-diffusive heat and mass transfer in directional solidification

Multicrystalline Silicon Crystal Growth for Photovoltaic Applications

Effect of Argon Flow on Oxygen and Carbon Coupled Transport in an Industrial Directional Solidification Furnace for Crystalline Silicon Ingots

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