Gravity effect on solute transport in dissolution and growth of silicon

Kimura, Masakazu; Sukegawa, Tokuzo

doi:10.1016/s0022-0248(08)80124-8

Cited by 19 publications

(14 citation statements)

References 9 publications

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“…Following Kimura et al [22], a schematic view of the model considered in this study is given in figure 1. Horizontal silicon substrates of 2 cm × 2 cm are set face to face, 4 mm apart.…”

Section: Numerical Modelmentioning

confidence: 99%

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Simulation of dissolution of silicon in an indium solution by spectral methods

Cosckun

Yener

Arinç

2002

Modelling Simul. Mater. Sci. Eng.

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The results of a numerical simulation of natural convection due to concentration gradients during dissolution of silicon in an indium solution in a horizontal substrate-solution-substrate system are presented. The Chebyshev-Tau spectral method has been used for the simulations. The results are in very good agreement with the experimental data available in the literature. It is concluded that the discrepancies in the dissolution depths between the previous simulations and experimental data, especially at the earlier stages of the process, are mostly due to combined effects of uncertainties in the predicted properties and insufficient numerical accuracy.

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“…Following Kimura et al [22], a schematic view of the model considered in this study is given in figure 1. Horizontal silicon substrates of 2 cm × 2 cm are set face to face, 4 mm apart.…”

Section: Numerical Modelmentioning

confidence: 99%

“…This indicated that solutal convection accelerates the transport of silicon upwards. Kimura et al [22] carried out a similar experiment 3 Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Simulation of dissolution of silicon in an indium solution by spectral methods

Cosckun

Yener

Arinç

2002

Modelling Simul. Mater. Sci. Eng.

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“…Sukegawa et al [73,214,215] developed a 'yo-yo' technique for silicon and III-V compounds. Analysis of convectively driven growth in silicon LPE systems has been described by Kimura et al [217][218][219][220], Dost et al [221], and Coşkun et al [222]. The temperature is programmed to cycle between two constant temperature stages.…”

Section: Convection ("Yo-yo" Method)mentioning

confidence: 99%

Liquid-Phase Epitaxy

Mauk

2015

Handbook of Crystal Growth

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“…Huang et al (2015) remarkably demonstrated the recession of a dissolving solid in a high-speed laminar flow and the effect of the solid body geometry on the dissolution process. Accordingly, to predict the dissolution rate and pattern formation successfully, several factors, including the flow and body geometry, must be considered in addition to the mass transfer on the dissolving surface (Kimura, Tanaka & Sukegawa 1990;Sullivan, Liu & Ecke 1996;Huang et al 2015;Nakouzi, Goldstein & Steinbock 2015;Philippi et al 2019;Cohen et al 2020). The effects of gravitational instability on the dissolution rate and pattern formation under a stationary solvent condition have been studied, but only in a limited manner.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

Hong

Kim

2023

J. Fluid Mech.

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The dissolution of a horizontal salt body is theoretically and numerically investigated by considering the coupled dynamics of the dissolution reaction and the diffusive and convective mass transfer at the salt surface. To take into account the nature of the recessing salt surface and the dissolution-driven convection, a dynamic moving boundary condition coupled with a dissolution reaction are employed By employing a newly derived moving interface condition and parameters, a theoretical analysis predicts the onset of gravitational instability, suggesting scaling relationships between parameters to describe the onset of instability (in transport-dominant (Damkholer number $Da \to \infty $ and Rayleigh number $Ra > {10^5}$ ), onset time ${\tau _d}\sim R{a^{ - 2/3}}$ and ${\tau _d}\sim (RaDa)^{1/4}$ for reaction-dominant regimes $(Da \to 0)$ ). The scaling relationships on dissolution (the average height change, $\Delta {h_{avg}}\sim \sqrt \tau $ for the diffusion-dominant regime and $\Delta {h_{avg}}\sim R{a^{0.79/3}}{\tau ^{0.86}}$ for the convection-dominant regime) are also suggested to explain the pattern formation. Under a convective mass transfer condition, the concentration gradient of the solute developed during the recession of the salt surface results in an adverse density gradient, which causes gravitational instability motion and finally determines the formation of a dissolution pattern. In addition, two-dimensional and three-dimensional numerical simulations visualize dissolution-driven convective flow fields, the recession of the liquid-solid interface and pattern formation on the dissolving interface. Theoretical and numerical analyses of the dissolution process suggest that the control of gravitational instability is important to prevent or enhance dissolution pattern formation. This systematic parameter study provides a deep understanding of the effect of gravitational instability on convection-driven dissolution in a horizontal geometry.

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Gravity effect on solute transport in dissolution and growth of silicon

Cited by 19 publications

References 9 publications

Simulation of dissolution of silicon in an indium solution by spectral methods

Simulation of dissolution of silicon in an indium solution by spectral methods

Liquid-Phase Epitaxy

Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

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