Spoke patterns on molten silicon in Czochralski system

Kyung Woo Yi, Koichi Kakimoto, Minoru Eguchi, Masahito Watanabe, Toshiyuki Shyo, Taketoshi Hibiya

研究成果: ジャーナルへの寄稿記事

65 引用 (Scopus)

抄録

Asymmetric temperature profiles similar to the spoke patterns and related asymmetric flow in Si melts of the Czochralski (CZ) system are verified for the first time by three-dimensional (3D) numerical simulation of heat and momentum transfer and by X-ray radiography technique. These profiles appear as the temperature difference between the wall and the crystal becomes large with symmetric boundary conditions. The 3D simulation leads to the conclusion that the vertical temperature gradient in the unstable layer near the free surface is an important cause of making the asymmetric profile. The profile is estimated to be caused by both Rayleigh-Bénard and Marangoni-Bénard instabilities in the Si melt. It is shown that the relative strength of these two instabilities depends on the coefficients of temperature dependence of the density and surface tension. If the temperature coefficient of surface tension (∂γ/∂T) is greater than 1 x 10-4 N/m {dot operator}, the Marangoni-Bénard instability mainly causes asymmetry, while if ∂γ/∂T is less than this value, the Rayleigh-Bénard instability mainly causes asymmetry.

元の言語英語
ページ(範囲)20-28
ページ数9
ジャーナルJournal of Crystal Growth
144
発行部数1-2
DOI
出版物ステータス出版済み - 1 1 1994
外部発表Yes

Fingerprint

spokes
Silicon
Molten materials
silicon
Surface tension
causes
temperature gradients
interfacial tension
profiles
asymmetry
X ray radiography
Temperature
Momentum transfer
radiography
coefficients
temperature profiles
Thermal gradients
momentum transfer
simulation
heat transfer

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Inorganic Chemistry
  • Materials Chemistry

これを引用

Spoke patterns on molten silicon in Czochralski system. / Yi, Kyung Woo; Kakimoto, Koichi; Eguchi, Minoru; Watanabe, Masahito; Shyo, Toshiyuki; Hibiya, Taketoshi.

:: Journal of Crystal Growth, 巻 144, 番号 1-2, 01.01.1994, p. 20-28.

研究成果: ジャーナルへの寄稿記事

Yi, KW, Kakimoto, K, Eguchi, M, Watanabe, M, Shyo, T & Hibiya, T 1994, 'Spoke patterns on molten silicon in Czochralski system', Journal of Crystal Growth, 巻. 144, 番号 1-2, pp. 20-28. https://doi.org/10.1016/0022-0248(94)90005-1
Yi, Kyung Woo ; Kakimoto, Koichi ; Eguchi, Minoru ; Watanabe, Masahito ; Shyo, Toshiyuki ; Hibiya, Taketoshi. / Spoke patterns on molten silicon in Czochralski system. :: Journal of Crystal Growth. 1994 ; 巻 144, 番号 1-2. pp. 20-28.
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abstract = "Asymmetric temperature profiles similar to the spoke patterns and related asymmetric flow in Si melts of the Czochralski (CZ) system are verified for the first time by three-dimensional (3D) numerical simulation of heat and momentum transfer and by X-ray radiography technique. These profiles appear as the temperature difference between the wall and the crystal becomes large with symmetric boundary conditions. The 3D simulation leads to the conclusion that the vertical temperature gradient in the unstable layer near the free surface is an important cause of making the asymmetric profile. The profile is estimated to be caused by both Rayleigh-B{\'e}nard and Marangoni-B{\'e}nard instabilities in the Si melt. It is shown that the relative strength of these two instabilities depends on the coefficients of temperature dependence of the density and surface tension. If the temperature coefficient of surface tension (∂γ/∂T) is greater than 1 x 10-4 N/m {dot operator}, the Marangoni-B{\'e}nard instability mainly causes asymmetry, while if ∂γ/∂T is less than this value, the Rayleigh-B{\'e}nard instability mainly causes asymmetry.",
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AU - Shyo, Toshiyuki

AU - Hibiya, Taketoshi

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N2 - Asymmetric temperature profiles similar to the spoke patterns and related asymmetric flow in Si melts of the Czochralski (CZ) system are verified for the first time by three-dimensional (3D) numerical simulation of heat and momentum transfer and by X-ray radiography technique. These profiles appear as the temperature difference between the wall and the crystal becomes large with symmetric boundary conditions. The 3D simulation leads to the conclusion that the vertical temperature gradient in the unstable layer near the free surface is an important cause of making the asymmetric profile. The profile is estimated to be caused by both Rayleigh-Bénard and Marangoni-Bénard instabilities in the Si melt. It is shown that the relative strength of these two instabilities depends on the coefficients of temperature dependence of the density and surface tension. If the temperature coefficient of surface tension (∂γ/∂T) is greater than 1 x 10-4 N/m {dot operator}, the Marangoni-Bénard instability mainly causes asymmetry, while if ∂γ/∂T is less than this value, the Rayleigh-Bénard instability mainly causes asymmetry.

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