Turbulent heat transfer through the melt in silicon Czochralski growth

Kobayashi, Sumio; Miyahara, Shunji; Fujiwara, T.; Kubo, Teruichiro; Fujiwara, Hideki

doi:10.1016/0022-0248(91)90171-z

Cited by 23 publications

(7 citation statements)

References 7 publications

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“…20,21 Such a complex structure allows for the effective scattering of phonons and thus, thermal conductivities as low as 0.8 W/mÁK have been reported for SBN single crystals. 22 In addition, a change in the SBN stoichiometry leads to variations in the ferroelectric-paraelectric phase transition temperature. Within the limits of single phase Sr x Ba 1Àx Nb 2 O 6 stability (0.25…”

Section: Introductionmentioning

confidence: 99%

Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis

et al. 2013

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The thermoelectric properties of bulk polycrystalline Sr0.5Ba0.5Nb2O6 (SBN50) fabricated via solution combustion synthesis (SCS) and reduced at temperatures of 900°C–1150°C were explored. The Seebeck coefficient (S) of all samples increased over the entire range of testing temperatures; a peak S value of −281 μV/K was obtained at 930 K for the sample reduced at 900°C. A metal‐insulator transition was observed in the electrical conductivity (σ) of samples reduced at 1000°C–1150°C, whereas only semiconducting electrical behavior was observed for the sample reduced at 900°C. An optimal balance between S and σ was achieved for the pellet reduced at 1000°C, which exhibited a maximum power factor of 1.78 μW/cm·K2 at 930 K. Over a temperature range of 300–930 K, the thermal conductivity (κ) of as‐processed and reduced (1000°C) SBN50 was found to be 1.03–1.4 and 1.46–1.84 W/m·K, respectively. A maximum figure of merit (ZT) of 0.09 was obtained at 930 K for the 1000°C‐reduced sample. X‐ray photoelectron spectroscopy revealed that the Nb2+ peak intensity increased at higher reduction temperatures, which could possibly lead to a distortion of NbO6 octahedra and a decrease in the Seebeck coefficient.

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Section: Introductionmentioning

confidence: 99%

Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis

et al. 2013

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“…Temperature distributions of the melt are modified by crucible rotation in the case of the Czochralski method [10]. Both equilibrium oxygen concentration at the melt-crucible interface expressed by Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Convection in the melt plays a key role for the distribution of oxygen concentration in the melt and a crystal. It has been reported that convection in the melt can be suppressed by rotation of a crucible [9,10].…”

Section: Oxygen Transfermentioning

confidence: 99%

Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells

Matsuo¹,

Ganesh²,

Nakano³

et al. 2009

Journal of Crystal Growth

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“…Momentum + rClpvt ~ G -rC2p ~ [6] In the k-epsilon model, the eddy dynamic viscosity ,t can be evaluated as follows 6 k 2 ,t = CD- [7] This vt is used in Eq. 2-4.…”

Section: O( Ru )mentioning

confidence: 99%

Thermal Analysis of the Double‐Crucible Method in Continuous Silicon Czochralski Processing: II . Numerical Analysis

Ono

1993

J. Electrochem. Soc.

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Numerical simulations were performed for the melt temperature and convection in a double-crucible method. The k-epsilon turbulent flow model was applied and its results were compared to the experimental data. The calculation using the k-epsilon model converged successfully to a stable solution, while that with the laminar flow model did not. By the application of the k-epsilon model, we could simulate the temperature gradient in the thickness of the inner quartz crucible and the forced convection under the crystal. Moreover, the conclusion that the time-averaged isotherms were not much deformed was investigated from the model.

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Turbulent heat transfer through the melt in silicon Czochralski growth

Cited by 23 publications

References 7 publications

Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis

Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis

Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells

Thermal Analysis of the Double‐Crucible Method in Continuous Silicon Czochralski Processing: II . Numerical Analysis

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Turbulent heat transfer through the melt in silicon Czochralski growth

Cited by 23 publications

References 7 publications

Thermoelectric Properties of Reduced Polycrystalline Sr0.5Ba0.5Nb2O6 Fabricated Via Solution Combustion Synthesis

Thermoelectric Properties of Reduced Polycrystalline Sr0.5Ba0.5Nb2O6 Fabricated Via Solution Combustion Synthesis

Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells

Thermal Analysis of the Double‐Crucible Method in Continuous Silicon Czochralski Processing: II . Numerical Analysis

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Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis

Thermoelectric Properties of Reduced Polycrystalline Sr_0.5Ba_0.5Nb₂O₆ Fabricated Via Solution Combustion Synthesis