Experimental observation and numerical simulation of wave patterns in a Czochralski silicon melt

Seidl, A.; McCord, G.; Müller, G.; Leister, H.-J.

doi:10.1016/0022-0248(94)90969-5

Cited by 60 publications

(27 citation statements)

References 14 publications

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“…Contrarily, Seidl et al [20] observed that the azimuthal m-folded (m=2, 3, 4, … ) waves propagated in a direction opposite to the crucible at higher crucible rotation rates, both by experiments and numerical simulations. With the higher crucible rotation rate, the wave number is larger and the phase velocity of the wave is faster, but always lower than the crucible rotation rate [21].…”

Section: Introductionmentioning

confidence: 96%

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

2010

Sci. China Technol. Sci.

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The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations. The results show that the basic flow state of this system is axisymmetric and steady, but has rich structures at the meridian plane. However, when the rotation Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, characterized by the velocity fluctuation waves traveling in the azimuthal direction. The main characteristics of the flow patterns are presented, including the propagating direction, velocity, amplitude and wave number, which depend on the rotation rates and directions of the disk and the cylindrical pool, and the critical conditions for the onset of oscillatory flow are also determined. For the case of disk-only rotation, the centrifugal instability is responsible for the flow transition, and when the disk iso-and counter-rotates with the cylindrical pool, the mechanisms for the transition are elliptic and of circular shear instabilities, respectively. rotation, flow transition, flow instabilityCitation:Wu C M, Li Y R. Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface.

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Section: Introductionmentioning

confidence: 96%

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

2010

Sci. China Technol. Sci.

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“…Ristorcelli et al [9] summarized many possible flow instabilities in the melt of the Czochralski cystal growing system. Among the instabilities, researchers thought that the rotating RayleighBenard instability [10] or the baroclinic [11] instability might be the origin of the asymmetric profile.…”

Section: Results Of the Calcula~ons And Discussionmentioning

confidence: 99%

Oxygen concentration inhomogeneity in the silicon melt of the czochralski single crystal growth system

Kim

1998

Metals and Materials

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The momentum, heat and mass transfer in the silicon melt of the Czochralski crystal growth system were calculated with a three dimensional numerical simulation technique. Several types of non-axisymmetric profiles of velocities, temperature and oxygen concentration appeared in the melt with axisymmetrical boundary conditions. Since the asymmetric profiles and the rotations of fluid, temperatures and oxygen concentration fluctuated in the melt. The correlations between both fluctuations at the same point became larger, as the convection grew stronger. The calculation also showed that the temperature and oxygen concentration near the interface also fluctuated. The results suggested that the oxygen concentration could be considered one of the causes of the striation pattern in grown silicon single crystals.

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“…[45] Die periodischen Oszillationen werden durch konvektive Instabilitäten bewirkt, [49] wenn in rotierenden Flüssigkeiten dominante, vertikale Temperaturgradienten auftreten. [50] Schaltet man das Cusp-Magnetfeld aus (Ha = 0), so verlieren die Oszillationen im beschriebenen Modell ihre Periodizität. Bei Z (Abbildung 11, oben) liegt Ein Cusp-Magnetfeld wirkt sich auch sehr güns-tig auf die Temperaturverteilung in der Siliciumschmelze und an der Grenzfläche zum CZ-Siliciumeinkristall aus.…”

Section: Numerische Simulation Des Kristallziehensunclassified

Czochralskis schöpferischer Fehlgriff: ein Meilenstein auf dem Weg in die Gigabit‐Ära

et al. 2003

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Experimental observation and numerical simulation of wave patterns in a Czochralski silicon melt

Cited by 60 publications

References 14 publications

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

Oxygen concentration inhomogeneity in the silicon melt of the czochralski single crystal growth system

Czochralskis schöpferischer Fehlgriff: ein Meilenstein auf dem Weg in die Gigabit‐Ära

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