Yasunori Okano^1,*, Tsuyoshi Miyamoto¹, Sadik Dost²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.2, pp. 1-1, 2024, DOI:10.32604/icces.2024.011685

Abstract We have developed a machine learning model, called Hybrid-PINNs (Physics Informed Neural Networks), and applied for fast predictions of transport structures (flow and thermal fields) in the silicon (Si) melt during the Czochralski (Cz) bulk single crystal growth. Si bulk single crystals are mostly grown by the Cz method. For the growth of high-quality Si crystals with this method, it is essential to understand and control these transport structures in the melt. Since the direct observation of such transport fields in the melt during growth is usually impossible, numerical simulations provide a powerful tool for… More >

H. Azoui¹, D. Bahloul^1,*, N. Soltani²

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.2, pp. 87-105, 2018, DOI:10.3970/fdmp.2018.01149

Abstract In this work we have performed a three-dimensional numerical investigation in order to find the optimal conditions for growing efficiently high quality sapphire crystals with good thermal properties. We have studied thermal instabilities near the melt-crystal interface and the convective heat transfer under the Czochralski (Cz) process. We performed 3-D CFD simulation in cylindrical coordinates and used the Fast Fourier Transform method to analyze the temperature fluctuations. We present a detailed investigation on the effects of the crystal rotation speed and the temperature distribution on thermal instabilities of sapphire melt under forced convection. Where the More >

N. Soltani¹, S. Rahal¹

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.1, pp. 1-17, 2017, DOI:10.3970/fdmp.2017.013.001

Abstract A three-dimensional time-dependent numerical study of the flow instabilities in a simulated Czochralski system is conducted. The comparison with previously published experimental results is reported. The simulations were performed using a refined grid in order to investigate flow instabilities in the crucible. Simulations have been carried out for various crystal rotational speeds, by taking into account the effects of Rayleigh and Marangoni numbers. The temperature fluctuations near the crystal/liquid interface are analyzed. The method used for that purpose is the Fast Fourier Transform with the corresponding spectra. From numerical simulations, it has been observed that More >

V. Haslavsky, E. Miroshnichenko, E. Kit, A. Yu. Gelfgat

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.3, pp. 209-234, 2013, DOI:10.3970/fdmp.2013.009.209

Abstract Experimental and numerical observations of oscillatory instability of melt flow in a Czochralski model are compared, and a disagreement observed at small crystal dummy rotation rates is addressed. To exclude uncertainties connected with flow along the free surface, the latter is covered by a no-slip thermally insulating ring. Experiments reveal an appearance of oscillations at temperature differences smaller than the numerically predicted critical ones. At the same time, a steep increase of the oscillations amplitude is observed just beyond the computed threshold values. By increasing the dummy rotation gradually, we are able to qualitatively confirm More >

Koichi Kakimoto, Lijun Liu

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 167-174, 2006, DOI:10.3970/fdmp.2006.002.167

Abstract This paper deals with the investigation of the flow instability of molten silicon in a magnetic field during crystal growth by means of the Czochralski method. The flow exhibits a three-dimensional structure due to a transverse non-axisymmetric pattern of the magnetic field. The melt-crystal interface is found to be nearly two-dimensional. The azimuthal non-uniformity of the temperature field is much weaker on the crystal and crucible sidewalls in the case of high rotation rates of crucible and crystal than in the case of non-rotating crucible and crystal. More >

Haruhiko Kohno, Takahiko Tanahashi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 155-170, 2001, DOI:10.3970/cmes.2001.002.155

Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10^-2, Marangoni number Ma = 0.0 - 6.2067 × 10², Grashof number Gr = 7.1104 × 10⁶, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σ_T =0.0 - 1.5 × 10^-5N/mK. Although… More >