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 melt forced convection, the radiative… 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 for rotational speeds of the… More >

N. Armour¹, S. Dost^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.4, pp. 331-344, 2009, DOI:10.3970/fdmp.2009.005.331

Abstract A combined numerical and experimental investigation has been undertaken to explore the benefits of an applied static magnetic field on Silicon transport into a Germanium melt. This work utilized a similar material configuration to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The measured concentration profiles from the samples processed with and without the application of magnetic field showed very similar shape. The amount of silicon transport into the melt is slightly higher in the samples processed under magnetic field, and there is a substantial difference in dissolution interface shape indicating a change in… More >

M.M. Shemirani¹, M.Z. Saghir²

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.3, pp. 211-230, 2009, DOI:10.3970/fdmp.2009.005.211

Abstract A three-dimensional numerical modeling of Ge0.98Si0.02crystal growth is conducted to investigate the effect of g-jitter along with rotating magnetic field on the heat and mass transfer in the solvent region. It was found that the speed in the flow under the low frequency g-jitter is in the nano-centimeter per second and is too weak to have any impact on the silicon concentration in the process of crystallization near the growth interface. Different magnetic field intensities for different rotational speeds were examined. It was also found that rotating magnetic field not only did not suppress the convection but also generated an… More >

Shuwang Li¹, Xiangrong Li¹, John Lowengrub^1,2, Martin Glicksman³

FDMP-Fluid Dynamics & Materials Processing, Vol.4, No.1, pp. 27-42, 2008, DOI:10.3970/fdmp.2008.004.027

Abstract In this paper, we suggest a deterministic mechanism for the generation and development of side-branches in dendritic growth. The present authors investigated recently [Glicksman, Lowengrub, and Li (2006)] the existence of such a deterministic branching mechanism induced through the Gibbs-Thomson-Herring (GTH [Herring (1951)]) anisotropic capillary boundary condition. In this paper, we focus our study on an anisotropic kinetic boundary condition. We develop and apply accurate boundary integral methods in 2D and 3D, in which a time and space rescaling scheme is implemented, that are capable of separating the dynamics of growth from those of morphology change. Numerical results reveal that… More >

Y. Okano¹, A. Ishii¹, H. Miyashita¹, H. Minakuchi¹, S. Dost²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.4, pp. 261-270, 2006, DOI:10.3970/fdmp.2006.002.261

Abstract The article presents the results of a numerical simulation study that was carried out to examine the effect of g-jitter on the flow and concentration structures observed in the solution of a growth crucible under microgravity conditions. The simulation model considers a simple crucible of electroepitaxy, and assumes crucible rotation and applied axial static magnetic fields to control and minimize the effect of g-jitter induced flow oscillations. More >

C.P. Hong¹, M.F. Zhu², S.Y. Lee¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.4, pp. 247-260, 2006, DOI:10.3970/fdmp.2006.002.247

Abstract In typical solidification processes the flow of molten metal is usually regarded as an unavoidable phenomenon potentially affecting the morphology of dendritic growth. Fundamental understanding of such flow is thus important for predicting and controlling solidification microstructures. This paper presents numerical simulations on the evolution of dendritic microstructures with melt convection. A two-dimensional modified cellular automaton (MCA) coupled with a transport model is developed to simulate solidification of binary and ternary alloys in the presence of fluid flow. This model takes into account the effects of the constitutional undercooling and curvature undercooling on the equilibrium interface temperature. It also considers… More >

Marcello Lappa¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.2, pp. 141-152, 2006, DOI:10.3970/fdmp.2006.002.141

Abstract Numerical simulations and computer-graphics animation can be used as useful tools to discern the physicochemical environmental factors affecting the surface kinetics of growing biological tissues as well as their relative importance in determining growth. A mathematical formalism for such kinetics is proposed through parametric investigation and validated through focused comparison with experimental results. The study relies on the application of a CFD moving boundary (Volume of Fluid) method specially conceived for the simulation of these problems. In the second part of the analysis the case of two samples hydrodynamically interacting in a rotating bioreactor is considered. The interplay between two… More >

M. Sohail¹, M. Z. Saghir¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.2, pp. 127-140, 2006, DOI:10.3970/fdmp.2006.002.127

Abstract A numerical simulation study is carried out for the crystal growth of Ge1-xSixby the Traveling Heater Method (THM). The effects of a geometrical misalignment on the crystal growth are investigated. The full Navier-Stokes equations together with the energy, mass transport and continuity equations are solved numerically using the finite element technique. The application of a misalignment is shown to have a considerable effect on the buoyancy induced flow. An optimal misalignment is determined, that weakens the convective flow, provides a uniform concentration along the growth interface and gives symmetrical characteristics to the three-dimensional buoyancy induced flow. More >

Nancy Ma¹, John S. Walker²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.2, pp. 119-126, 2006, DOI:10.3970/fdmp.2006.002.119

Abstract For semiconductor crystal growth from a melt, stirring due to the interaction of a steady electric current and a steady magnetic field can lead to a more uniform distribution of the additives in the crystal. This paper treats the electromagnetic stirring in a cylinder with a weak uniform axial magnetic field and with an electric current between an electrode in the center of the top of the cylinder and an electrode at the vertical wall of the cylinder. The magnitude and distribution of the stirring are studied as functions of the aspect ratio of the cylinder and of the strength… More >