التفاصيل البيبلوغرافية
| العنوان: |
Optimal Control of Temperature Gradient in a Large Size Magnetic Czochralski Silicon Crystal Growth by Response Surface Methodology. |
| المؤلفون: |
Yao, Z. H., Yuan, M. W., Yu, H. P., Sui, Y. K., Wang, J., Dai, X. L., An, G. P. |
| المصدر: |
Computational Methods in Engineering & Science; 2007, p330-330, 1p |
| مستخلص: |
Numerical simulation of a Czochralski crystal growth is a very helpful tool in optimizing the real experiment to produce high-quality single crystals in microelectronic industry. With the increase of silicon crystal size by Czochralski method, the melt volumes and the corresponding crucible diameters have to increase as well, which make the melt flows become more and more turbulent, laminar model is no longer suitable, so a low-Reynolds number k -ɛ model of Jones and Launder considered Lorentz force were used to describe a large-scale crystal growth process in this paper. The SIMPLE algorithm was employed to couple velocity and pressure field. A finite volume method was employed and a staggered grid arrangement was used to avoid zigzag pressure field. A third order QUICK (Quadratic Upwind Interpolation of Convective Kinematics) was used to discretize the convection term in the governing equations. In order to get low defects crystal ingot, the growth interface should be kept flat or slightly concave. This means that the isotherm at the growth interface is approximately perpendicular to the growth direction, the isotherm should be flatter, and the small temperature gradient at the interface is suitable. While the temperature gradient is strongly influenced by the flow pattern in the crucible, the strength of the magnetic field, the crystal and crucible rotations are the three major factors in determining the melt flow pattern, in this study, we aim at optimizing this three design variable to control the temperature gradient at the interface. Concepts and techniques of response surface methodology (RSM) have been widely applied in many branches of engineering, especially in the chemical and manufacturing areas. The basic idea of RSM is to approximate the actual state function, which may be implicit and/or very time-consuming to evaluate, with the so-called response surface function that is easier to deal with complex problem. This paper presents an application of the methodology with a turbulence model to optimize the temperature gradient. The simulation demonstrates that the response surface methodology is a feasible algorithm for the optimization of the Czochralski crystal growth process. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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