关键词: 晶体生长/
固-液相变/
浸入边界法/
格子Boltzmann法
English Abstract
Effects of process parameters on melt-crystal interface in Czochralski silicon crystal growth
Zhang Ni1\21,2,Liu Ding1\21,2,
Feng Xue-Liang2
1.National and Local Joint Engineering Research Center of Crystal Growth Equipment and System Integration, Xi'an University of Technology, Xi'an 710048, China;
2.Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an 710048, China
Fund Project:Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 61533014), the National Basic Research Program of China (Grant No. 2014CB360508), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136118130001).Received Date:07 February 2018
Accepted Date:28 July 2018
Published Online:05 November 2018
Abstract:A two-dimensional axisymmetric immersed boundary thermal lattice Boltzmann (IB-TLB) model is presented to study the phase transition in Czochralski silicon crystal growth for improving the morphology of the melt-crystal interface and the crystal quality. Specifically, the Euler grid and the Lagrange grid are established, respectively. The melt-crystal interface is considered as an immersed boundary, and it is described by a series of Lagrange nodes. In this paper, the melt-crystal interface is tracked by the immersed boundary method, and the melt flow and heat transfer are simulated by the lattice Boltzmann method. The D2Q9 model is adopted to solve the axial velocity, radial velocity, swirling velocity and temperature of the melt. The finite difference method is used to solve the temperature distribution of the crystal. Then the solid-liquid transition in crystal growth with moving boundary is solved by the proposed IB-TLB model. The proposed model is validated by the solid-liquid phase transition benchmark. In addition, the flatness of the melt-crystal interface is evaluated by the mean value of the absolute value of the interface deviation and the standard deviation of the interface deviation. The effects of the process parameters on the morphology of melt-crystal interface, melt flow structure and temperature distribution are analyzed. The results show that the morphology of the melt-crystal interface is relevant to the interaction of the crystal pulling rate, the crystal rotation parameter, and the crucible rotation parameter. When the crystal and crucible rotate together, the deviation and fluctuation of the melt-crystal interface can be effectively adjusted, whether they rotate in the same direction or rotate in the opposite directions. And a flat melt-crystal interface can be obtained by appropriately configurating the ratio of crystal rotation parameter to crucible rotation parameter. Finally, according to a series of computations, it is found that when the crucible and crystal rotate in the opposite directions, the crystal rotation parameter and the crucible rotation parameter satisfy a functional relation, with a flat interface maintained. The obtained relationship has a certain reference for adjusting and improving the crystal growth parameters in practice.
Keywords: crystal growth/
solid-liquid phase change/
immersed boundary method/
lattice Boltzmann method
