Finite element simulation of single crystal growth process using GSMAC method

The characteristics of the melt convection and the melt deformation process in two crystal growth techniques, Czochralski (CZ) and floating zone (FZ) methods, are investigated with three-dimensional numerical simulation using generalized simplified marker and cell—finite element method (GSMAC-FEM). Large eddy simulation (LES) with the Smagorinsky model is applied to calculate the melt convection with high Rayleigh numbers in the CZ method, and level set method (LSM) is adopted for the computation of liquid bridge deformation. First, the CZ (LSM) melt convections are investigated with the boundary conditions in terms of the free surface and the rotational rate changed. As a result, it is found that the heat radiation and the Marangoni effect on the free surface encourage the instability of flows, and the Coriolis’ force can largely suppress the natural convection. Second, a series of simulations in terms of liquid bridge deformation are carried out with the coil position, coil shape, and the magnitude of surface tension varied. After that, it turns out that those are important factors in the melt shape. Moreover, it is proved numerically that the deformation of the liquid bridge is kept small by the skin effect and large surface tension in the real FZ crystal growth.