Combined heat transfer in ßoating zone growth of large silicon crystals with radiation on di⁄use and specular surfaces

Numerical analyses are conducted to investigate the combined heat transfer in ßoating zone growth of large Si crystals with needle-eye technique. The radiation element method, REM2, is employed to determine the radiative heat exchange, in which the view factors associated with the components in the ßoat zone furnace and both the di⁄use and specular reßection components are incorporated. The boundary element method and the Þnite di⁄erence method are adopted to calculate the electromagnetic Þeld and the heat conduction, respectively. The e⁄ect of surface radiative characteristics of Si melt and crystal, i.e., di⁄use and/or specular, is discussed in detail. It is found that the consideration of specular surfaces increases the Joulean heat and the radiative heat ßux. The temperature Þelds are obtained for the cases of di⁄use and specular, and the di⁄erence between the two di⁄erent cases is obvious in the crystal and molten zone areas. The molten zone is enlarged when the specular surface is accounted for. The interface shape is examined and found to be in goo