Combined heat transfer in floating zone growth of large silicon crystals with radiation on diffuse and specular surfaces

Numerical analyses are conducted to investigate the combined heat transfer in floating 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 float zone furnace and both the diffuse and specular reflection components are incorporated. The boundary element method and the finite difference method are adopted to calculate the electromagnetic field and the heat conduction, respectively. The effect of surface radiative characteristics of Si melt and crystal, i.e., diffuse and/or specular, is discussed in detail. It is found that the consideration of specular surfaces increases the Joulean heat and the radiative heat flux. The temperature fields are obtained for the cases of diffuse and specular, and the difference between the two different 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 good agreement with the experiment. (C) 1998 Elsevier Science B.V. All rights reserved.