Global analysis of heat transfer in Si CZ furnace with specular and diffuse surfaces

For the single-crystal growth of silicon, a global analysis of heat transfer in a CZ furnace was carried out using the finite element method, where the radiative heat transfer between the surfaces that possess both specular and/or diffuse reflectance components was taken into account, and then the effect of the specular reflection of the crystal and/or melt on the CZ crystal growth was numerically investigated. This was compared with the results based on the assumption of diffuse reflection which has been adopted in previous studies. As a result, it was found that the pulling rate of the crystal with a purely specular surface becomes faster than that with a diffuse surface to maintain the crystal diameter constant for a given heater power. Also, the effect of the radiative characteristic of the melt surface on the crystal growth strongly depends on the surface shape. The effect of the specular reflection should be considered in the precise numerical simulation of heat transfer in the CZ furnace, especially for a relatively large diameter, if the crystal and/or melt surfaces are specular.