A Model of Thermal Transfer in Czochralski Silicon Molten

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Abstract
Simultaneous multipoint measurement has been performed to determine the temperature of silicon molten of a Czochralski (CZ) system during the growth of a monocrystalline ingot. A high magnitude of temperature fluctuation was found to be totally random without correlation among temperatures of various points in the molten, a phenomenon which could not be explained by models based on a lamina flow. The magnituge of the fluctuation, however, was observed to be related with effective thermal transfer of the molten. A model which took account of thermal transfer induced by local dynamical random motion, a kind of turbulence, of the molten was proposed. The time-averaged temperature distribution taken from the solution of a static diffusion equation with the effective thermal diffusivity agreed very well with the experimental results.