Spoke patterns on molten silicon in Czochralski system

Asymmetric temperature profiles similar to the spoke patterns and related asymmetric flow in Si melts of the Czochralski (CZ) system are verified for the first time by three-dimensional (3D) numerical simulation of heat and momentum transfer and by X-ray radiography technique. These profiles appear as the temperature difference between the wall and the crystal becomes large with symmetric boundary conditions. The 3D simulation leads to the conclusion that the vertical temperature gradient in the unstable layer near the free surface is an important cause of making the asymmetric profile. The profile is estimated to be caused by both Rayleigh-Bénard and Marangoni-Bénard instabilities in the Si melt. It is shown that the relative strength of these two instabilities depends on the coefficients of temperature dependence of the density and surface tension. If the temperature coefficient of surface tension (∂γ/∂T) is greater than 1 x 10^-4 N/m {dot operator}, the Marangoni-Bénard instability mainly causes asymmetry, while if ∂γ/∂T is less than this value, the Rayleigh-Bénard instability mainly causes asymmetry.