Journal of Crystal Growth, Vol.305, No.1, 185-191, 2007
Three-dimensional instabilities in Czochralski process of crystal growth from silicon melt
This paper deals with axisymmetry breaking instabilities in Czochralski process of crystal growth from silicon melt (Prandtl number Pr = 0.01). Numerical 3D linear stability analysis was carried out on the axisymmetric bulk flow model. Stability diagram of critical Grashof numbers Gr(c) dependent on aspect ratio alpha( = height/radius) in the range 0.4 <= alpha <= 1.0 was computed. Computations were carried out using the spectral element method in the meridional plane with Fourier decomposition in the azimuthal direction. It was found that convective instability sets in through an Hopf bifurcation displaying oscillations in time. Sensitivity of mode transitions was observed at parameter range of alpha > 0.65 and in some regions modes were observed approaching each other closely. Dangerous modes in the 0.65