Numerical study of hydrodynamic instabilities during growth of dielectric crystals from the melt

A numerical study of hydrodynamic instabilities of melt flows in Czochralski growth has been carried out. The background is that high temperature melting rare-earth scandates show often undesirable spiral growth and cork screw instabilities. The flow is driven by buoyancy, thermocapillarity and rotation forces. Using a simple numerical model, bifurcation analysis has been performed in order to separate the unstable from stable parameter regions. By applying an extended bifurcation analysis it is possible to find that solutions can be ambiguous, steady state and oscillatory. The numerical approach is based on a finite element discretisation using a fast solver for steady flow state calculation and bifurcation analysis. Results which confirm the hypothesis of initiating undesired spiral instabilities by heat and momentum disturbances are presented in order to help crystal growers to choose parameters which do not lead to spiral instability.