Numerical analysis and parameter identification during Czochralski crystal growth

Heat and mass transport taking place during growth of Y3Al5O12 crystals by the Czochralski method is analysed using a finite element method. Dopant segregation in the melt only happens in regions where the convection is weak, i.e. along the interface, centreline and crucible bottom, while in the rest of the melt the dopant is distributed uniformly. Radial dopant segregation along the interface strongly depends on the equilibrium segregation coefficient of the dopant, the Schmidt number and the convection type and its intensity. The inhomogeneity in the radial segregation of dopants along the interface significantly decreases for flat interfaces. Therefore we can use the level of dopant concentration at that interface as a measure of the diffusion characteristics in the melt.