3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth

摘要

In the present work, 3D features of melt convection during sapphire growth of 100 mm diameter Cz and of 200 mm diameter Ky crystals are studied. The approach accounting for radiative heat exchange with absorption and a specular reflection in the crystal, which we applied in 2D modeling [1-3], has been extended to 3D computational domains and coupled to 3D heat transfer in the melt, crystal, and crucible. 3D melt unsteady convection together with crystallization front formation are taken into account within the Direct Numerical Simulation (DNS) approach. Results of 3D modeling are discussed in detail and quantitatively compared to the previously reported data of 2D modeling and experiments [2,3]. It has been found that the features of unsteady melt convection during the "before seeding", "seeding", and "shouldering" growth stages are quite different from each other, which necessitates a flexible control of the radial and vertical temperature gradients in the crucible to provide optimal conditions for stable growth of high quality sapphire crystals.