Interface effect on titanium distribution during Ti-doped sapphire crystals grown by the Kyropoulos method

Large ingot Ti-doped sapphire crystals were successfully grown by Kyropoulos method. Optical characterization of 10 cm diameter crystals shows non-uniform radial distribution of titanium. The measurements of Ti3+ ion distribution in several slices cut perpendicular to the growth direction show that the concentration is higher at the periphery of the crystal as compared to the central part of the ingot. Numerical modeling is applied to investigate heat transfer, melt convection and species transport during the Kyropoulos growth process. The transient simulation shows an unsteady convection generated by the strong interaction between the flow and the thermal field. The distribution of Ti in the melt is nearly uniform due to the intense convective mixing. The radial distribution of titanium depends mainly on the shape of the crystal-melt interface. The measured U-shaped concentration profile is explained by accounting the conical shape of the interface. High curvatures of the growth interface observed in experiments are explained by the increased thermal conductivity of the sapphire crystal, which is participating to the radiative heat transfer. The interface curvature depends on the absorption coefficient, which is higher for Ti-doped sapphire crystals than for undoped crystals. Therefore, the initial Ti concentration in the melt should be decreased in order to reduce the absorption coefficient and the interface curvature. The comparison of numerically computed titanium distribution in the crystals to experimental measurements shows a good agreement.