Modeling Interface Shape in Czochralski Growth of Sapphire Crystals. Issue 12 (2nd November 2017) - Stelian, Carmen
Abstract: Numerical modeling is applied to investigate the factors affecting the shape of the crystal‐melt interface in Czochralski growth of sapphire crystals having 10 cm in diameter. The modeling is performed for a 2D – axisymmetric furnace configuration, where all the furnace components are included. The shape of the crystal‐melt interface is computed by using the deformable mesh technique. Numerical results show that the conical shape of the interface depends essentially on the internal radiative heat exchanges in the semi‐transparent sapphire crystal, being less influenced by the buoyancy convection. The Marangoni effect enhances the flow near the triple solid‐liquid‐gas point, leading to convex‐concave shape of the growth interface, which is prone to facet formation. Numerically computed shape of the interface is compared to experimental results taken from literature. Applying crystal/crucible rotation has a significant impact on the flow pattern and the shape of the growth interface. Computations performed by applying only crystal rotation at rates higher than a critical value, show a reversed convection at the sample centre, underneath the crystal. This flow affects the shape of the interface, which is less curved and exhibits a convex shape. If the rotation rate is too much increased, the interface shape can be distorted by the intense flow. Application of crucible rotation intensifies the downward flow at the sample centre, leading to increased interface curvature. Rotating both the crystal and crucible in opposite directions generates a complex flow pattern, but has no flattening effect on the interface. Abstract : Numerical computations of the crystal‐melt interface shape in Czochralski growth of 10 cm diameter sapphire crystals are validated by comparing to experimental results taken from literature. The present computations suggest that a flat interface growth is not attainable in the present system, since the increase of crystal rotation rate results in a distorted shape of the interface, while crystal/crucible counter rotation has no flattening effect. However, crystal rotation at low rates (5 rpm) should be used in practice in order to prevent too high curvatures of the growth interface.