Modeling Interface Shape in Czochralski Growth of Sapphire Crystals

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.

Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

“…The P1 approximation model takes into account an additional heat source term in Equation that describes the radiative heat transfer for an absorbing, emitting, and scattering medium (the scattering effect is not considered in the present simulations). Numerical modeling based on this model has shown that deep convex shapes of the crystal‐melt interface are explained by the internal radiative heat exchanges . Numerical simulations in refs.…”

“…More details about the numerical and physical model used to simulate crystal growth of oxides are given in ref. []. The physical properties for sapphire and LGT are taken from refs.…”

“…Therefore, the temperature field in the crystal and the shape of the growth interface are significantly affected by the internal radiative heat transfer. Deep convex shapes of the crystal‐melt interface are experimentally and numerically reported in these systems . Crystal rotation is usually applied to flatten the growth interface and to reduce thermal stresses .…”

“…Deep convex shapes of the crystal‐melt interface are experimentally and numerically reported in these systems . Crystal rotation is usually applied to flatten the growth interface and to reduce thermal stresses . Recently, Stelian et al .…”

“…Crystal rotation is usually applied to flatten the growth interface and to reduce thermal stresses . Recently, Stelian et al . revealed by means of numerical modeling that applying crystal/crucible rotation in some systems results in distorted shapes of the growth interface and increased stresses in the ingots.…”