Below we  show the results of numerical simulation of single leucosapphire crystal growth by the Kyropoulos method using CGSim software. The computations in the crystallization zone include the turbulent flow of the sapphire melt, laminar gas flow, radiative heat exchange in the semi-transparent crystal including specular reflectivity at the boundaries, internal absorption and scattering. Moreover, attempts to apply a simplified model, ignoring semitransparency of the crystal and the melt, give physically unrealistic results for the crystallization front geometry and temperature gradients at the metl-crystal interface.

Numerical simulation comes very helpful in the analysis and optimization of growth systems since it gives us an insight into the processes that are otherwise extremely difficult to observe or measure. For example, temperature distribution inside the melt and the structure of the flow are practically inaccessible for direct measurement.

Heat exchange in the furnace

Global heat transfer in a Ky furnace is strongly affected by a particular number and geometrical parameters of molybdenum heat shields. Sets of heat shields and other insulation blocks are positioned at the side, top, and bottom of the furnace (right). They help to maintain optimal temperature distribution around the crucible and growing crystal that, in turn, affects melt flow structure and the crystallization front geometry. Temperature of elements surrounding the crystal will also affect thermal stresses in the crystal.

Improving the hot zone of the Kyropoulos furnace to decrease thermal gradients at the crystallization front results in higher yield ratio and better crystal quality. Using the CGSim package, several configurations of the industrial furnace have been considered (*). In the initial configuration (Modification 1), the melt flow had a two-vortex structure with a larger vortex occupying the melt core and a vortex of lower intensity located near the melt free surface during the lateral crystal growth and disappearing at the cylindrical growth stage. Such flow pattern provided direct delivery of the hot melt to the crystallization front, resulting in high temperature gradients along the melt/crystal interface.

After considering several hot zone modifications, we found a furnace configuration providing one-vortex flow structure in the melt (Modification 2). Such flow pattern results in gradual cool-down of the melt as it approaches the growing crystal, thus, decreasing the temperature gradients in the crystal by up to 30%. Originally, in the top part of the crystal, there were well defined regions of decreasing crystal diameter, which might be due to remelting or slow crystallization. After modifications of growth technology, the remelting regions have mainly disappeared (right ), see [3] for more details.

Temperature gradients inside the crystal and thermal stress values have also been reduced as a result of the proposed modifications. Comparison of von Mises stress norm distributions before and after the technology optimization is given below.

Improvement of the crystal quality has been confirmed experimentally. For instance, morphological and optical investigation of wafer samples obtained close to the region of remelting had shown that the dislocation density in morphological R-plane after modifications dropped from 103 cm-2 to 102 cm-2 (right), see [3] for details.

Crystal seeding is successful only if there is prevailing downward melt motion in the point of seeding on the melt free surface. Upward melt flow in the seeding point may result in meldown of the seed. 3D unsteady modeling of melt convection and crystallization helps to find optimal heating conditions for smooth and stable seeding and shouldering stages. Animated images below show rapid transitions of the melt flow after start of seeding and at shouldering stage.