Optical crystals grown by Czochralski technique from a solute-rich melt usually suffer defects of melt inclusion or bubble core defects, which severely affect the optical, thermal and mechanical properties of the material. It is well known that the formation of melt inclusion or bubble core is highly related to species distribution in the growth system especially at the solidification interface and the shape of the growth interface. This paper has examined the flow pattern and solidification interface changes by changing the forced convection, e.g., crystal rotation and by changing the natural convection, e.g., inserting a horizontal disk plate. The relative effect of fluid-flow convection modes in the melt associated with crystal rotation rate is represented by a dimensionless parameter, Gr/Re2. Increasing the rotation rate will cause the solid-liquid interface change from the convex shape to concave. When the crystal rotation rate is relatively low and natural convection is strong, Gr/Re2 is large. In this case, the concentration of species pertinent to melt inclusion moves down along the axis of rotation. When the crystal rotation rate is increased, the value of Gr/Re2 decreases. The precipitated composition spreads over the growing interface may then be swiped away from the growth interface by increased crystal rotation. Melt inclusion-free crystals can thus be obtained. The relationship between Gr/Re2 and growth interface shape change is achieved by numerical simulations. The stagnant point location as a function of crystal rotation is also presented, which shows that the stagnant point moves outward by increasing Reynolds number and/or reducing Grashof number. From such understanding, the interface shape and melt inclusion position can then be controlled through control of Gr/Re2 in the growth system. Many times, it is, however, not practical in the experiments to use a high rotation rate for optical crystal growth since high rotation rate will introduce the striation defects. A new design to reduce natural convection is then proposed to improve the effect of crystal rotation and to control the solidification interface shape. Numerical simulations have been performed to demonstrate the possibility of the new design. Results show that such design is very effective and practical to control the melt inclusion and the solidification interface shape.
Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm
