Development of numerical models for Czochralski sapphire single crystal growth system

Abstract

Currently sapphire single crystal mass production for LED substrate mostly takes place through the Kyropoulos method. Other mass production methods include HEM and VHGF methods. However, all of these methods are limited by their low yield, as they involve a-axis crystal growth. However, the Czochralski (CZ) method involves crystal growth in the c-axis direction, so that there is less loss due to coring. This means that the yield is higher than other growth methods. In spite of sapphire single crystals can be obtained with good throughput through the CZ method with growth in the c-axis direction, the CZ method is avoided in mass production because of issues with crystal quality. The quality of sapphire single crystals used as substrates for LED production are largely influenced by two defects: dislocation density and bubbles trapped in the crystal. High dislocation densities can lead to substrate fracture during GaN deposition and diminished LED efficiency. And the presence of bubble defects affect the optical performance and mechanical properties of the crystals, thus limiting their utilization in the components. Therefore in the present study, we developed numerical models for Czochralski (CZ) sapphire single crystal growth system to investigate improving growth conditions to enable higher-quality crystal growth. We calculate decreased convexity and thermal gradient at the crystal front (CF) through the use of an additional heater in an induction heated CZ system. Changes in the CF shape with the use of an additional heater were found through changes in the melt flow direction and hot-zone temperature distribution, and in comparison with previous crystal growth methods, this was found to result in lower absolute values for the thermal gradient at the CF as well as smaller deviations according to location. Moreover, using additional heater, power consumption deceased. In addition, we develop a solute concentration model by which the location of bubble formation in CZ growth is calculated, and the results are compared with experimental results. The model was used to predict that under growth conditions involving an additional heater, bubbles would be trapped at the crystal peripheral edges. This is expected to be of great value in improving crystal quality. We calculated the influence of both crystal and crucible rotation to reduce dislocation density in a resistance heated CZ system. Compared to a configuration with no crystal or crucible rotation, rotating the crystal and crucible in the same direction results in a lower variation of the thermal gradient depending on radial location, but this is accompanied by undesirable convexity. In contrast, rotating the crystal and crucible in opposite directions results in both a lower thermal gradient variation with radial location, and improved convexity.