Modeling and Control of Transport Processes during Melt Crystal Growth

In this thesis, detailed, realistic, multi-scale numerical models are developed and employed to study various systems applied for the growth of crystals from melt, including the melt growth of single-crystal Cadmium Zinc Telluride(CZT) and Sapphire. .;The melt growth of single-crystal Cadmium Zinc Telluride(CZT), a very promising high- value crystal widely used in radiation detectors and other applications, has been challenging to the crystal growers in terms of yield and quality. In order to address such challenges, a transient, coupled model has been developed to analyze the segregation of zinc in CZT grown in an electrodynamic gradient freeze (EDG) furnace used at Pacific Northwest National Laboratories and Washington State University. The coupled model consists of a local model that solves for time-dependent melt flow, heat transfer, melt-crystal interface position, and zinc distribution in both melt and solid phases and a quasi-steady-state global model that features realistic furnace heat transfer. Surprisingly, anomalous zinc segregation is predicted, featuring a non-monotonic axial concentration profile and several local minima and maxima across the boule. A mechanistic explanation is put forth based on the cumulative effect of changes in multi-cellular melt flow structures, a particularly susceptible occurrence for CZT systems.;Furthermore, optimized EDG furnace profiles are developed that promote the growth of CZT crystals with a uniformly convex interface shape. Such interface shapes are expected to improve the single-crystalline yield of this material. These computations clearly show how interface shape modification can be put directly into practice simply by changing thermal set points in existing EDG growth systems. In addition, the quenching process for CZT crystals has also been investigated by global model.;Finally, a similar model has also been applied to investigate the single-crystal growth of sapphire, a very important substrate material for the fabrication of gallium-nitride light-emitting-diodes (LEDs), by Heat Exchanger Method (HEM). Both quasi-steady-state and transient analysis have been performed to investigate the effects of furnace geometry and processing parameters on the temperature distribution, convection, and melt-crystal interface shape. Results have provided key insight into the further optimized design of HEM furnace.