Quasi-steady-state (QSS) and transient models, developed using the CrysMAS code, are employed to study the effects of transport mechanisms and cold finger design on the temperature distribution, melt flow field, and melt-crystal interface shape during the crystal growth of sapphire by a small-scale, modified heat exchanger method (HEM). QSS computations show the importance and effects of various heat transfer mechanisms in the crystal and melt, including conduction, internal radiation, and melt convection driven by buoyant and Marangoni forces. The design of the cold finger is demonstrated to have significant effects on growth states. Notably, transient computations on an idealized heat transfer model, supplemented with QSS calculations of a model with rigorous heat transfer representation, show that non-uniform growth conditions arise under uniform cooling of the system via a linear decrease in furnace set points. We suggest that more uniform HEM growth conditions may be achieved by using non-linear cool-down strategies.
Bibliographical noteFunding Information:
This work was conducted during a sabbatical visit to the University of Minnesota of HGP, who wishes to thank the Korea Polytechnic University for support. We thank Dr. Jochen Friedrich of the Crystal Growth Laboratory of the Fraunhofer IISB for significant technical interactions and for allowing us generous use of the CrysMAS code. Computational resources were provided by the Minnesota Supercomputer Institute.
- A1. Computer simulation
- A1. Convection
- A1. Heat transfer A2. Growth from melt
- B1. Sapphire