Sapphire is the most popular substrate material for GaN thin-film crystal growth during the Light-emitting diode (LED) fabrication. The performance of GaN films is directly influenced by the quality of the substrates. The control of the growth front, i.e., solid /liquid interface, is critical to improve the quality of the sapphire. As a semi-transparent material, sapphire has an intermediate optical thickness, which requires considering of internal radiation for an accurate prediction of temperature field and interface shape. In the paper, a coupled model has been applied on the modeling of transport phenomena during the Czochralski (Cz) sapphire growth. Especially, the role of the internal radiation with or without melt inclusions has been examined carefully by Discrete Ordinates (DO) method. The interface convexity is influenced by the parameters of the models as well as by the melt inclusions. By setting the different optical properties at the inclusion regions, as observed in the experiments, the entrapment of gas or solid inclusions inside the crystal and its effect on the interface shape are examined.

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