3D Computer simulations using the commercial code FIDAP and CFDRC, which are based on finite element techniques, were performed to investigate the effects of the anisotropic conductivity in a heat-exchanger-method crystal growth system on the convexity of the melt-crystal interface and the hot spots of sapphire crystal. Both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled by the convection boundary conditions.

The cross section flow pattern and the melt-crystal interface shape of the 3-D modeling results are confirmed to comparing with the previous 2-D simulation results. For the 3-D model, “hot spots” on the corners of the crucible are present as a donut type, and the hot spot shapes are changed with the values of the anisotropic crystal's conductivities. The outline of crystal becomes more convex when the crystal’s conductivity of the z direction (k_sz) increases. The outline of crystal-melt interface is ellipse for anisotropic conductivity in the radial direction(k_sx and k_sy). Outline touch the crucible bottom is smaller than the maximum outline of the crystal so that the “hot spot” shapes are changed with the values of the anisotropic crystal's conductivities.

Keyword: HEM, oxide, crystal growth, solidification, numerical

* Corresponding author. E-mail address:[email protected]

References:

[1] D. Viechnicki and F. Schmid, J. Crystal Growth 26, 162 (1974)

[2l F. Schmid and D. J. Viechnicki , U.S. Patent 3,653,432 (1972)

[3l C. J. Jing, N. Imaishi, T. Sato, Y. Miyazawa, J. Crystal Growth 216, 372 (2000)

[4] C. W. Lu and J. C. Chen, J. Crystal Growth 225, 274 (2001).

[5] C. W. Lu and J. C. Chen, Modelling and Simulation in Materials Science and Engineering 10, 147 (2002).

[6] J. C. Chen and C. W. Lu, J. Crystal Growth 266, 239 (2004).

The flow diagram of cross section is shown in Figure 1.

Figure 2 and 3 demonstrate the sapphire crystal shape with different T_iref, for constant h_c

(h_c is the convection coefficient of the heat exchanger).

(T_iref is the environmental temperature outside the crucible)

Figure 1

Figure 2 Figure 3

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