Translated Abstract
Sapphire crystal is the most important substrate material for LED (light emitting diode) devices. Production of large-size sapphire crystals with high quality is very important for reducing the cost and improving the performance of LED devices. Heat exchanger method is one of the major methods to produce large-size and high-quality sapphire crystals. The heat transfer in the crystal growing system determines the temperature distribution, melt flow and melt-crystal interface shape, and further influences the crystal quality and energy consumption. Therefore, it is necessary to investigate and control the heat transfer during the sapphire crystal growth to improve the crystal quality and reduce its cost.
Based on the heat transfer phenomenon, some numerical methods, which can reflect the characteristics of the heat transfer in the system, is developed. A global heat transfer model is established for the sapphire crystal growing system by heat exchanger method. The internal radiation heat transfer in sapphire crystal is studied. The effects of crucible cover and crucible location on heat transfer during crystal growth are investigated in detail. The issue of the melt-crystal interface shape in different solidification stages are analyzed. Consequently, some improvement of the structure are proposed to control the melt-crystal interface shape.
First, a quasi-steady enthalpy method based on fixed-grid to consider the latent heat of phase change during a solidification/melting process of a pure material is proposed. The latent heat of phase change released or absorbed at the solid-liquid interface disperses into a region at the interface in the proposed method. It is verified through comparing to the solutions obtained with the adaptive mesh method which is commonly accepted for its accuracy in modeling solidification/melting processes for pure materials. The effect of the mesh size and type, the dispersed region size and the phase change rate on the simulation accuracy of the proposed method are investigated. Based on the proposed method, a general form of the distribution function of the latent heat of phase change is proposed. The distribution of the latent heat of phase change in the dispersed region is controlled by selecting different forms of distribution function to improve the simulation accuracy. The selecting principle of the distribution function is proposed on the basis of concentrating the latent heat of phase change at the solid-liquid interface. Following the selecting principle, the accuracy can be controlled and the size of the dispersed region does not need to be determined in advance. Two distribution functions of the latent heat of phase change are investigated. Results show that the proper concentration of the latent heat of phase change at the solid-liquid interface is favorable for the simulation accuracy.
Second, a radiation heat transfer model is established for the crystal internal radiation during sapphire crystal growth by heat exchanger method. According to the phenomenon of the control angle overhanging induced by specular reflection in the finite volume method, an improved method is proposed to treat the specular reflection boundary condition. Comparing to the solutions obtained with the original method, the improved method can effectively reduce the error caused by the control angle overhanging. Based on the improved method, internal radiation in the crystal domain during sapphire crystal growth by heat exchanger method is investigated. Results show that crystal internal radiation can enhance the heat transfer in the sapphire domain and enlarge the convexity of the melt-crystal interface.
Third, global simulations of heat transfer are carried out to investigate the effects of crucible cover and crucible location in the axial direction on the thermal field and melt flow in the crucible during the growth of sapphire crystal.
It is found that the crucible cover has significant effect on the thermal field in the melt. When the crucible cover is installed, the radial temperature gradient in the melt at the melt-crystal interface decreases while the axial temperature gradient increases. The melt flow is weakened accordingly. The melt-crystal interface becomes flatter and the thermal stress in the crystal is reduced with the installed crucible cover. It can be therefore concluded that use of a crucible cover is favourable for crystal growth.
The crucible location has a significant effect on the heat transfer in the crystal and melt domains. When the crucible rises up, the melt flow is enhanced and the convexity of the melt-crystal interface increases at the crystallization stage. The thermal stress in the growing crystal decreases at the annealing stage. Therefore, it can be concluded that the crucible should be lowered at the crystallization stage, and raised up at the annealing stage to improve the quality of sapphire crystals.
Finally, the melt-crystal interface shape is investigated in the early stage of solidification process where the diameter of the sapphire crystal enlarges when growing and the later stage where the diameter of the crystal keeps constant. The issues and the influencing factors of the melt-crystal interface in different growth stages are discussed. In the early stage, the contact angle between the melt-crystal interface and the crucible bottom wall is found obtuse, which is unfavorable for the crystal quality. Installing a heat shield near the crucible bottom can suppress the obtuse contact angle. In the later stage, the melt-crystal interface is too convex. Segmented control of the emissivity of crucible side wall can effectively reduce the convexity of the melt-crystal interface. A heat insulation block designed near the crucible bottom is proposed to control the melt-crystal interface shape in the whole solidification process. Results indicate that the installation of a heat insulation block can suppress the obtuse contact angle in the early stage, and decrease the convexity of the melt-crystal interface in the later stage.
Those studies reveal the heat transfer mechanism in the growing system and the influencing mechanism of the structure on the thermal field and melt flow. It can provide guidance for the hot zone design and process optimisation in production to improve the crystal quality and reduce the cost.
Translated Keyword
[Heat exchanger method, Heat transfer, Numerical simulation, Radiation heat transfer, Sapphire]
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