Numerical analysis of sapphire crystal growth by the Kyropoulos technique

Demina, S.E.; Bystrova, E.N.; Lukanina, M.A.; Mamedov, V. M.; Yuferev, V. S.; Eskov, E.V.; Николенко, Н. В.; Postolov, V.S.; Kalaev, V.V.

doi:10.1016/j.optmat.2006.11.012

Cited by 51 publications

(34 citation statements)

References 2 publications

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“…We have depicted in figure 3 as an example using , ρ c =3980 kgm -3 [10], r f =-1 [11]. (These data and u/v // =0.4 would be used, if not specified, in the calculations of the following figures).…”

Section: Model Constructionmentioning

confidence: 99%

Theoretical analysis of the shape evolution of crystals grown by pulling

Zhang

Zuo

Sun

et al. 2011

Cryst. Res. Technol.

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This paper proposes a geometric model for crystal growth by pulling. On the basis of the model, effects of the growth processes on the evolution of crystal shape were studied. Besides some effects already adopted in practice to control the crystal diameter, our results revealed several novel effects: a crystal grown under fixed process parameters could grow with a self-stabilized diameter after shoulder-expanding; decreasing the convex degree of solid liquid interface would enhance the increasing rate of crystal diameter or reduce the decreasing rate of crystal diameter.

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Section: Model Constructionmentioning

confidence: 99%

Theoretical analysis of the shape evolution of crystals grown by pulling

Zhang

Zuo

Sun

et al. 2011

Cryst. Res. Technol.

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“…However, most of the numerical studies in the literature were devoted to Cz [3][4][5][6][7][8][9][10][11] and Kyropoulos (Ky) [11][12][13][14][15] processes, which are not referenced in detail here. Directional solidification (DS) techniques, such as heat exchanger method (HEM), gradient solidification method (GSM) and vertical Bridgman (VB) method, are also widely used to produce oxide single crystals.…”

Section: Introductionmentioning

confidence: 99%

Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method

Liu

2017

Crystals

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Internal radiation was investigated using the finite volume method for the heat exchanger method (HEM) growth of oxide crystals. Special attention was devoted to the temperature and thermal stress distributions in the bottom region of the grown crystal at the end of the solidification process. The numerical results show that internal radiation strongly strengthens heat transport through the crystal. However, it causes isotherms to intensively concentrate in the crystal bottom region, leading to a significant increase in the temperature gradient and thermal stress in this region. Then, the effect of absorption coefficient on this phenomenon was numerically investigated. It was found that the radiation heat transfer rate at the bottom surface of the crystal monotonically decreases as the absorption coefficient is increased, while the conduction heat transfer rate first increases and then decreases as the absorption coefficient is increased, under the interaction between internal radiation and heat conduction. The variations of the maximum temperature gradient and thermal stress in the crystal bottom show the same tendency as the conduction heat transfer rate. This study indicates that the role of internal radiation on the heat transfer and thermal stress in oxide crystal by HEM process shows some differences from that by Czochralski and Kyropoulos processes.

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“…[1][2][3][4][5][6][7][8] This method is similar to the Kyropoulos method. [9][10][11] In the NOC method, however, a low-temperature region must be intentionally established in a Si melt. The method enables the production of Si bulk single crystals without crucible contact owing to the distinct lowtemperature region in the Si melt.…”

Section: Introductionmentioning

confidence: 99%

Growth of Si Bulk Crystals with Large Diameter Ratio Using Small Crucibles by Creating a Large Low-Temperature Region Inside a Si Melt Contained in an NOC Furnace Developed Using Two Zone Heaters

Nakajima¹,

Ono²,

Murai³

et al. 2016

Journal of Elec Materi

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Three zone heaters were generally used for a noncontact crucible (NOC) furnace. For practical reasons a simpler NOC furnace was developed with two zone heaters, which had a carbon heat holder to cover the three roles of each heater. Large low-temperature regions were obtained, and silicon ingots were grown in small crucibles with a large diameter and diameter ratio. Here, the diameter ratio is the ratio of the ingot diameter to the crucible diameter and can be as large as 0.90. The diameter ratio was controlled mainly by the temperature reduction of the first heater. Power changes of the second heater did not have a significant impact on the ingot diameter. Using this NOC furnace, maximum ingot diameters of 28.0, 33.5, and 45.0 cm were obtained using crucibles of 33, 40, and 50 cm in diameter, respectively. The oxygen concentration of the ingots did not strongly depend on the diameter ratio and were always low because convection in the Si melt was markedly suppressed by the carbon heat holder. Moreover, the oxygen concentration of the ingots has a tendency to become lower as the crucible diameter becomes larger.

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Numerical analysis of sapphire crystal growth by the Kyropoulos technique

Cited by 51 publications

References 2 publications

Theoretical analysis of the shape evolution of crystals grown by pulling

Theoretical analysis of the shape evolution of crystals grown by pulling

Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method

Growth of Si Bulk Crystals with Large Diameter Ratio Using Small Crucibles by Creating a Large Low-Temperature Region Inside a Si Melt Contained in an NOC Furnace Developed Using Two Zone Heaters

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