Effect of crucible geometry on melt convection and interface shape during Kyropoulos growth of sapphire single crystal

Lee, W.J.; Lee, Y.C.; Joo, Gea‐Jae; Park, Y.H.

doi:10.1016/j.jcrysgro.2011.03.032

Cited by 23 publications

(5 citation statements)

References 17 publications

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“…The applied models are similar to our recent papers , without calculation of magnetic field and with a minor modification of crystallization front tracking. The growth conditions determines interface shape and crystal surface shape . The surface shape of the crystal can be obtained by ex‐situ measurements.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Fang

Wang

Jin

et al. 2013

Crystal Research and Technology

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Kyropoulos (Ky) method is the most suitable technique for the growth of high‐quality sapphire single crystal for substrate applications. Cracks are often observed in the grown ingot that significantly reduces industrial productivity. In the paper, cracking causes are analyzed by examining crystal shape, thermal stress and three‐dimensional effects during the stable growth of sapphire crystal. It is found that locally induced thermal stress around the shoulder of the crystal is the largest. However, thermal stress is not fully responsible for the cracks, since the predicted stress level is lower than a critical value regarding crystal cracking. Polycrystalline growth or/and other crystal defects must be another factor that degrades the critical value and makes the crystal more fragile. Simulation results further show that crystal shape has less effect on the thermal stress level, although experiments have shown that crack‐free crystals usually have smooth surfaces. The initial cracking position in the ingot predicted in simulation agrees well with experimental observation after considering crystal defects in a qualitative discussion. From the view of three‐dimensional simulation, the variation of heating condition during growth may result in high thermal stress locally that leads to the cracks at one side of the crystal. Additionally, three‐dimensionally unexpected temperature drop of the heater may be responsible for the sticking‐to‐crucible phenomenon at the shoulder region of the grown crystal.

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Section: Mathematical Modelsmentioning

confidence: 99%

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Fang

Wang

Jin

et al. 2013

Crystal Research and Technology

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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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“…Numerical modeling is a useful tool to investigate and optimize the Kyropoulos growth process. Several papers have been dedicated to the numerical analysis of the thermal field, stresses, melt convection and the shape of the crystal-melt interface [3][4][5][6][7][8][9].I n their work, Demina et al [3,4] used numerical simulation to investigate the influence of the growth parameters on the temperature field, melt convection and the crystallization front shape. The formation of so-called "remelting zone" or "temporal concave shape of the crystal" during the shouldering stage of the growth is explained as an effect of two-vortex pattern of the flow.…”

Section: Introductionmentioning

confidence: 99%

“…Chen et al [5,6] investigated the influence of the input power in the heater on the melt convection and the shape of the crystalmelt interface. Other papers [7,8] have been dedicated to the analysis of the effect of the crucible geometry on the temperature field and convection in a Kyropoulos growth system. The effect of the Marangoni convection on the interface shape has been numerically investigated by Gao et al [9].…”

Section: Introductionmentioning

confidence: 99%

“…They found that the Marangoni convection increases the curvature of the growth interface and influences the flow pattern, causing the temporal concave shape of the crystal. Although different models have been applied to simulate the internal radiation in the sapphire crystal [3][4][5][6][7][8][9], the influence of the internal radiative exchanges on the temperature and the flow field is not fully understood. The numerical studies in [5][6][7][8][9] apply steady-state computations to investigate the thermal and the flow field in the sample-crucible system at different stages of the growth process.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison between numerical modeling and experimental measurements of the interface shape in Kyropoulos growth of Ti-doped sapphire crystals

Stelian

Sen

Barthalay³

et al. 2016

Journal of Crystal Growth

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Effect of crucible geometry on melt convection and interface shape during Kyropoulos growth of sapphire single crystal

Cited by 23 publications

References 17 publications

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

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

Comparison between numerical modeling and experimental measurements of the interface shape in Kyropoulos growth of Ti-doped sapphire crystals

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