Sapphire Crystal Growth Research Articles

Computational Study of Convective and Radiative Heat Transport in Czochralski Growth of Oxides

For a Czochralski crystal growth of sapphire, influence of radiative heat transfer and gas convection on the temperature field of the system and the crystal-melt interface have been studied numerically using the finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. Comparison between the results presented here and those of previous works demonstrate the importance of heat radiation, gas flow and realistic heat transfer boundary conditions on the thermal field of oxide Czochralski growth systems.

Numerical study of heat transfer during sapphire crystal growth by heat exchanger method

We developed a transient global model to study the heat transfer in sapphire crystal growth by heat exchanger method (HEM). Internal radiation in the semi-transparent sapphire was modeled with a rigorous discrete ordinate model and phase change was calculated based on a fixed-grid method in our simulations. The evolutions of thermal field, melt flow and melt-crystal (m-c) interface shape were predicted during the whole crystal growth process. Simulation results show that a U-shape distribution of axial temperature gradient appears along the centerline of the sapphire crystal and melt, respectively, due to the effect of internal radiation. The m-c interface is severely curved near the crucible wall and relatively flat at the central region with an increasing convexity when crystal grows. The sapphire melt flow is in a laminar state dominated by the thermal buoyancy force. The high growth rate at the final stage of the solidification process resulted in bubbles at the top layer of the grown crystal. The formation mechanism of the grain boundaries at the crystal periphery was discussed. The numerical simulation results show a good agreement with the experiment data. The developed global model herein provides important information to improve the growth process of sapphire crystal by the HEM technique.

Vertical Bridgman growth of sapphire crystals, with thin-neck formation process

A new technique is proposed in the traditional vertical Bridgman growth of sapphire crystals, in which thin-neck formation follows the initial seeding. Low-angle grain boundaries generated at the periphery of the seeding interface were eliminated at the thin neck, and the c-axis sapphire crystals with main bodies free from low-angle grain boundaries were grown.

Effect of crucible shape on heat transport and melt–crystal interface during the Kyropoulos sapphire crystal growth

In this work, a special crucible shape with a round shape for the outer wall and an inverted conical shape for the inner wall is presented to investigate the thermal and flow transport, as well as the shape of the crystal–melt interface during the Kyropoulos sapphire crystal growth, by using the numerical simulation method. The results show that the growth system with proposed crucible shape can result in more suitable thermal and flow fields, a lower convexity at shouldering and equal-diameter growth stage and a higher convexity at the following stage. Thus, the results are benefit for the quality of the sapphire crystal.

Evolution of interface configuration in sapphire single crystal growth via Czochralski method

The evolution of interface configuration during sapphire crystal growth by Czochralski method was studied on the basis of chemical bonding conditions at crystal/melt interface. On the basis of chemical bonding theory of single crystal growth, when sapphire single crystal was grown along the c axis direction in Czochralski system, crystal/metal interface is composed of six crystallographically equivalent {110} interfaces thermodynamically. With the rotation of sapphire single crystal in the growth process, the interface configuration developed from hexagon to circle due to the appearance of {100} surfaces and {h10} microfacets at the intersection of two adjacent interfaces. The (h10) microfacet is made of (100) and (110) planes. Lower chemical bonding densities at the {100} surfaces and {h10} microfacets relative to that at {110} surfaces thermodynamically drive the formation of round interface configuration in sapphire Czochralski crystal growth along the c axis direction.

Role of internal radiation at the different growth stages of sapphire by Kyropoulos method

Internal radiation is investigated using discrete ordinates (DO) model for the Kyropoulos growth of large-size LED-grade sapphire crystals. Its effects on the solid/liquid interface shape, melt convection, temperature and thermal stress are presented for the different growth stages characterized by the crystal length. The results are validated by observing cracked locations and remelting regions of the grown ingot. Internal radiation makes temperature distribution uniform by increasing heat transfer ability of the material, weakens natural and Marangoni convections in the melt, and reduces stress level in the crystal. It is also found that a slightly distorted interface is predicted affected by internal radiation, which is consistent with experimental observation. More reasonable flow patterns in the melt can be achieved taking into account the internal radiation. Natural convection at the early growth stage and Marangoni convection at the late growth stage are responsible for the interface and surface remelting. By analyzing thermal stresses, it is further concluded that the excessive stress is not the major cause of crystal cracking during Ky-sapphire growth. The maximum von Mises stress is always below the critical value predicted by other researchers. Consequently, the locally polycrystalline growth or the three-dimensionally non-uniform heating conditions are the most possible factors of crystal cracking.

Optimization of temperature conditions for the growth of large-size sapphire crystals by the method of horizontally directed crystallization

Optimization of temperature conditions for the growth of large-size sapphire crystals by the method of horizontally directed crystallization

Demonstration of crack-free c-axis sapphire crystal growth using the vertical Bridgman method

We have applied the vertical Bridgman (VB) technique to c-axis sapphire crystal growth. Molybdenum (Mo) and tungsten (W) were used as the crucible materials. In both cases, c-axis, 3-in. diameter sapphire single crystals were successfully grown, and as-grown crystals were easily released from the respective crucibles nondestructively. In the case of the W crucible, crack-free sapphire crystals, up to 120mm in length, were grown reproducibly, and the same W crucible could be reused repeatedly. However in crystals grown in the Mo crucible a few cracks were often observed. Dimensional variations during the cooling process, calculated from the linear thermal expansions of Mo, W, and sapphire, were investigated. It was found that a sapphire crystal grown in a W crucible is stress-free from the inner crucible wall during the cooling process, because the gap between the periphery of the crystal and the inner crucible wall expands gradually to several hundred micrometers for 3-in. diameter sapphire growth.

Simulation of heat transfer and convection during sapphire crystal growth in a modified heat exchanger method

Quasi-steady-state (QSS) and transient models, developed using the CrysMAS code, are employed to study the effects of transport mechanisms and cold finger design on the temperature distribution, melt flow field, and melt–crystal interface shape during the crystal growth of sapphire by a small-scale, modified heat exchanger method (HEM). QSS computations show the importance and effects of various heat transfer mechanisms in the crystal and melt, including conduction, internal radiation, and melt convection driven by buoyant and Marangoni forces. The design of the cold finger is demonstrated to have significant effects on growth states. Notably, transient computations on an idealized heat transfer model, supplemented with QSS calculations of a model with rigorous heat transfer representation, show that non-uniform growth conditions arise under uniform cooling of the system via a linear decrease in furnace set points. We suggest that more uniform HEM growth conditions may be achieved by using non-linear cool-down strategies.

Study of melt convection and interface shape during sapphire crystal growth by Czochralski method

Global simulation is performed to predict electromagnetic field, heat transfer, melt flow, and interface shape during the different growth stages of sapphire crystal by RF-heated Czochralski (Cz) process. Melt flow in the Cz-sapphire growth system includes Marangoni convection due to the variation of surface tension at the free surface, natural convection due to the complex thermal boundary conditions on the crucible walls, and forced convection due to the crystal rotation. As the crystal grow longer, the effects of the convections on the melt flow, temperature distribution and interface shape varies due to the drop of melt, which can be characterized by Grashof number (Gr) with the melt height as the characteristic length. It is found that as melt height reduces, natural convection gets weaker, and the interface becomes flatter. To examine systematically the effects of the convections on the crystal growth process, three dimensionless parameters, Nσ, Gr/Re2 and Nσ2, are further introduced. Nσ denotes the influence of surface tension in the boundary layer as compared with buoyancy in the melt, Gr/Re2 is the ratio of convective forces to the normalizing convective velocities with viscosity, and Nσ2 represents the relative strength of Marangoni flow to forced convection. The effects of the parameters on the melt flow and heat transfer are examined, and their relationships to the interface convexities are obtained. The understanding of melt convection and interface shape is not only important for the optimization of a stable sapphire crystal growth, but also critical for an accurate modeling of the growth process.

Chemical processes in the Mo-W-Al2O3 system during sapphire crystal growth from melt

The main chemical reactions occurring in the Mo-W-Al2O3 system at T = 2400 K and P = 1 bar in an inert controlled atmosphere are considered. The mechanisms of Mo and W oxidation by the dissociative evaporation of melt products are determined. It is established that, at a formally low fraction of evaporating Al2O3, multiply repeated evaporation-condensation and oxidation-reduction cycles are unfavorable for the operation of W heater and Mo-containing elements of heating-unit elements. It is found that gaseous Mo oxides (MoO and MoO3) can also affect the degradation of the W heater. A detailed study of the chemical processes should facilitate the optimization of the conditions of sapphire crystal growth from melt.

사파이어 단결정의 Kyropoulos 성장시 도가니 형상에 따른 유동장 및 결정성장 거동의 CFD 해석

사파이어 단결정은 GaN계 화합물 증착이 용이하여 고휘도의 청색을 구현하기 위한 LED(Light Emitting Diode)용 기판으로 크게 각광받고 있다. 공업용 사파이어의 제조 방법으로는 Kyropoulos법, Czochralski법 HEM(Heat Exchager Method)등 다양한 방법이 시도되고 있으며, 그 중 Kyropoulos법은 고품질의 대구경 사파이어 단결정 성장이 가능한 대표적인 방법으로 알려져 있다. 그러나 Kyropoulos 공정의 특성상 결정성장로 내에서 용융 사파이어의 유동장이 단결정의 최종 품질을 결정하는데, 유동장의 변화와 이에 따르는 결정성장 거동을 관찰하기가 어렵다는 단점이 있다. 대구경화와 동시에 고품질의 사파이어 단결정을 생산하기 위해서는 성장로내의 유동장 해석을 통해 결정 성장조건을 최적화 하는 것이 필요하다. 본 연구에서는 유한요소법을 기반으로 한 전산유동해석을 통해 Kyropoulos 성장로 내의 도가니 형상의 종횡비(h/d)에 따른 용융 사파이어의 대류거동을 관찰하여 도가니의 형상이 단결정 성장에 미치는 영향을 분석하였으며, 성장로의 설계시 도가니의 종횡비를 작게 고려하면 용융 사파이어의 대류속도를 늦추고 계면의 convexity를 줄여 사파이어 단결정의 품질향상에 도움이 된다는 결과를 얻었다. Sapphire single crystals have been highlighted for epitaxial gallium nitride films in high-power laser and light emitting diode (LED) industries. Among the many crystal growth methods, the Kyropoulos process is an excellent commercial method for growing larger, high-optical-quality sapphire crystals with fewer defects. Because the properties and growth behavior of sapphire crystals are influenced largely by the temperature distribution and convection of molten sapphire during the manufacturing process, accurate predictions of the thermal fields and melt flow behavior are essential to design and optimize the Kyropoulos crystal growth process. In this study, computational fluid dynamic simulations were performed to examine the effects of the crucible geometry aspect ratio on melt convection during Kyropoulos sapphire crystal growth. The results through the evolution of various growth parameters on the temperature and velocity fields and convexity of the crystallization interface based on finite volume element simulations show that lower aspect ratio of the crucible geometry can be helpful for the quality of sapphire single crystal.

Effect of power arrangement on the crystal shape during the Kyropoulos sapphire crystal growth process

The Kyropoulos (KY) method is commonly used to grow large sized sapphire single crystals. The shape of the sapphire crystal thus grown is determined by the heater arrangement and the power reduction history in the Kyropoulos furnace. In order to grow high-quality sapphire single crystal, the heater arrangement should allow different power inputs in different sections in order to control the thermal field in the melt during the growth process. In this study, a numerical computation is performed to investigate the effects of the heater arrangement on the thermal and flow transport, the shape of the crystal–melt interface, and the power requirements during the Kyropoulos sapphire crystal growth process in a resistance heated furnace. Four different power ratio arrangements in a three-zone heater are considered. The results show that for the power arrangements considered herein, the temperature gradients along the crystallization front do not exceed 0.05K/mm, and that, after the growth of the crown, the crystal maintains an almost constant diameter. The remelting phenomenon may occur during growth when the input power of the upper side of the heater is higher than that of the lower side of the heater.

Modern trends in crystal growth and new applications of sapphire

We provide an overview of the latest market trends and modern competing methods of sapphire crystal growth and the application of sapphire wafers as LED substrates. Almost all methods of high temperature growth from the melt are suitable for sapphire production, but each of these methods has its advantages and disadvantages depending on the application and required finished product form factor. Special attention is paid to the review of defects and imperfections that allow the engineering of new active devices based on sapphire.

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

In this work, the numerical simulations were performed to investigate the rolls of crucible shape on temperature distribution, melt convection behavior and shape of the melt/crystal interface during the Kyropoulos sapphire crystal growth process. Cylindrical crucibles with different bottom corner radii were considered, and the Kyropoulos growth process was simulated using the finite volume method. Through numerical analyses, it was found that an increase in bottom corner radius of the crucible decreased the convexity of melt/crystal interface and the velocity of convectional flows of the molten sapphire during crystallization. As a consequence, it was concluded that the crucible with a curved bottom had advantages for the crystallization of the sapphire using the Kyropoulos method.

3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth

In the present work, 3D features of melt convection during sapphire growth of 100 mm diameter Cz and of 200 mm diameter Ky crystals are studied. The approach accounting for radiative heat exchange with absorption and a specular reflection in the crystal, which we applied in 2D modeling [1–3], has been extended to 3D computational domains and coupled to 3D heat transfer in the melt, crystal, and crucible. 3D melt unsteady convection together with crystallization front formation are taken into account within the Direct Numerical Simulation (DNS) approach. Results of 3D modeling are discussed in detail and quantitatively compared to the previously reported data of 2D modeling and experiments [2,3]. It has been found that the features of unsteady melt convection during the “before seeding”, “seeding”, and “shouldering” growth stages are quite different from each other, which necessitates a flexible control of the radial and vertical temperature gradients in the crucible to provide optimal conditions for stable growth of high quality sapphire crystals.

Simulation of temperature and flow fields in an inductively heated melt growth system

AbstractThe goal of the research presented here is to apply a global analysis of an inductively heated Czochralski furnace for a real sapphire crystal growth system and predict the characteristics of the temperature and flow fields in the system. To do it, for the beginning stage of a sapphire growth process, influence of melt and gas convection combined with radiative heat transfer on the temperature field of the system and the crystal‐melt interface have been studied numerically using the steady state two‐dimensional finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. The numerical results demonstrate that there are a powerful vortex which arises from the natural convection in the melt and a strong and large vortex that flows upwards along the afterheater side wall and downwards along the seed and crystal sides in the gas part. In addition, a wavy shape has been observed for the crystal‐melt interface with a deflection towards the melt. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical simulation of thermal and mass transport during Czochralski crystal growth of sapphire

AbstractThe thermal and flow transport in an inductively heated Czochralski crystal growth furnace during a crystal growth process is investigated numerically. The temperature and flow fields inside the furnace, coupled with the heat generation in the iridium crucible induced by the electromagnetic field generated by the RF coil, are computed. The results indicate that for an RF coil fixed in position during the growth process, although the maximum value of the magnetic, temperature and velocity fields decrease, the convexity of the crystal‐melt interface increases for longer crystal growth lengths. The convexity of the crystal‐melt interface and the power consumption can be reduced by adjusting the relative position between the crucible and the induction coil during growth. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Chemical transformations in the W-Al2O3 system under pressure P = 1 bar near the melting point of aluminum oxide

The W-Al2O3 system has been considered at a temperature of 2400 K and a pressure of 1 bar. The main chemical processes providing the interaction between the components of the system have been determined. It is shown that evaporation of Al2O3 into the gas phase gives rise to numerous reactions, which involve not only tungsten but also Al2O3 melt. It is concluded that such interactions can be reduced by decreasing the Al2O3 evaporation, which can be done by increasing the inert gas pressure. This approach makes it possible both to optimize the parameters of sapphire crystal growth and increase the lifetime of a tungsten heater and other units of crystallization systems.

Effects of RF coil position on the transport processes during the stages of sapphire Czochralski crystal growth

The effect of the RF coil position during the stages of sapphire crystal growth process in an inductively heated Czochralski crystal growth furnace on the thermal and flow transport, the shape of the crystal–melt interface shape, and the power requirements is investigated numerically. The results show that although the maximum values of temperature and velocity decrease, the convexity of the crystal–melt interface increases as the crystal length grows. It is found that the least input power is required if the central position of the RF coil is maintained below the central position of the melt during the crystal growth process. Under such crystal growth conditions, the temperature gradients along the crystalline front are small.