Sapphire Crystal Growth Research Articles

Enabling cryogenic gravitational wave detectors: growth of sapphire crystals with record low absorption in the near infrared

Sapphire was grown by Czochralski and ultra-low absorption (11 ppm cm−1) was achieved. The Fe2+–Fe3+ and Ti3+–Ti3+ pairs are crucial for the absorption at 1064 nm. The result is promised to grow large sapphire for the next generation of GW detector.

Sapphire crystal growth and solid–liquid interface structure: An investigation by molecular dynamic simulation and Czochralski growth

Sapphire has increasing demand toward optoelectrical devices like LED; its big challenge is to find reasonable growth mechanisms for high quality large size single crystals. In this paper, we proposed both theoretical and experimental studies to clarify multiscale behaviors within the Al2O3 growth system. Molecular dynamics simulation for sapphire crystal growth along c-, a-, and m-axes, and solid–liquid interface structure, and grown 2″ sapphire via the Czochralski method along the c-axis, were reported herein. Our studies show that α-Al2O3 growth behaviors along different crystal directions are different, which is different from the amorphous Al2O3 phase transition at the various α-Al2O3 planes. α-Al2O3 crystal growth in the c-axis system may be a complex process involving solid–liquid and solid–solid transformations, rather than a single solid–liquid transformation that happened in the systems growing along the a- and m-axes. Within the time scale of simulation, the crystals cannot be grown by the lattice period of the seed crystal along the c-axis and transform into γ-Al2O3 rather than α-Al2O3, while it is opposite along the a- and m-axes. This may be the microscopic reason why it is difficult to grow sapphire along the c-axis in the experiment. An abrupt change in the interfacial structure is the key reason to inhibit the transformation of liquid Al2O3 into α-Al2O3 along the c-axis.

Chemical model of sapphire crystal growth by Ky technique

Sapphire crystal (Al2O3) has been successfully used in various kinds of covering materials and LED substrates. Usually, sapphire crystals exhibit microscopic defects known as ‘‘micro-bubbles’’ or ‘‘micro-voids’’. A detailed chemical model coupled with heat and mass transport has been developed for the gas phase and for Al2O3 liquid phase. There was found a reason for arising a remarkable excess of Al3+ ions over O2– those and for converting their excess to gas voids or bubbles. The main purpose of the present study is to recommend an optimal configuration of the sapphire growth chamber, providing a minimal concentration of gas voids in the crystal. It has been explained by the model that some reasons of the formation of voids are eliminated by using the tungsten heater and crucible.

Thermodynamic Calculations of Ti Ion Concentrations and Segregation Coefficients during Ti:Sapphire Crystal Growth

Thermodynamic Calculations of Ti Ion Concentrations and Segregation Coefficients during Ti:Sapphire Crystal Growth

Control methodology for EFG sapphire crystals

A control methodology is presented for the growth of sapphire crystals by the Edge-defined, Film-fed Growth (EFG) process. This technique is particularly useful for crystals with large cross sections and lengths. To prevent the crystal from sticking, i.e., freezing, to the die, a unique algorithm for calculating the growth rate is described.

Growth of large sapphire crystals: Lessons learned

The article reviews current state of the art in growing large sapphire crystals used for epitaxial substrates of GaN light-emitting diodes and optical windows. Results of crystal growth with the Czochralski, Kyropoulos, heat-exchanger methods, horizontal directional crystallization, and edge-defined film-fed growth are demonstrated and discussed, along with recommendations of useful tools to increase crystal size.

Physico-chemical model for dopant charge state conversion during Ti:sapphire crystal growth

An original physico-chemical model is proposed that accounts for the conversion mechanism between Ti3+ and Ti4+ during Ti:sapphire crystal growth process. This model involves release of O2 from the crystal surface, which consumes aluminum vacancies. Consequently, these vacancies diffuse from the bulk crystal toward the surface, leading to the conversion of Ti4+ into Ti3+. A set of mass balance differential equations is established for these chemical species, taking into account diffusion and chemical reaction. The boundary condition for concentration of aluminum vacancies on crystal surface is given as the function of PO2 and temperature. A preliminary numerical simulation is performed to study the proposed model, using COMSOL Multiphysics® software. The obtained radial concentration distribution profiles of Ti3+ and Ti4+ are in qualitative agreement with the experimental results, showing that the proposed model has potential for further studying point defect reactions during crystal growth of ionic crystals.

Effect of Internal Radiation on Heat Transfer during Ti:sapphire Crystal Growth Process by Heat Exchanger Method

In this study, the effect of internal radiation on the heat transfer during titanium-doped sapphire (Ti:sapphire) crystal growth process by heat exchanger method (HEM) was comprehensively investigated based on a global heat transfer model. Radiation absorption, emission and scattering in the semitransparent melt and crystal were modeled with the rigorous finite volume method. The numerical results show that internal radiation strongly enhances the heat transport in the melt and crystal, strengthens the melt convection and reduces the temperature gradient in the central body of the crystal. However, it renders the isotherms intensively concentrated in the narrow bottom region of the crystal, resulting in a significant increase in the temperature gradient in this region compared to the case without internal radiation. What's more, internal radiation makes the melt-crystal interface deeply convex towards the melt, which could be responsible for the radial non-uniformity of titanium concentration in the large Ti:sapphire crystal by HEM. The sensitivity of internal radiation to the optical properties was also parametrically studied. It was found that the heat transfer is strongly depended on the absorption coefficients of the crystal and melt. Particularly, the interaction between internal radiation and heat conduction in the crystal is strongest at the intermediate value of the absorption coefficient of the crystal, leading to the largest values of conduction heat transfer rate and maximum temperature gradient at the bottom of the crystal. The influence of scattering in the crystal becomes significant only after the scattering coefficient is larger than absorption coefficient. This study suggested that the effect of internal radiation on the heat transfer during HEM Ti:sapphire crystal growth process shows some difference from that during Kyropoulos and Czochralski oxide crystal growth processes.

Analysis of Bulk Radiative Heat Transfer in a Crystal and in a Melt Using Numerical Simulation of the Sapphire Crystal Growth by the Stepanov Method

The effect of bulk radiative heat transfer during the growth of profiled sapphire crystals from the melt is studied by the numerical simulation method. The peculiarities in the structure of a lightguide flow in the crystal and in the melt, as well as the possibility of radiation instability of the interface, are considered. It is shown that overcooled regions with the size determined by the growth rate appear under the crystallization front. It is found that the use of a conical shaper ensures a more stable growth.

Machine learning application for prediction of sapphire crystals defects

We investigate the impact of different numbers of positive and negative examples on machine learning for sapphire crystals defects prediction. We obtain the models of crystal growth parameters influence on the sapphire crystal growth. For example, these models allow predicting the defects that occur due to local overcooling of crucible walls in the thermal node leading to the accelerated crystal growth. We also develop the prediction models for obtained crystal weight, blocks, cracks, bubbles formation, and total defect characteristics. The models were trained on all data sets and later tested for generalization on testing sets, which did not overlap the training set. During training and testing, we find the recall, precision of prediction and analyze the correlation among the features. The results have shown that the precision of neural network method for predicting defects formed by local overcooling of the crucible reached 0.94.

Analysis of heat transfer processes for sapphire growth by horizontal directed crystallization method

This research summarizes the analytical and experimental results of heat-transfer processes influence on defects formation during sapphire crystal growth by horizontal directed crystallization method (HDC). The shape of solid-melt interface significantly influences the process of sapphire crystals growth by this method. We receive the Stefan problem solution for sapphire crystals growth. It allows investigating the crystal growth process and the related factors (thermal stresses on different stages of growth process), their influence on defects formation. We investigate the main reasons for the formation of defective structures of the solid phase of sapphire crystals and the influence of thermal unit construction, the crystal geometry on the quality of the resulting sapphire crystal. We study the structure formation process, impurity distribution, and the nature of the defects in the crystal during it growth.

蓝宝石长晶过程中Ga元素的性能研究

蓝宝石长晶过程中Ga元素的性能研究

Study of influence of volumetric radiating overcooling of a melt on the form of front of crystallization by means of numerical modeling processes of heat transfer at growth of sapphire crystals from the melt

It is lead numerical modeling of processes of heat exchange at growth of crystals of sapphire from a melt by Stepanov and Czochralski methods. The influences of volumetric radiating overcooling of a melt and of growth speed on the form of front of crystallization and distribution of temperature near to it is studied. It is shown, that the account of absorption of thermal radiation in a melt can lead to formation of volumetric supercooled areas near to crystallization front and to appreciable change of its shape.

The MIVD method of optimal seeding state detection using image processing technology for sapphire crystal growth via the Kyropoulos method

The seeding technique is critical to the quality of the sapphire single crystal. The core of the seeding technique is the identification of seeding state. The MIVD method is proposed in the paper to detect the optimal seeding state. Compared with the OCS method, the MIVD method detects the characteristics of spoke pattern before a single point is formed on melt surface. Based on the similarity and periodicity of the melt motion, the optimal seeding state is detected by Fréchet distance. In the experiment, the MIVD method was compared with the OCS method and the artificial seeding method in terms of seeding efficiency and crystal quality. The MIVD method improves the quality of the sapphire crystal, at same time, it ensures seeding efficiency. The MIVD method is more suitable for practical production.

An Analysis Approach to the Sapphire Crystals Growth by Horizontal Directed Crystallization Method

The model for sapphire crystals growth parameters estimation has been suggested. It can be served as a basis for the analysis of heat transfer processes during sapphire crystals obtaining. It allows to predict the bubbles, stresses and cracks appearing during sapphire crystals growth. We describe the results of the analysis and parameters estimation of sapphire crystals growth on all stages by horizontal directed crystallization method.

Computational approach to the simulation of sapphire crystals growth by horizontal directed crystallization method

In this article we present an integrated approach to sapphire crystals growth simulation. Thermally induced stresses in sapphire crystals growing by horizontal directed crystallization are simulated by finite element method. The simulation results correspond to experimental observations. The results of the investigation allow to improve the process of crystal growth to obtain high quality large sapphire crystal.

Investigation of Influence of Sapphire Crystals Shape Factor on Its Growth by Horizontal Directed Crystallization

The value of shape factor allows to determine what processes (the surface or in crystal volume) define the dynamics of sapphire crystal growth by horizontal directed crystallization method and, as a result, estimate the influence of these processes on crystal quality. We receive the Stefan problem closed solution for sapphire crystals growth by horizontal directed crystallization method. It allows to investigate the growth process and the related factors (thermal stresses on different stages of growth process), melt hydrodynamics and its influence on defects formation. 1.

Axisymmetric lattice Boltzmann simulation of the heat-exchanger method-based sapphire crystal growth

The crystal-growth process in a heat-exchanger method (HEM)-based system was simulated using the lattice Boltzmann technique. The two-dimensional enthalpy-based lattice Boltzmann model was extended to treat the axisymmetric solid-liquid phase change problems. The proposed model demonstrates high accuracy over a large range of Biot and Stefan numbers and exhibits superiority over the first-order perturbation method, especially, in cases involving large Stefan numbers. Macroscopic crystal-growth simulations primarily focus on flow patterns in the melt and heat-transfer processes inside the crucible. Effects of dimensionless convective boundaries and Rayleigh numbers (Ra) on transport phenomena and the crystal/melt interface have also been discussed. It was observed that a decrease in the superheating temperature causes an increase in crystal fraction and decline in convection intensity. The area of the cooling zone mainly influences crystal growth rate during the initial stages of the process. In the later stages, however, the Biot number corresponding to the heating boundary assumes a more significant role. At low Rayleigh numbers, heat transfer via conduction is dominant in the melt. With increase in Ra values, melt convection tends to strengthen, thereby tending to deform the isothermal lines and phase interface.

Comparison of thermal stress computations in Czochralski and Kyropoulos growth of sapphire crystals

Thermal stress computations during sapphire growth are compared between a resistive Czochralski furnace and a Kyropoulos inductive furnace. 2D – axisymmetric global simulations are performed to compute the thermal field in the furnace and the convection in the melt. Temperatures carried out from global modeling at a given stage of the growth process, are used for thermal stress computations in the crystal. Three-dimensional stress analysis, which takes into account the anisotropic elastic constants of sapphire, shows nearly axisymmetric von Mises stress distribution in the crystal. It is shown that applying 2D – axisymmetric modeling of thermal stress may result in significant errors. Computations performed for a crystal of 10 cm in diameter grown in a Kyropoulos furnace show only a thin region of 2–3 mm with high thermal stress located at the crystal periphery. The model predicts very low thermal stresses in the central part of the crystal. Simulations of an ingot grown by Czochralski technique, show higher thermal stresses in almost the whole volume of the crystal. Numerical computations are in agreement with our previous measurements of dislocation density in sapphire crystals grown by the Kyropoulos method. The present numerical results can explain the experimental observations showing that sapphire crystals grown by Czochralski technique have a much higher dislocation density than Kyropoulos grown ingots.

Modeling Czochralski growth of oxide crystals for piezoelectric and optical applications

Numerical modeling is applied to investigate the impact of crystal and crucible rotation on the flow pattern and crystal-melt interface shape in Czochralski growth of oxide semi-transparent crystals used for piezoelectric and optical applications. Two cases are simulated in the present work: the growth of piezoelectric langatate (LGT) crystals of 3 cm in diameter in an inductive furnace, and the growth of sapphire crystals of 10 cm in diameter in a resistive configuration. The numerical results indicate that the interface shape depends essentially on the internal radiative heat exchanges in the semi-transparent crystals. Computations performed by applying crystal/crucible rotation show that the interface can be flattened during LGT growth, while flat-interface growth of large diameter sapphire crystals may not be possible.