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13 pages, 1382 KiB

Open AccessArticle

The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity

by Radeesha Laknath Agampodi Mendis, Atsushi Sekimoto, Yasunori Okano, Hisashi Minakuchi and Sadik Dost

Crystals 2021, 11(2), 116; https://doi.org/10.3390/cryst11020116 - 26 Jan 2021

Cited by 12 | Viewed by 2192

Abstract

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios

A_{s}

has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model [...] Read more.

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios

A_{s}

has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (

A_{s}

) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (

M a_{T} A_{s} ≲ 1800

)) has the same dependence on

A_{s}

as the critical thermal Marangoni number (under small solutal Marangoni numbers (

400 ≲ M a_{C} A_{s} ≲ 800

)), i.e., it decreases with increasing

A_{s}

. The azimuthal wavenumber of the traveling wave mode increases as decreasing

A_{s}

, i.e., larger azimuthal wavenumbers (

m = 6, 7, 11, 12

, and 13) appear for

A_{s} = 0.25

, and only

m = 2

appears when

A_{s}

is one and larger. The oscillatory modes of the hydro waves have been extracted as the spatiotemporal structures by using dynamic mode decomposition (DMD). The present study suggests a proper parameter region of quiescent steady flow suitable for crystal growth for smaller aspect ratios of the liquid bridge. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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10 pages, 3187 KiB

Open AccessArticle

Numerical Analysis of Phosphorus Concentration Distribution in a Silicon Crystal during Directional Solidification Process

by Satoshi Nakano, Xin Liu, Xue-Feng Han and Koichi Kakimoto

Crystals 2021, 11(1), 27; https://doi.org/10.3390/cryst11010027 - 30 Dec 2020

Cited by 3 | Viewed by 2374

Abstract

For bulk doping, boron and phosphorus are usually used as p-type and n-type dopants, respectively. The distribution of these dopant concentrations in a silicon crystal along the vertical direction is governed by the segregation phenomena. As the segregation coefficient of phosphorus is small, [...] Read more.

For bulk doping, boron and phosphorus are usually used as p-type and n-type dopants, respectively. The distribution of these dopant concentrations in a silicon crystal along the vertical direction is governed by the segregation phenomena. As the segregation coefficient of phosphorus is small, phosphorus concentration distribution in a silicon crystal becomes inhomogeneous; inhomogeneous phosphorus concentration distribution affects the distribution of resistivity in the crystal. Therefore, it is important to control the phosphorus concentration distribution in a silicon crystal and make it uniform. In this study, by numerical analysis, we investigated the effect of the evaporation flux at the melt surface on phosphorus concentration distribution during the directional solidification process. To obtain a homogeneous phosphorus concentration distribution in the silicon crystal, we had to control the phosphorous evaporation flux at the melt surface and maintain approximately the same phosphorus concentration in the melt during the entire solidification process even though the growth rate was always changing. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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12 pages, 2596 KiB

Open AccessArticle

Use of Growth-Rate/Temperature-Gradient Charts for Defect Engineering in Crystal Growth from the Melt

by Thierry Duffar

Crystals 2020, 10(10), 909; https://doi.org/10.3390/cryst10100909 - 08 Oct 2020

Viewed by 2246

Abstract

As the requirements in terms of crystal defect/quality and production yield are generally contradictory, it is necessary to develop methods in order to find the best compromise for the growth conditions of a given crystal. Simple growth-rate/temperature-gradient charts are a possible tool in [...] Read more.

As the requirements in terms of crystal defect/quality and production yield are generally contradictory, it is necessary to develop methods in order to find the best compromise for the growth conditions of a given crystal. Simple growth-rate/temperature-gradient charts are a possible tool in this respect. After the recall of the classical analytical equations useful for describing the process and defect engineering, a simple pedagogic case explains the building and use of such charts. The more complex application to the directional casting of photovoltaic Si necessitated the development of new physical models for twinning and equiaxed growth. This allowed plotting charts that proved useful for industrial applications. The conclusions discuss the drawbacks and advantages of the method. It finally proves to be a pedagogic tool for teaching crystal growth engineering. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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13 pages, 3313 KiB

Open AccessEditor’s ChoiceArticle

Optimal Control of SiC Crystal Growth in the RF-TSSG System Using Reinforcement Learning

by Lei Wang, Atsushi Sekimoto, Yuto Takehara, Yasunori Okano, Toru Ujihara and Sadik Dost

Crystals 2020, 10(9), 791; https://doi.org/10.3390/cryst10090791 - 07 Sep 2020

Cited by 8 | Viewed by 3104

Abstract

We have developed a reinforcement learning (RL) model to control the melt flow in the radio frequency (RF) top-seeded solution growth (TSSG) process for growing more uniform SiC crystals with a higher growth rate. In the study, the electromagnetic field (EM) strength is [...] Read more.

We have developed a reinforcement learning (RL) model to control the melt flow in the radio frequency (RF) top-seeded solution growth (TSSG) process for growing more uniform SiC crystals with a higher growth rate. In the study, the electromagnetic field (EM) strength is controlled by the RL model to weaken the influence of Marangoni convection. The RL model is trained through a two-dimensional (2D) numerical simulation of the TSSG process. As a result, the growth rate under the control of the RL model is improved significantly. The optimized RF-coil parameters based on the control strategy for the 2D melt flow are used in a three-dimensional (3D) numerical simulation for model validation, which predicts a higher and more uniform growth rate. It is shown that the present RL model can significantly reduce the development cost and offers a useful means of finding the optimal RF-coil parameters. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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12 pages, 8150 KiB

Open AccessArticle

Numerical Study of Three-Dimensional Melt Flows during the TSSG Process of SiC Crystal for the Influence of Input Parameters of RF-Coils and an External Rotating Magnetic Field

by Lei Wang, Yuto Takehara, Atsushi Sekimoto, Yasunori Okano, Toru Ujihara and Sadik Dost

Crystals 2020, 10(2), 111; https://doi.org/10.3390/cryst10020111 - 12 Feb 2020

Cited by 3 | Viewed by 2518

Abstract

Three-dimensional numerical simulations were conducted for the Top-Seeded Solution Growth (TSSG) process of silicon carbide (SiC) crystals. We investigated the influence of coils frequency and peak current, and an applied rotating magnetic field (RMF) on the melt flow developing in this system. Numerical [...] Read more.

Three-dimensional numerical simulations were conducted for the Top-Seeded Solution Growth (TSSG) process of silicon carbide (SiC) crystals. We investigated the influence of coils frequency and peak current, and an applied rotating magnetic field (RMF) on the melt flow developing in this system. Numerical simulation results show that the Marangoni flow in the melt becomes stronger at higher coils frequencies due to the decreasing coils-induced electromagnetic field strength. Results also show that the use of external RMF may improve supersaturation uniformity along the seed if it is properly adjusted with respect to the coils-induced electromagnetic field strength. Furthermore, it is predicted that the application of RMF and seed rotation in the same direction may enhance supersaturation below the seed. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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15 pages, 3290 KiB

Open AccessArticle

Homogeneous Nucleation Mechanism of NaCl in Aqueous Solutions

by Qiang Sun, Shuai Cui and Meixi Zhang

Crystals 2020, 10(2), 107; https://doi.org/10.3390/cryst10020107 - 12 Feb 2020

Cited by 10 | Viewed by 5982

Abstract

In this study, molecular dynamic simulations are employed to investigate the homogeneous nucleation mechanism of NaCl crystal in solutions. According to the simulations, the dissolved behaviors of NaCl in water are dependent on ion concentrations. With increasing NaCl concentrations, the dissolved Na⁺ [...] Read more.

In this study, molecular dynamic simulations are employed to investigate the homogeneous nucleation mechanism of NaCl crystal in solutions. According to the simulations, the dissolved behaviors of NaCl in water are dependent on ion concentrations. With increasing NaCl concentrations, the dissolved Na⁺ and Cl^- ions tend to be aggregated in solutions. In combination with our recent studies, the aggregate of dissolved solutes is mainly ascribed to the hydrophobic interactions. Different from the two-step mechanism, no barrier is needed to overcome the formation of the aggregate. In comparison with the classical nucleation theory (CNT), because of the formation of solute aggregate, this lowers the barrier height of nucleation and affects the nucleation mechanism of NaCl crystal in water. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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14 pages, 2565 KiB

Open AccessArticle

A Linear Regression Model for Determining the Pre-Exponential Factor and Interfacial Energy Based on the Metastable Zone Width Data

by Lie-Ding Shiau

Crystals 2020, 10(2), 103; https://doi.org/10.3390/cryst10020103 - 11 Feb 2020

Cited by 3 | Viewed by 2145

Abstract

A linear regression model is presented in this study to determine the pre-exponential factor and interfacial energy of the crystallized substance based on classical nucleation theory using the metastable zone width data. The nucleation event is assumed corresponding to a point at which [...] Read more.

A linear regression model is presented in this study to determine the pre-exponential factor and interfacial energy of the crystallized substance based on classical nucleation theory using the metastable zone width data. The nucleation event is assumed corresponding to a point at which the total number density of the nuclei has reached a fixed (but unknown) value. One equation is derived for any temperature-dependent functional form of the solubility. Another equation is derived for the van’t Hoff solubility expression. The pre-exponential factor and interfacial energy obtained from these two equations are found consistent for the studied systems, including glutamic acid, glycine, and 3-nito-1,2,4-triazol-5-one. The results obtained from these two equations are also compared with those obtained from the integral method and classical 3D nucleation theory approach. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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8 pages, 3243 KiB

Open AccessArticle

Improvement of Growth Interface Stability for 4-Inch Silicon Carbide Crystal Growth in TSSG

by Botao Liu, Yue Yu, Xia Tang and Bing Gao

Crystals 2019, 9(12), 653; https://doi.org/10.3390/cryst9120653 - 07 Dec 2019

Cited by 4 | Viewed by 4047

Abstract

The growth interface instability of large-size SiC growth in top-seeded solution growth (TSSG) is a bottleneck for industrial production. The authors have previously simulated the growth of 4-inch SiC crystals and found that the interface instability in TSSG was greatly affected by the [...] Read more.

The growth interface instability of large-size SiC growth in top-seeded solution growth (TSSG) is a bottleneck for industrial production. The authors have previously simulated the growth of 4-inch SiC crystals and found that the interface instability in TSSG was greatly affected by the flow field. According to our simulation of the flow field, we proposed a new stepped structure that greatly improved the interface stability of large-size crystal growth. This stepped structure provides a good reference for the growth of large-sized SiC crystals by TSSG in the future. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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14 pages, 3204 KiB

Open AccessArticle

Growth of KDP: Fe³⁺ Crystals from Oversaturated Aqueous Solutions

by Vera Manomenova, Elena Rudneva, Svetlana Baskakova and Alexey Voloshin

Crystals 2019, 9(12), 646; https://doi.org/10.3390/cryst9120646 - 05 Dec 2019

Cited by 5 | Viewed by 3512

Abstract

The KH₂PO₄ solubility curves in pure water and in water with the addition of 50 ppm Fe³⁺ were refined. The KH₂PO₄ and KH₂PO₄: Fe³⁺ solutions stability to supercooling was evaluated by [...] Read more.

The KH₂PO₄ solubility curves in pure water and in water with the addition of 50 ppm Fe³⁺ were refined. The KH₂PO₄ and KH₂PO₄: Fe³⁺ solutions stability to supercooling was evaluated by polythermal studies of the width of metastable zone. It was shown that Fe³⁺ addition makes the solution more stable. A series of Fe³⁺ doped KDP crystals were grown at different temperature and hydrodynamic regimes at supersaturation level up to 0.45. Their real structure was studied by X-ray projection topography and, as a result, the most suitable growth conditions are chosen. The transmittance spectra of prism sectors with ferric iron concentrations C_Fe up to 102 ppm were obtained. It was found that KDP crystals with C_Fe >60 ppm can be used as optical filters for suppressing transmission in UV-C and UV-B ranges. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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Review

Jump to: Research

17 pages, 4315 KiB

Open AccessReview

Application of Artificial Neural Networks in Crystal Growth of Electronic and Opto-Electronic Materials

by Natasha Dropka and Martin Holena

Crystals 2020, 10(8), 663; https://doi.org/10.3390/cryst10080663 - 01 Aug 2020

Cited by 17 | Viewed by 4949

Abstract

In this review, we summarize the results concerning the application of artificial neural networks (ANNs) in the crystal growth of electronic and opto-electronic materials. The main reason for using ANNs is to detect the patterns and relationships in non-linear static and dynamic data [...] Read more.

In this review, we summarize the results concerning the application of artificial neural networks (ANNs) in the crystal growth of electronic and opto-electronic materials. The main reason for using ANNs is to detect the patterns and relationships in non-linear static and dynamic data sets which are common in crystal growth processes, all in a real time. The fast forecasting is particularly important for the process control, since common numerical simulations are slow and in situ measurements of key process parameters are not feasible. This important machine learning approach thus makes it possible to determine optimized parameters for high-quality up-scaled crystals in real time. Full article

(This article belongs to the Special Issue Crystal Growth from Liquid Phase)

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