Special Issue "Crystal Growth from Liquid Phase"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystal Engineering".

Deadline for manuscript submissions: 31 December 2021.

Special Issue Editors

Prof. Dr. Yasunori Okano
E-Mail Website
Guest Editor
Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
Interests: crystal growth; computer simulation; fluid flow; heat transfer; mass transfer
Prof. Dr. Sadik Dost
E-Mail Website
Co-Guest Editor
Crystal Growth Laboratory, Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada
Interests: crystal growth; computer simulation; fluid flow; heat transfer; mass transfer

Special Issue Information

Dear Colleagues,

Bulk single crystals of semiconductors, oxides, borides, halides, and biomaterials are mostly grown from the melt or solution known as the liquid phase. During crystal growth from the liquid phase, transport structures developing in the growth solution/melt, such as fluid flow, temperature, and concentration fields, significantly affect the quality of grown crystals. Therefore, such transport structures must be better understood and controlled for the growth of high-quality crystals. In this direction, the application of applied electric and magnetic fields and crystal/crucible rotations is considered. Microgravity conditions have also been utilized.

Recent developments in numerical simulations and experimental techniques shed light on the understanding of the relations between the transport structures developing in the growth melt/solution and the crystal quality. Various optimization techniques have been considered to obtain optimum growth conditions for the growth of high quality crystals. Even artificial intelligence (AI), such as neural networks, has been utilized for the optimization of growth techniques and the design of new functional materials.

This Special Issue aims at publishing research findings from various perspectives on bulk crystal growth from the liquid phase. We encourage the submission of original articles in this field by means of numerical simulations and/or experimental approaches, including novel design of growth process, by considering external applied fields and new approaches. Moreover, reviews and feature articles are also welcome. Topics for this issue may include:

  • Transport phenomena occurring during growth of bulk crystals from the liquid phase; numerical and experimental;
  • Study and control of transport structures in the melt/solution under external fields; numerical and experimental;
  • Development and utilization of new growth processes and systems for bulk crystal growth.

Prof. Dr. Yasunori Okano
Prof. Dr. Sadik Dost
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bulk single crystal growth
  • Liquid phase
  • Melt and solution growth
  • Applied magnetic and external fields
  • Semiconductors
  • Oxides
  • Numerical simulations

Published Papers (10 papers)

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Research

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Article
The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity
Crystals 2021, 11(2), 116; https://doi.org/10.3390/cryst11020116 - 26 Jan 2021
Viewed by 431
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 As 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 (As) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (MaTAs1800)) has the same dependence on As as the critical thermal Marangoni number (under small solutal Marangoni numbers (400MaCAs800)), i.e., it decreases with increasing As. The azimuthal wavenumber of the traveling wave mode increases as decreasing As, i.e., larger azimuthal wavenumbers (m=6,7,11,12, and 13) appear for As=0.25, and only m=2 appears when As 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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Article
Numerical Analysis of Phosphorus Concentration Distribution in a Silicon Crystal during Directional Solidification Process
Crystals 2021, 11(1), 27; https://doi.org/10.3390/cryst11010027 - 30 Dec 2020
Viewed by 499
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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Article
Use of Growth-Rate/Temperature-Gradient Charts for Defect Engineering in Crystal Growth from the Melt
Crystals 2020, 10(10), 909; https://doi.org/10.3390/cryst10100909 - 08 Oct 2020
Viewed by 562
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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Article
Optimal Control of SiC Crystal Growth in the RF-TSSG System Using Reinforcement Learning
Crystals 2020, 10(9), 791; https://doi.org/10.3390/cryst10090791 - 07 Sep 2020
Cited by 1 | Viewed by 675
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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Article
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
Crystals 2020, 10(2), 111; https://doi.org/10.3390/cryst10020111 - 12 Feb 2020
Cited by 2 | Viewed by 785
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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Article
Homogeneous Nucleation Mechanism of NaCl in Aqueous Solutions
Crystals 2020, 10(2), 107; https://doi.org/10.3390/cryst10020107 - 12 Feb 2020
Cited by 1 | Viewed by 1618
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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Article
A Linear Regression Model for Determining the Pre-Exponential Factor and Interfacial Energy Based on the Metastable Zone Width Data
Crystals 2020, 10(2), 103; https://doi.org/10.3390/cryst10020103 - 11 Feb 2020
Cited by 1 | Viewed by 572
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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Article
Improvement of Growth Interface Stability for 4-Inch Silicon Carbide Crystal Growth in TSSG
Crystals 2019, 9(12), 653; https://doi.org/10.3390/cryst9120653 - 07 Dec 2019
Cited by 1 | Viewed by 1109
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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Article
Growth of KDP: Fe3+ Crystals from Oversaturated Aqueous Solutions
Crystals 2019, 9(12), 646; https://doi.org/10.3390/cryst9120646 - 05 Dec 2019
Cited by 1 | Viewed by 852
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 CFe up to 102 ppm were obtained. It was found that KDP crystals with CFe >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

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Review
Application of Artificial Neural Networks in Crystal Growth of Electronic and Opto-Electronic Materials
Crystals 2020, 10(8), 663; https://doi.org/10.3390/cryst10080663 - 01 Aug 2020
Cited by 1 | Viewed by 811
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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