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Crystals
Special Issues
Heat and Mass Transfer Modeling in Crystal Growth
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Heat and Mass Transfer Modeling in Crystal Growth

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

Deadline for manuscript submissions: closed (30 August 2023) | Viewed by 7751

Special Issue Editors

Dr. Xuefeng Han

E-Mail Website
Guest Editor
Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, China
Interests: crystal growth; silicon carbide; silicon; heat and mass transfer
Dr. Xin Liu

E-Mail Website
Guest Editor
Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Interests: multi-scale modeling on crystal growth; solidification process; materials informatics; silicon; machine learning; process optimization
Dr. Andrejs Sabanskis

E-Mail Website
Guest Editor
Institute of Numerical Modelling, Faculty of Physics, Mathematics, and Optometry, University of Latvia, 3 Jelgavas Street, LV-1004 Riga, Latvia
Interests: floating-zone process; Czochralski method; silicon; germanium; point defects; thermal stresses; dislocations

Special Issue Information

Dear Colleagues,

Crystal growth is of great significance in the development of quantum computing, clean energy, next-generation communication infrastructure, and other related fields. In recent years especially, the rapid development of semiconductor device applications requires high-quality crystal materials. The continuous quality improvement of traditional semiconductor materials, such as Si, Ge, GaAs, and InP, and wide bandgap compound semiconductor materials, such as SiC, GaN, and Ga2O3, has attracted the attention of researchers. Crystal growth is a very complex and multi-physical field coupling system, including processes of heat transfer, thermal radiation, melt convection, and impurity diffusion. The interdisciplinary nature of this field demands prerequisite knowledge of crystallography, transport phenomena, thermodynamics, phase transformation, and mechanical behavior. The successful application of this knowledge will facilitate the growth of high-quality, low-defect crystals.

Based on computational heat and mass transfer, the coupling of multi-scale and multi-physics modelling provides an efficient tool for analyzing and optimizing the crystal growth process, helping to prepare cutting-edge materials. Modelling, combined with data science, can also save huge human and material costs in frontier exploration.

To promote the enrichment and exchange of knowledge about crystal growth between scientists and engineers, and to establish a bridge between crystal growth experiments and theory, this Special Issue encourages colleagues to have discussions around—and publish research on—different aspects of crystal growth simulations. We invite submissions regarding heat and mass modelling concerning bulk or thin-film crystal growth. The possible scope of this Special Issue includes, without being limited to, the following topics: metals, minerals, semiconductors, superconductors, magnetics, inorganic, and organic substances. We are also interested in submissions covering numerical methods, schemes, or algorithms, which are useful in the field of crystal growth.

Dr. Xuefeng Han
Dr. Xin Liu
Dr. Andrejs Sabanskis
Guest Editors

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 submissions that pass pre-check are 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 2600 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

  • numerical modeling
  • heat transfer
  • bulk crystal growth
  • epitaxy growth
  • solution growth
  • vapor growth
  • multi-scale or multi-physics coupling

Published Papers (5 papers)

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Research

16 pages, 5433 KiB  
Article
Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields
by Xianrong Cen and Shuangxi Guo
Crystals 2023, 13(10), 1436; https://doi.org/10.3390/cryst13101436 - 27 Sep 2023
Cited by 1 | Viewed by 887
Abstract
The application of magnetic fields has become a standard control technique in the CZ-Si growth industry. To investigate the impact of cusp-shaped magnetic fields (CMF) on heat and mass transfer in the melt, a series of transient three-dimensional simulations were conducted for the [...] Read more.
The application of magnetic fields has become a standard control technique in the CZ-Si growth industry. To investigate the impact of cusp-shaped magnetic fields (CMF) on heat and mass transfer in the melt, a series of transient three-dimensional simulations were conducted for the growth of a 100 mm CZ-Si crystal with a cylindrical crucible. The turbulent melt motion was modeled using the large eddy simulation (LES) method. Six configurations of CMF with various zero-Gaussian plane (ZGP) positions were examined and numerically compared. The computed results showed that different ZGP positions resulted in distinct types of melt convection, buoyant plumes, and thermal waves. Additionally, it was observed that the studied CMF configurations effectively reduced oxygen dissolution from the crucible wall along with oxygen impurity incorporation into the crystal. These findings demonstrate the potential for precise control of the heat and mass transfer process in CZ-Si growth through the application of suitable CMF. Full article
(This article belongs to the Special Issue Heat and Mass Transfer Modeling in Crystal Growth)
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13 pages, 4077 KiB  
Article
Study on Motion and Deposition of Nanoparticles in Rotary MOCVD Reactors of Gallium Nitride
by Peng Su, Daihui Lu, Jinping Luo, Guangyu Zheng, Yukang Sun and Lijun Liu
Crystals 2023, 13(9), 1328; https://doi.org/10.3390/cryst13091328 - 30 Aug 2023
Viewed by 669
Abstract
Nanoparticles have a negative effect on the preparation of Gallium Nitride (GaN) by Metal-Organic Chemical Vapor Deposition (MOCVD). We developed a particle tracking and particle-wall collision model coupled with the bulk gas flow solver to investigate the motion and deposition of nanoparticles in [...] Read more.
Nanoparticles have a negative effect on the preparation of Gallium Nitride (GaN) by Metal-Organic Chemical Vapor Deposition (MOCVD). We developed a particle tracking and particle-wall collision model coupled with the bulk gas flow solver to investigate the motion and deposition of nanoparticles in single-wafer and multi-wafer reactors. The results indicated that for the single-wafer reactor, there is no particle deposition on the reactor wall and susceptor, but there is the endless movement of some particles within the reactor, which should be avoided. For the multi-wafer reactors, some of the nanoparticles are deposited near the axis, and those whose initial position is beyond a certain position from the axis are trapped in a vortex above the receptor, resulting in more complex by-products, although no particles are trapped in endless motion. Moreover, the effects of the rotational speed of the susceptor on the deposition rate for both the single-wafer reactor and the multi-wafer reactor were also simulated and analyzed. Full article
(This article belongs to the Special Issue Heat and Mass Transfer Modeling in Crystal Growth)
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11 pages, 8177 KiB  
Article
Numerical Simulation of β-Ga2O3 Single Crystal Growth by Czochralski Method with an Insulation Lid
by Dan Wu, Ning Xia, Keke Ma, Jiabin Wang, Cheng Li, Zhu Jin, Hui Zhang and Deren Yang
Crystals 2022, 12(12), 1715; https://doi.org/10.3390/cryst12121715 - 25 Nov 2022
Cited by 4 | Viewed by 1683
Abstract
The effect of an insulation lid on the growth of 4-inch β-Ga2O3 single crystals by the Czochralski method is analyzed by numerical simulation. The insulation lid mainly hinders upward radiant heat transfer from the melt and crucible and increases the [...] Read more.
The effect of an insulation lid on the growth of 4-inch β-Ga2O3 single crystals by the Czochralski method is analyzed by numerical simulation. The insulation lid mainly hinders upward radiant heat transfer from the melt and crucible and increases the axial temperature gradient in the crystal. Such benefits make the melt/crystal interface convex, which is conducive to suppressing spiral growth and growing large crystals with high quality. Materials with low thermal conductivity λ and low emissivity ε are the optimal choices for making an insulation lid. The inner hole has a great influence on the isolation of radiant heat, and it is determined that the maximum size of the inner diameter Din should not be larger than 130 mm. Thermal stress analysis results indicated that the insulation lid will cause a better stress distribution, illustrating the effect of the insulation lid on the quality of a cylindrical crystal. Full article
(This article belongs to the Special Issue Heat and Mass Transfer Modeling in Crystal Growth)
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9 pages, 693 KiB  
Article
The Correlation for Effective Distribution Coefficient with Initial Impurity Concentration and Growth Rate for Acrylic Acid in Melt Crystallization
by Lie-Ding Shiau
Crystals 2022, 12(5), 709; https://doi.org/10.3390/cryst12050709 - 16 May 2022
Cited by 2 | Viewed by 1557
Abstract
The layer growth rates and resulting crystal purity during solid-layer melt crystallization were experimentally measured for acrylic acid (AA) with impurity propionic acid (PA) operated at various cooling temperatures. A power law was adopted to correlate the growth rate with the temperature difference [...] Read more.
The layer growth rates and resulting crystal purity during solid-layer melt crystallization were experimentally measured for acrylic acid (AA) with impurity propionic acid (PA) operated at various cooling temperatures. A power law was adopted to correlate the growth rate with the temperature difference between melt and coolant. The effective distribution coefficient was determined from the resulting crystal purity for each condition. An empirical equation modified from the analytical solution for the mass transfer boundary layer was proposed in this work to relate the effective distribution coefficient to the initial impurity concentration and growth rate. Full article
(This article belongs to the Special Issue Heat and Mass Transfer Modeling in Crystal Growth)
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14 pages, 7041 KiB  
Article
Design and Numerical Study of Argon Gas Diversion System Using Orthogonal Experiment to Reduce Impurities in Large-Sized Casting Silicon
by Jiulong Li, Wenjia Su, Zhen Zhang, Zhicheng Guan, Jiaqi Li and Junfeng Wang
Crystals 2022, 12(4), 562; https://doi.org/10.3390/cryst12040562 - 17 Apr 2022
Cited by 4 | Viewed by 1848
Abstract
To reduce oxygen and carbon impurities while casting silicon, an argon gas diversion system is proposed. A series of two-dimensional global transient numerical simulations are carried out using Fluent software according to the orthogonal experimental design, including heat transfer, convection of silicon melt [...] Read more.
To reduce oxygen and carbon impurities while casting silicon, an argon gas diversion system is proposed. A series of two-dimensional global transient numerical simulations are carried out using Fluent software according to the orthogonal experimental design, including heat transfer, convection of silicon melt and argon gas, and the fully coupling transport of impurities. The numerical results show that when the distance between the outer tube outlet and the cover is 10 mm, the backflow is inhibited by lateral outflow, thus the generation of CO is suppressed and the penetration of impurities into the silicon melt is decreased. The larger the flow rate, the more obvious the effect is. When the outer tube outlet is far from the cover, the effect of removing impurities is no longer significant. In addition, too large or too small an inner tube flow rate is not conducive to impurity reduction. The optimal parameter combination of outer tube flow rate, inner tube flow rate, and the distance between outer tube outlet and the cover are determined by the orthogonal experiment. Compared with the original furnace, the average concentration of oxygen and carbon in casting silicon ingots could be decreased by 7.4% and 59.9%, respectively, by using the optimized argon gas diversion system. Full article
(This article belongs to the Special Issue Heat and Mass Transfer Modeling in Crystal Growth)
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