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Crystals
Special Issues
Modeling of Crystal Growth
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Modeling of Crystal Growth

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

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 13679

Special Issue Editors

Dr. Wolfram Miller

E-Mail Website
Guest Editor
Leibniz Institute for Crystal Growth IKZ, Max-Born-Str. 2, 12489 Berlin, Germany
Interests: crystal growth; epitaxial growth; numerical modeling; growth kinetics; crystal growth engineering
Prof. Dr. Koichi Kakimoto

E-Mail Website
Guest Editor
Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga Fukuoka 816-8580, Japan
Interests: fluid dynamics; quantum mechanics; molecular dinamics; Monte Carlo simulation; solution growth
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Modeling of crystal growth is an important tool to understand fundamental aspects, support experimental work, and contribute to optimization of industrial processes. The classical numerical methods listed below are being extended by the concept of big data and machine learning.

We invite all authors to contribute to this Special Issue by giving an overview of the current methods, limits, and challenges linked to modeling of crystal growth.

Articles are welcome applying calculations on:

  • Atomistic scale, such as:
    • Ab initio calculations;
    • Molecular dynamics;
    • Kinetic Monte Carlo;
  • Microscopic and mesoscopic scale, such as:
    • Phase field models;
    • Enthalpy models;
    • Lattice Boltzmann methods;
  • Macroscopic scale, such as:
    • Finite element methods;
    • Finite volume methods;
    • Thermal radiation models;
  • Coupling scales and multiphysics.

Type of crystal growth might be:

  • Bulk crystal growth;
  • Epitaxy;
  • Growth of nanostructures;
  • Industrial crystallization.

Subjects might include:

  • Growth conditions and polymorphism;
  • Growth kinetics;
  • Defect dynamics;
  • Thermal and stress fields;
  • Influence of convection;
  • Optimization of growth process.

Dr. Wolfram Miller
Prof. Koichi Kakimoto
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

  • crystal growth
  • modeling
  • numerical methods
  • calculations
  • growth kinetics

Published Papers (5 papers)

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Research

14 pages, 4250 KiB  
Article
Evaluation of the Performance of Published Point Defect Parameter Sets in Cone and Body Phase of a 300 mm Czochralski Silicon Crystal
by Andrejs Sabanskis, Matīss Plāte, Andreas Sattler, Alfred Miller and Jānis Virbulis
Crystals 2021, 11(5), 460; https://doi.org/10.3390/cryst11050460 - 21 Apr 2021
Cited by 4 | Viewed by 2497
Abstract
Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been [...] Read more.
Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been proposed. In this paper the transient temperature, thermal stress and point defect distributions are simulated for 300 mm Czochralski growth of the whole crystal including cone and cylindrical growth phases. Simulations with 12 different published point defect parameter sets are compared to the experimentally measured interstitial–vacancy boundary. The results are evaluated for standard and adjusted parameter sets and generally the best agreement in the whole crystal is found for models considering the effect of thermal stress on the equilibrium point defect concentration. Full article
(This article belongs to the Special Issue Modeling of Crystal Growth)
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14 pages, 6380 KiB  
Article
Nucleation and Post-Nucleation Growth in Diffusion-Controlled and Hydrodynamic Theory of Solidification
by Frigyes Podmaniczky and László Gránásy
Crystals 2021, 11(4), 437; https://doi.org/10.3390/cryst11040437 - 17 Apr 2021
Cited by 5 | Viewed by 2654
Abstract
Two-step nucleation and subsequent growth processes were investigated in the framework of the single mode phase-field crystal model combined with diffusive dynamics (corresponding to colloid suspensions) and hydrodynamical density relaxation (simple liquids). It is found that independently of dynamics, nucleation starts with the [...] Read more.
Two-step nucleation and subsequent growth processes were investigated in the framework of the single mode phase-field crystal model combined with diffusive dynamics (corresponding to colloid suspensions) and hydrodynamical density relaxation (simple liquids). It is found that independently of dynamics, nucleation starts with the formation of solid precursor clusters that consist of domains with noncrystalline ordering (ringlike projections are seen from certain angles), and regions that have amorphous structure. Using the average bond order parameter q¯6, we distinguished amorphous, medium range crystallike order (MRCO), and crystalline local orders. We show that crystallization to the stable body-centered cubic phase is preceded by the formation of a mixture of amorphous and MRCO structures. We have determined the time dependence of the phase composition of the forming solid state. We also investigated the time/size dependence of the growth rate for solidification. The bond order analysis indicates similar structural transitions during solidification in the case of diffusive and hydrodynamic density relaxation. Full article
(This article belongs to the Special Issue Modeling of Crystal Growth)
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11 pages, 3234 KiB  
Article
Effect of Argon Flow on Oxygen and Carbon Coupled Transport in an Industrial Directional Solidification Furnace for Crystalline Silicon Ingots
by Xiaofang Qi, Yiwen Xue, Wenjia Su, Wencheng Ma and Lijun Liu
Crystals 2021, 11(4), 421; https://doi.org/10.3390/cryst11040421 - 14 Apr 2021
Cited by 11 | Viewed by 2244
Abstract
Transient global simulations were carried out to investigate the effect of argon flow on oxygen and carbon coupled transport in an industrial directional solidification furnace for quasi-single crystalline silicon ingots. Global calculation of impurity transport in the argon gas and silicon melt was [...] Read more.
Transient global simulations were carried out to investigate the effect of argon flow on oxygen and carbon coupled transport in an industrial directional solidification furnace for quasi-single crystalline silicon ingots. Global calculation of impurity transport in the argon gas and silicon melt was based on a fully coupled calculation of the thermal and flow fields. Numerical results show that the argon flow rate affects the flow intensity along the melt–gas surface, but has no significant effect on the flow patterns of silicon melt and argon gas above the melt–gas surface. It was found that the evaporation flux of SiO along the melt–gas surface decreases with the increasing argon flow rate during the solidification process. However, the net flux of oxygen atoms (SiO evaporation flux minus CO dissolution flux) away from the melt–gas surface increases with the increasing argon flow rate, leading to a decrease in the oxygen concentration in the grown ingot. The carbon concentration in the grown ingot shows an exponential decrease with the increase of the argon flow rate, owing to the fact that the dissolution flux of CO significantly decreases with the increasing argon flow rate. The numerical results agree well with the experimental measurements. Full article
(This article belongs to the Special Issue Modeling of Crystal Growth)
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Graphical abstract

9 pages, 3633 KiB  
Article
Control of Oxygen Impurities in a Continuous-Feeding Czochralski-Silicon Crystal Growth by the Double-Crucible Method
by Wenhan Zhao, Jiancheng Li and Lijun Liu
Crystals 2021, 11(3), 264; https://doi.org/10.3390/cryst11030264 - 08 Mar 2021
Cited by 13 | Viewed by 3397
Abstract
The continuous-feeding Czochralski method is a cost-effective method to grow single silicon crystals. An inner crucible is used to prevent the un-melted silicon feedstock from transferring to the melt-crystal interface in this method. A series of global simulations were carried out to investigate [...] Read more.
The continuous-feeding Czochralski method is a cost-effective method to grow single silicon crystals. An inner crucible is used to prevent the un-melted silicon feedstock from transferring to the melt-crystal interface in this method. A series of global simulations were carried out to investigate the impact of the inner crucible on the oxygen impurity distributions at the melt-crystal interface. The results indicate that, the inner crucible plays a more important role in affecting the O concentration at the melt-crystal interface than the outer crucible. It can prevent the oxygen impurities from being transported from the outer crucible wall effectively. Meanwhile, it also introduces as a new source of oxygen impurity in the melt, likely resulting in a high oxygen concentration zone under the melt-crystal interface. We proposed to enlarge the inner crucible diameter so that the oxygen concentration at the melt-crystal interface can be controlled at low levels. Full article
(This article belongs to the Special Issue Modeling of Crystal Growth)
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13 pages, 3714 KiB  
Article
Hydrodynamics and Mass Transfer during the Solution Growth of the K2(Co,Ni)(SO4)2•6H2O Mixed Crystals in the Shapers
by Anatoly I. Prostomolotov, Nataliya A. Verezub, Natalia A. Vasilyeva and Alexey E. Voloshin
Crystals 2020, 10(11), 982; https://doi.org/10.3390/cryst10110982 - 29 Oct 2020
Cited by 3 | Viewed by 1574
Abstract
Mathematical models of the hydrodynamics and mass transfer processes during the mixed crystal growth from low-temperature aqueous solutions have been analyzed. The features of these processes are caused by complex design of the crystallizer with a shaper. Two models of the solution flowing [...] Read more.
Mathematical models of the hydrodynamics and mass transfer processes during the mixed crystal growth from low-temperature aqueous solutions have been analyzed. The features of these processes are caused by complex design of the crystallizer with a shaper. Two models of the solution flowing into the shaper have been considered. In the first model, the solution is fed to the central part of the crystal. The second model presents a peripheral solution supply along the shaper perimeter, which allows us to create a swirling flow. The calculation models correspond to laminar and turbulent regimes of solution flow during the growth of K2(Co,Ni)(SO4)2•6H2O mixed crystal from an aqueous solution. Full article
(This article belongs to the Special Issue Modeling of Crystal Growth)
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