thesis of crystal growth

• My Shodhganga
• Receive email updates
• Edit Profile

Shodhganga : a reservoir of Indian theses @ INFLIBNET

• Shodhganga@INFLIBNET
• Anna University
• Faculty of Science and Humanities

Items in Shodhganga are licensed under Creative Commons Licence Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Introduction to Crystal Growth Techniques

Related Papers

International Journal for Research in Applied Science & Engineering Technology (IJRASET)

IJRASET Publication

The crystal, with its regular atomic construction, is the most commonly encountered state of solid materials. In the earth's surface, crystals were grown by extreme conditions of high temperature, pressure and other environmental factors. To be specific each crystal starts small and grows as more atoms are added. Many grow from water rich in dissolved minerals, but they can also be grown from melted rock and even vapor. Under the influence of different temperatures and pressures, atoms combine in an amazing array of crystal shapes. The process can take as little as a few days to maybe a thousand years. Crystals that are found in Earth's crust are often formed in this manner. These crystals were formed over a million years ago inside the Earth's crust. They occurred when the liquid in the Earth consolidates. Crystals are not new to mankind, as they exist in the ancient period. Salt crystals were used in many cultures for food and other purposes. These salt crystals were grown by evaporating seawater in direct sun. In some cultures, pure salt crystals were used as currency and for trading as it was viewed as a precious resource. Some even waged wars against the salt accusation. The Ancient Egyptians used lapis lazuli, turquoise, carnelian, emerald, and clear quartz in their jewelry. They used some stones for protection and health, and some crystals for cosmetic purposes, like galena and/or malachite as eye shadow. Every part of the world considers Diamond, sapphire, and Ruby as a valuable resources. In India, the Mughals and other kingdoms used Diamond and Sapphire for exquisite ornaments and necklaces. This was the reason India was constantly colonized by the Mughals and by the British. India is the first country to open mines to produce diamonds. Probably the first reference to crystals in Ancient Rome was reported by Pliny the Elder (I Century AD) in his "Natural History", where he describes windows and greenhouses of the richer inhabitants of the Roman Empire being covered by crystals of "Lapis specularis", the Latin name for large transparent crystals of gypsum. This dehydrated form of calcium sulfate was extracted by Romans in Segóbriga (Spain) because of its crystal clarity, size (up to one meter), and perfect flatness. The German mathematician, astronomer, and astrologer Johannes Kepler (1571-1630) marveled when a snowflake landed on his coat showing its perfect six-cornered symmetry. In 1611 Kepler wrote" Six-cornered Snowflake" (Latin title" Strena Seu de Nive Sexangula") the first mathematical description of crystals. II. CRYSTALS IN MODERN ERA. We cannot think of a modern technology that would be half as good without the use of crystals. Crystals are the unacknowledged pillars of modern technology. Without crystals, there would be no electronic industry, no photonic industry, and no fiber-optic communications, which depend on materials/crystals in the field of semiconductors, superconductors, polarizers, transducers, radiation detectors, ultrasonic amplifiers, ferrites, magnetic garnets, solid-state lasers, non-linear optics, piezoelectric, electro-optic, acoustic-optic, photosensitive, refractory of different grades, crystalline films for microelectronics and computer industries. The list is almost endless. In the past few decades, there has been a growing interest in crystal growth, particularly given the increasing demand for materials for technological applications. Quartz crystals are one of the common components in devices like cell phones, television receivers, and, of course, watch and clocks. One of the main reasons quartz is used in so many electronic devices is because of its piezoelectric property. Garnet crystals are used to make sandpaper. Corundum crystals are used to make grinding wheels and durable sandpaper. Diamond crystals are used in rock-cutting drill bits and saws. Calcite crystals are ground up and used to make Tums and heated to make cement. Gypsum crystals are heated and powdered to make plaster. Halite (salt) crystals are used on food and in many industrial chemical processes. Magnetite and hematite crystals are iron ore. Ruby crystals were used in the earliest red lasers. Even in this modern civilized world ornaments such as Rings, necklaces, bracelets, and other cosmetic jewelry made from Diamond, Sapphire, and Ruby are crazed over and still regarded as a prized possession. But the slight twist is that now these crystals can be manmade and can be grown in Labs.

Journal of Crystal Growth

stanislav nikanorov

Acta Crystallographica Section A Foundations of Crystallography

Robert Heimann

Ian McDougall

Various methods of crystal growth are reviewed, considering solid, melt, solution, and vapor phase growth methods, as well as more exotic methods. The commonalities between the mechanisms of these different methods is also considered. Recent developments in the theory of near-equilibrium crystal growth are examined more in-depth, and an experiment is proposed towards an empirical understanding of the genesis of screw dislocations, integral to spiral growth patterns which predominate at near-equilibrium conditions. The experiment measures the formation of these dislocations in gold crystals grown from solution, on a substrate that has no initial dislocations. This is achieved by using a gold-functionalized Langmuir-Blodgett film for a substrate, as compared with a normal cloven gold substrate.

Hikmat Ahmed

Progress in Crystal Growth and Characterization of Materials

Keshra Sangwal

Journal of the Serbian Chemical Society

Aleksandar Golubovic

Springer Series in Materials Science

Jacob Greenberg

Canadian Metallurgical Quarterly

Chris Parfeniuk

RELATED PAPERS

Maricielo Qwistgaard Calle

Vitaly Chepel

Antonio Giarola

Journal of Nuclear Medicine

Anthony Walker

Wahana Forestra: Jurnal Kehutanan

Hery Kurniawan

arXiv: Combinatorics

Gabriela Araujo-pardo

The International Journal of Lower Extremity Wounds

Ruben Saurral

JOMAR CAMARINHA

amelia wallin

Diva Sascha

Antonella Muscella

luqman hakim abu hassan

Rozprawy Społeczne

Zofia Kubińska

Hans Brügelmann

Research, Society and Development

Gilson Alves Ribeiro

Politics of Quality in Education

Tuomas Takala

Andrea Menegotto

• Mathematics

Thrombosis Research

Else-marie Bladbjerg

pkl bandung

Andikaputra Pklbandung

Oncoimmunology

Xavier Calvo

HIP International

Prof. Dr. Burak Akan

Fordítástudomány

Péter Csatár

Biochemical Systematics and Ecology

Tzong-der Tzeng

Psychonomic Bulletin & Review

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Computer Science
• Academia ©2024

• < Previous

Home > Theses and Dissertations > 2641

Theses and Dissertations

Hydroflux synthesis: a new and effective technique for exploratory crystal growth.

Michael William Chance , University of South Carolina Follow

Date of Award

Document type.

Open Access Dissertation

Chemistry and Biochemistry

Sub-Department

First advisor.

Hans-Conrad zur Loye

Exploratory crystal growth is the best way to discover new phases with potentially improved properties or new crystal structures that could lead to new properties. As time goes on and researchers explore the synthetic techniques in the literature, diminishing returns will be met. Innovation in the synthetic tools used for synthesis is necessary to keep the field of materials chemistry advancing at its current pace and to allow us to reach more shallow minima of phase space. By combining wet hydroxide flux synthesis and hydrothermal synthesis, a hybrid technique for crystal growth has been created.

Using hydroxide hydrofluxes, a number of new materials have been synthesized and their relevant physical properties have been characterized. New oxides, hydroxides and oxyhydroxides incorporating transition metals in reduced states, manganese in highly oxidized states, rare earth ions, and iron in a new and unusual framework have been grown by this method. Crystal growth and physical properties of these systems are the focus of this dissertation. These investigations demonstrate the capabilities of hydroflux synthesis as a new route for exploratory synthesis.

© 2014, Michael William Chance

Recommended Citation

Chance, M. W.(2014). Hydroflux Synthesis: A New and Effective Technique for Exploratory Crystal Growth. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/2641

Since June 24, 2014

Included in

Chemistry Commons

Advanced Search

• Notify me via email or RSS
• Collections
• Disciplines

Submissions

• Give us Feedback
• University Libraries

Home | About | FAQ | My Account | Accessibility Statement

Privacy Copyright

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• My Account Login
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Review Article
• Open access
• Published: 24 January 2023

Research progress of large size SiC single crystal materials and devices

• Xiufang Chen 1 ,
• Xianglong Yang 1 ,
• Xuejian Xie 1 ,
• Yan Peng 1 ,
• Longfei Xiao 1 ,
• Chen Shao 1 ,
• Huadong Li 1 ,
• Xiaobo Hu 1 &
• Xiangang Xu 1  

Light: Science & Applications volume  12 , Article number:  28 ( 2023 ) Cite this article

7807 Accesses

12 Citations

2 Altmetric

Metrics details

• Electronics, photonics and device physics
• Photonic crystals

SiC semiconductor is the focus of recent international research. It is also an important raw material for China to achieve carbon emission peak and carbon neutrality. After nearly 20 years of research and development, we focus on the three types SiC crystals, n-type, p-type and semi-insulating, indicating the development of Shandong University for crystal growth. And defects control, electrical property, atomic polishing, and corresponding device authentication all obtain great progress. Total dislocation density of 6-inch n-type substrates decreases to 2307 cm −2 , where BPD (Basal Plane Dislocation) lowers to 333 cm −2 and TSD (Threading Screw Dislocation) 19 cm −2 . The full width at half maximum (FWHM) (0004) rocking curves is only 14.4 arcsec. The resistivity reaches more than 1E + 12 Ω·cm for semi-insulating SiC and lower than 20 mΩ·cm for n-type SiC. The impurity concentrations in 6-inch high-purity semi-insulating (HPSI) SiC crystals reach extreme low levels. The devices made of various substrate materials have good performance.

Similar content being viewed by others

High thermal conductivity in wafer-scale cubic silicon carbide crystals

Zhe Cheng, Jianbo Liang, … David G. Cahill

Carrier Depletion near the Grain Boundary of a SiC Bicrystal

Young-Wook Kim, Eita Tochigi, … Yuichi Ikuhara

Influence of Sr deficiency on structural and electrical properties of SrTiO3 thin films grown by metal–organic vapor phase epitaxy

Aykut Baki, Julian Stöver, … Jutta Schwarzkopf

Introduction

Silicon carbide (SiC) is a wide band gap semiconductor, and because of it has high thermal conductivity and excellent electronic properties, SiC is widely used in the manufacture of high-frequency, high-temperature, and high-power devices 1 , 2 . A key prerequisite for the fabrication of SiC devices is the availability of high-quality, polytypic stable and large diameter SiC substrate wafers 3 , 4 . Currently, the physical vapor transport (PVT) method is regarded as the most mature growth technique to obtain large SiC crystals.

The widespread use of n-type SiC is impeded by a relatively high dislocation density (about 10 3 –10 4  cm −2 ) in crystals used as substrates for the corresponding device structure 1 . So, the further decrease of extended defects, especially, dislocations in the crystal is crucial for improving device performance and reliability.

For semi-insulating crystals, it is very important to eliminate the foreign polytypes in the whole growth process, including nucleation and subsequent crystal growth, to further decrease defect density, otherwise, it can lead to serious quality degeneration in the field of nucleation of other defects. Also, it is imperative to remove basal plane bending and reduce the residual stresses.

Recently, p-type SiC has attracted extensive attention because of its application prospect in bipolar power and vertical electronic devices 1 . In high-voltage fields, gate turn off (GTO) thyristor and insulated gate bipolar transistor (IGBT)are mainstream devices owing to their lower dissipation 3 , 4 , 5 .

SiC semiconductor is the focus of recent international research. The research on SiC substrates in China has been carried out for 20 years, and realized industrialization. However, the cost of SiC substrates is still high. In addition, the low yield of SiC power devices is also an important constraint factor. Thus, the research and development of SiC materials and related devices have more work to do.

In this paper, we concentrate on the three types SiC crystals, n-type, p-type, and semi-insulating, indicating the development of Shandong University for crystal growth, defects and resistivity and corresponding device authentication. This work is supported by the State Key Laboratory of Crystal Materials and Institute of novel semiconductors. The research team actively cooperates with downstream industry or research institution to develop devices and applications, and makes contributions to the progress of SiC semiconductor in China.

N-type SiC growth and dislocation

In the past few years, the rapid development of SiC crystal PVT growth technology has facilitated the commercial application of high-quality, micropipe-free 4-inch SiC substrates 1 , 2 . However, a large number of crystallographic defects, such as stacking faults and dislocations, still exist in ordinary commercial SiC single crystals 3 . Therefore, it is very important to reduce the dislocation density because it degrades the performance and long-term reliability of the device.

6-inch nitrogen doping, low resistivity 4H-SiC crystals were grown by PVT on the C-face of 4H-SiC. By optimizing the structure design and improving the temperature distribution, and based on the growth mechanism of SiC vicinal face, the low resistivity 4H-SiC single crystals with low micropipe density, stable polytype, and high structure quality were grown in the temperature field with small radial gradient. The morphology and polytype distribution of 4H-SiC crystals were investigated by Micro-Raman spectroscopy and lext-3D measuring laser microscope. It was considered that there were two types of foreign polytype transitions in the growth of 4H-SiC crystals. A polytype transition interface existed at the beginning of step, which was related to the growth mechanism of step flow. By decreasing the crystal growth rate at the beginning of step, the generation of such polymorphisms could be controlled effectively. Another polytype transition interface existed in the late growth stage 4 , which was related to the temperature rise of the growth front. This polymorphism could be effectively reduced by lowering the temperature.

6-inch n-type SiC ingot

Xianglong Yang et al. reported that the use of off-axis seeds in PVT growth of 4H-SiC could change the growth mechanism 5 . By observing the surface morphology of SiC single crystals grown from off-axis seeds, two growth models were proposed, one was the spiral growth induced by screw dislocation and the other was the step flow growth induced by atomic steps 5 . By adjusting the thermal field, the formation and migration of facets could be controlled. The 6-inch n-type SiC ingot is shown in Fig. 1 , the substrate after CMP processing (Fig. 2 ), the micropipe density is lower than 0.1 cm −2 (Fig. 3 ), and 4H polytype occupies 100%. The FWHM of (0004) rocking curves is only 14.4 arcsec. The resistivity is 20 mΩ·cm with the nitrogen doping inhomogeneity <2%. The LTV distribution of 6-inch n-type SiC substrate is shown in Fig. 4 , and LTV max in the range of 10 mm × 10 mm is 0.546 μm.

6-inch n-type SiC wafer

The micropipe distribution of 6-inch n-type SiC substrate (only one micropipe)

The LTV distribution of 6-inch n-type SiC substrate

In order to reduce the dislocation density, Xianglong Yang and Xiufang Chen et al. reported the lateral growth on patterned seeds and removed the subsurface damage of seeds, respectively 6 , 7 . Growth of SiC on {11–20} and {1–100} surfaces of 6H-SiC seeds by PVT method was carried out at 1700–2000 °C. The anisotropy of growth rates along different crystal directions was studied. In transverse growth, the rate in <11–20> direction was the higher, followed by <1–100> direction. The lateral growth rate could be further increased by increasing the growth temperature and decreasing the reactor pressure. In addition, compared with vertical growth, the dislocation density of channels decreased significantly during transverse growth, which proved the possibility of reduction of the dislocation density of channels 6 . 6H-SiC crystals were grown on seeds treated by different methods by PVT method. The effects of surface state and subsurface damage on the dislocation density of SiC crystals were analyzed. The dislocation density of crystals grown on seeds treated with hydrogen etching was one order of magnitude lower than that grown on seeds treated with mechanical polishing. It was considered that hydrogen etching could completely eliminate the subsurface damage of seeds 7 .

The dislocation density in the different stage of growth

The dislocation distribution of the whole SiC wafer was obtained by scanning the SiC wafers etched by molten KOH. The dislocation distribution of SiC wafers was studied by special dislocation detector at different growth stages. The scanning etched mapping of the dislocation detector could fully display the dislocation etch pit information. According to the shape and size of the etch pits, three types of threading dislocations were identified. The dislocation detector was used to study the dislocation density and distribution of 6-inch n-type 4H-SiC crystal at different growth stages. The results show that the dislocation density decreases gradually with the growth of crystal. The total dislocation density of the wafer in the later stage of growth is reduced significantly than that in the early stage of growth, as shown in Fig. 6 . TED (Threading Edge Dislocation) occupies the largest proportion in the wafer 8 . TSD and BPD exist a small proportion in the wafer, and the density gradually decreases (Fig. 5 ). Total dislocation density of 6-inch n-type substrates decrease to 2307 cm −2 , where BPD lowers to 333 cm −2 and TSD 19 cm −2 (Fig. 6 ). It is helpful to feed back the information of the propagation and transformation characteristics of dislocation defects during the SiC crystal growth process 8 .

The dislocation distribution of 6-inch n-type SiC substrate

Cui Yingxin analyzed the effects of different nitrogen doping concentrations on lattice parameters and resistivity of 4H-SiC 9 . The structure of 4H-SiC was studied by high resolution X-ray diffractometer (HRXRD), and the lattice constants of 4H-SiC single crystals were determined. The resistivity value was tested by a non-contact resistivity testing system. It was concluded that the c - and a - lattice constants of 4H-SiC decreased, the hexagonality increased, and the resistivity decreased with the increase of nitrogen doping concentration 9 .

P-type SiC doping characteristic

The switching speed of n-channel IGBT is faster than that of p-channel IGBT has been proved by theoretical simulation 10 , 11 . N-channel SiC Based IGBT devices is considered to be one of the most promising electronic devices, because it has low resistance features in the high-voltage field because of the conductance modulation. In order to manufacture high capability n-channel IGBT, p-type SiC substrates are needed as the injector region 12 , 13 , 14 .

2-inch p-type 4H-SiC crystals were grown by Al doping and conventional PVT method. And the N concentration in SiC was about 5E + 17 cm −3 as the background 15 . The interrelations of Al element dopants on resistivity and polytype were studied. The results showed that the Al atoms could be effectively incorporated into 4H-SiC crystals as well as the color of Al-doped SiC crystal was blue. With the increase of Al content in 4H-SiC single crystals, the color of Al-doped crystal became darker and eventually opaque. The mechanism of transparent crystal color development is that the crystal absorbs some wavelengths of light for atomic transition, and the remaining unabsorbed light is transmitted to show the color of the crystal. The band gap width of intrinsic 4H-SiC is 3.26 eV. Visible light >380 nm can be transmitted, and ultraviolet light <380 nm can be absorbed. A small amount of Al impurities will introduce an acceptor level of 0.19 eV into 4H-SiC, which will fully absorb the wavelength above 1500 nm and below 380 nm, and partially absorbs the light in the range of 380–1500 nm. However, with the increase of doping concentration, the discrete Al impurity energy levels are split into energy bands, the range of light being fully absorbed moves to low wavelengths (that is, the wavelength of light being fully absorbed changes from more than 1500 nm to more than 600 nm, or even smaller), and the rest of the partially absorbed light (mainly blue light with a wavelength rang of 435–480 nm) is also absorbed enhanced. Finally, the transmittance of light decreases, and the crystal appears opaque. Under the condition of heavy Al doping, the polytype of 4H-SiC was unstable and 6H-SiC polytype appeared. N is the donor for doping SiC and substitutes the C lattice sites of SiC. B is the acceptor for SiC doping and occupies Si/C lattice sites. Al is the acceptor for SiC doping and occupies Si lattice sites. The atomic radii of N and B are both smaller than that of Si, and the incorporation into the crystal will lead to lattice contraction. The atomic radius of Al is larger than that of Si, and the incorporation into the crystal will lead to lattice expansion. When N or B is doped into SiC crystal, it has the effect of neutralizing the lattice expansion caused by Al atoms and stabilizing the atomic arrangement order of the crystal. Therefore, on the premise of ensuring the crystal quality, the doping concentration of Al element can be increased and the crystal resistivity can be reduced. In order to eliminate the polytype of 6H, Al-N co-doping was carried out. And results showed the polytype of p-type 4H-SiC single crystals returned to be stable 15 . However, owing to the difficulty in effectively to command the release of Al, Al-N co-doped 4H-SiC turned to n-p-n type. It was difficult to keep the high quality and low resistivity at the same time. Noncontact resistivity measurement showed p-type 4H-SiC wafers has the minimum resistivity of about 4 Ω·cm 15 , this resistivity value was a little high.

In order to continue to reduce the resistivity, p-type 4H-SiC crystals were grown by using Al-B co-doping technique, reported by Xuejian Xie et al. 16 . By adjusting the doping ratio of Al and B, p-type 4H-SiC single crystal without 6H polytypes were obtained. Similar to Al-N co-doping, the Al-B co-doping method also introduced small lattice distortion to 4H-SiC, which promoted the stabilization of the 4H-SiC polytype. Because the B element was the acceptor atom, and different from N element with donor atom, thus the lower resistivity was realized. The lowest resistivity of p-type 4H-SiC achieved 0.495 Ω·cm, in this case the doping concentration of Al and B were 2E + 19 cm −3 , 4.7E + 17 cm −3 , respectively 16 . To achieve lower resistivity, the Al and B concentrations should continue to be optimized, and the background N impurities should be minimized. The Al-B co-doping technique paved a new way for growing high-quality and low-resistivity p-type 4H-SiC, and played an important role in the development of high-voltage power electronic devices 16 . However, because of the memory effect of B element, it was still to develop and optimize the release of Al to obtain the high uniformity and low resistivity. According to the above proposal, 4-inch p-type SiC single crystals were grown with Al-B co-doping technique. Raman spectroscopy mapping test showed that p-type SiC was entirely 4H-SiC and no others polytype. The FWHM of (0004) X-ray rocking curve was <30 arcsec, implying the high crystalline quality of p-type 4H-SiC. Resistivity mapping results showed that the resistivity deviation of the obtained p-type SiC substrates was 23.51%, and the lowest resistivity achieved 0.30 Ω·cm 16 .

Because devices manufactured on p-type SiC substrates are usually power electronic devices with high current densities, it is significant to study the lattice vibration properties to help enhance the reliability of devices 17 . The Raman spectra of p-type 6H-SiC with different Al doping concentrations were investigated in the temperature range of 203–653 K 18 . Results exhibited all Raman peaks showed redshift and broadened with temperature rising. The E2(low) as well as E2(high) modes were smaller correlation on the Al doping contents, while A1(LO) mode exhibited a strong correlation of Al doping contents 18 . And the different characteristics of A1(LO) mode from E2(low) and E2(high) modes in heavily Al doped 6H-SiC showed that the A1(LO) mode was dominated by the thermal expansion and anharmonic effect as well as the acceptor ionization effect. Compared to other phonon modes of Raman spectra, the A1(LO) lifetime was more sensitive to the Al concentration and the intensity decreased with the increasing temperature 18 .

Semi-insulating SiC growth, stresses, and electrical properties

Due to the lack of large-size and high-quality homogeneous GaN substrates, sapphire, SiC, Si, and other foreign substrates are widely used in GaN-based HEMTs (High Electron Mobility Transistor) 19 , 20 . Among them, semi-insulated SiC is still the best choice for substrate due to its high thermal conductivity, high resistivity, and maturity in mass production of 6-inch large wafers 21 , 22 . For semi-insulating SiC, the polytype, basal plane bending, residual stress, and resistivity are main problems that need to be solved.

Yang Xianglong et al. used PVT method to grow 4H-SiC on on-axis seeds and analyzed the formation and transformation of polytype during the growth process 23 . It was found that at the initial stage of growth, heterogeneous nucleation occurred easily due to the high supersaturation in the periphery of the crystal plane, because the transverse growth of the 4H region could not extend to the periphery of the crystal plane. As the growth progressed, 4H-SiC in the central region became dominant and expanded to the edge, and the extraneous polytypes overlapped with 4H-SiC in the central region and gradually covered it 23 .

The effect of seed mounting methods on the bending degree of the basal plane in 4H-SiC grown by PVT method was analyzed by HRXRD 24 . The bending degree of the basal plane of the crystals grown by seeds in the open state was obviously better than the closed state. It was suggested that high-quality crystals could be grown from low-quality seeds by optimizing growth conditions 24 . Combined with the corrosion results of molten KOH, the effects of macroscopic shear stress and structural defects caused by the difference of thermal expansion coefficient between SiC seeds and graphite holder on the bending of 4H-SiC single crystal basal plane were discussed. The influence mechanism of dislocations was also discussed 24 .

The residual stresses in 4H-SiC bulk crystals were investigated by neutron diffraction method in three orthogonal directions (<0001>, <11–20> and <1–100>), and the stress and strain were quantitatively calculated by using Bragg equation and Hooke’s law 25 . The strain ranged from 10 −4 to 10 −3 along these three directions, while the stress was anisotropic. The stress along <0001> direction was compressive stress at the secondary flat side, and tensile stress on the opposite side. Along the direction <11–20>, the stress was compressive and relatively uniform, ranging from −763 to −490 MPa. However, along the direction <1–100>, the stress was tensile stress, and the stress gradient from the primary flat side to opposite side was as high as 17 MPa mm −1 , and the stress range was 673–2953 MPa. Therefore, it was considered that the crystal was prone to cracking in this direction 25 . It was proposed that the crystal with lower growth rate had less stress. Moreover, once stress was generated at the nucleation stage, it was inherited during subsequent growth 25 .

6-inch HPSI SiC crystals were obtained by above optimizing temperature field eliminating 6H or 15R polytype, improving seed crystal fixation and reducing residual stress. The HPSI SiC substrates are shown in Fig. 7 . The micropipe density by optical microscope is reduced lower than 0.5 cm −2 (Fig. 8 ), and 4H crystal type ratio is 100%. The results of (0004) rocking curves indicate high crystalline quality and virtually flat basal planes, the FWHM of the whole wafer is uniform, except one dot is slightly higher, as shown in Fig. 9 . The resistivity reaches more than 1E + 12 Ω·cm in the whole wafer area (Fig. 10 ). The impurity concentrations in 6-inch HPSI SiC crystals are as follows at the stage of growth process (Table 1 ).

6-inch HPSI SiC substrates

The micropipe distribution of 6-inch HPSI SiC substrate (only two micropipes)

The FWHM distribution of 6-inch HPSI SiC substrate

The resistivity distribution of 6-inch HPSI SiC substrate

Epitaxial growth and device results

AlGaN/GaN HEMTs have many excellent properties, such as large band gap energy, high electron saturation rate, high critical electric field strength, and the sheet charge density at the interface is high due to the large offset and strong polarization effect of the conductive band. Therefore, AlGaN/GaN HEMTs have great application prospects in high-power microwave devices and high-frequency devices 26 , 27 . AlGaN/GaN with high electron mobility was grown by metal-organic chemical vapor deposition (MOCVD) method on 4-inch semi-insulating 4H-SiC substrates 28 . X-band microwave power high electron mobility transistors were made. The hall mobility was 2291.1 cm 2 /(V·s), and the two-dimensional electron gas density was 9.954E + 12 cm −2 at 300 K. The maximum drain current density was 1039.6 mA/mm and the peak external transconductance was 229.7 mS/mm for the HEMT device with a gate length of 0.45 μm. The f T and f max values measured on the device were 30.89 GHz and 38.71 GHz. Uncooled devices showed high linear power gain of 17.04 dB and high power-added-efficiency of 50.56% at 8 GHz with drain bias (−3.5,28) V. In addition, when the drain bias was (−3.5,40) V, the saturation output power density was 6.21 W/mm, and the power-added efficiency was 39.56% and the power gain reached to 11.91 dB 28 .

In 2018, Shandong University made photoconductive switch by the same electrode with the HPSI 4H-SiC. The conduction resistance was <1 Ω, when the triggering wavelength was 355 nm, the triggering energy was 10 mJ, and the bias voltage was 6 kV 29 . In the same year, China Academy of Engineering Physics in cooperation with Shandong University, prepared a 4H-SiC photoconductive switch and discovered a microwave oscillation phenomenon with an oscillation frequency of 1 GHz 30 . This was the first time that the microwave oscillation caused by the characteristics of the material itself was found based on the SiC photoconductive switch.

Semi-insulating SiC could be used for other devices, such as UV optoelectronic devices 31 , GaN-based long wavelength light-emitting diodes 32 . Graphene was grown on semi-insulating 4H-SiC (0001) by thermal decomposition 33 , 34 , 35 , 36 . Graphene could effectively reduce the biaxial stress of GaN films, and the strain relaxation could improve the incorporation of indium atoms in InGaN/GaN multi-quantum wells (MQWS), resulting in a significant red-shift in the emission wavelength of InGaN/GaN MQWS 32 .

The I-V characteristics of typical Schottky Barrier Diodes (SBDs) lie in its lower forward voltage drop and reverse leakage current, as well as its better temperature performance. Standard 600 V SiC SBD (Schottky Barrier Diode) epitaxial process was performed on Epi-Ready N-type 4H-SiC substrates 37 . The specific structure was 0.5 μm thick N-type buffer layer with a doping concentration of 1E + 18 cm −3 , and 6.0 μm thick N-type drift layer with a doping concentration of 1E + 16 cm −3 . The surface roughness RMS was only 0.258 nm. A 600 V/50 A SiC Schottky diode with a single chip area of 4.2 mm × 4.2 mm was developed. When the conduction current was 50 A, the forward voltage was 1.9 V, and the reverse voltage was 600 V, the leakage current was <50 μA. The DC performance of the device closed to that of the imported substrate 37 .

After nearly 20 years of research and development, 6-inch high quality n-type and semi-insulating SiC crystals and 4-inch p-type SiC crystals were grown. Total dislocation density of 6-inch n-type substrates decreased to 2307 cm −2 , where BPD lowered to 333 cm −2 , the FWHM of (0004) rocking curves was only 14.4 arcsec. The micropipe density of 6-inch n-type and semi-insulating SiC crystals decreased to <0.5 cm −2 . The resistivity reached more than 1E + 12 Ω·cm for semi-insulating SiC and lower than 20 mΩ·cm for n-type SiC. The impurity concentrations in 6-inch HPSI SiC crystals were reduced to extreme levels. The HEMT devices made from semi-insulating SiC substrates exhibited a saturation output power density up to 6.21 W/mm at 8 GHz, with a power gain of 11.91 dB and a power-added efficiency of 39.56%. The photoconductive switch made from HPSI 4H-SiC demonstrated good performance indicators. Standard 600 V SiC SBD fabricated with n-type SiC substrates exhibited good performance. Semi-insulating SiC could be used for UV optoelectronic devices and GaN-based long wavelength light-emitting diodes.

Casady, J. B. & Johnson, R. W. Status of Silicon Carbide (SiC) as a wide-bandgap semiconductor for high-temperature applications: a review. Solid-State Electron. 39 , 1409–1422 (1996).

Article   ADS   Google Scholar  

Mueller, S. G. et al. The status of SiC bulk growth from an industrial point of view. J. Cryst. Growth 211 , 325–332 (2000).

Helava, H. I. et al. Growth of low-defect SiC and AlN crystals in refractory metal crucibles. Mater. Sci. Forum 742 , 85–90 (2013).

Article   Google Scholar  

Hu, G. et al. Formation Mechanism of Two Types of Polytype Transformation in off-axis 4H-SiC Boules. 2021 18th China International Forum on Solid State Lighting & 2021 7th International Forum on Wide Bandgap Semiconductors (SSLChina: IFWS), 74–77 (2021).

Yang, X. et al. Physical vapor transport growth of 4H-SiC on {000-1} vicinal surfaces. Trans. Tech. Publ. 821-823 , 68–72 (2015).

Google Scholar  

Xianglong, Y. et al. Growth of SiC single crystals on patterned seeds by a sublimation method. J. Cryst. Growth 439 , 7–12 (2016).

Chen, X. et al. Reduction of dislocation density of SiC crystals grown on seeds after H 2 etching. Mater. Sci. Forum 897 , 19–23 (2017).

YIN, P. et al. Dislocation distribution in SiC wafers studied by lattice distortion detector. J. Synth. Cryst. 50 , 19–23 (2021).

Cui, Y. et al. Influence of nitrogen concentrations on the lattice constants and resistivities of\\r, n\\r, -type 4H-SiC single crystals. Cryst. Growth Des. 15 , 3131–3136 (2015).

Wang, X. & Cooper, J. A. High-voltage n-channel IGBTs on free-standing 4H-SiC epilayers. IEEE Trans. Electron Devices 57 , 511–515 (2010).

Sui, Y., Walden, G. G., Wang, X. K. & Cooper, J. A. Device options and design considerations for high-Vvoltage (10-20 kV) SiC power switching devices. Mater. Sci. Forum, 527-529 , 1449–1452 (2006).

Sauvik, et al. 4H-SiC n-channel insulated gate bipolar transistors on (0001) and (000-1) oriented free-standing n(-) substrates. IEEE Electron Device Lett. 37 , 317–320 (2016).

Matsuura, H. et al. Dependence of conduction mechanisms in heavily Al-doped 4H-SiC epilayers on Al concentration. Appl. Phys. Express 11 , 101302.1–101302.5 (2018).

Shirai, T., Danno, K., Seki, A., Sakamoto, H. & Bessho, T. Solution growth of p-Type 4H-SiC bulk crystals with low resistivity. Mater. Sci. Forum 778-780 , 75–78 (2014).

Xie, X. et al. Growth and electrical characterization of Al-N Co-doping SiC single crystals. China International Forum on Solid State Lighting: International Forum on Wide Bandgap Semiconductors China , 136–139 (2017).

Xie, X. et al. Sublimation growth and property characterization of p-type 4H-SiC by Al B co-doping technique. Scr. Materialia 167 , 76–80 (2019).

I. Ahmad, V. et al. Self-heating study of an AlGaN/GaN-based heterostructure field effect transistor using ultraviolet micro-Raman scattering. Appl. Phys. Lett. 86 , 173503–173503 (2005).

Wang, R. et al. Anharmonic effect on first-order Raman modes of p-type 6H-SiC single crystals. J. Alloys Compounds 691 , 1033–1039 (2017).

Wang, X. et al. MOCVD-grown AlGaN/AlN/GaN HEMT structure with high mobility gan thin layer as channel on SiC. Chin. J. Semiconductors 27 , 1521–1525 (2006).

ADS   Google Scholar  

Fletcher, A., Nirmal, D., Ajayan, J. & Arivazhagan, L. An intensive study on assorted substrates suitable for high JFOM AlGaN/GaN HEMT. Silicon 3 , 1591–1598 (2021).

Gao, Y. et al. 150 mm 4H-SiC substrate with low defect density. Mater. Sci. Forum 858 , 41–44 (2016).

Jang, B. K., Park, J. H., Choi, J. W., Yang, E. & Lee, W. J. Modified hot-zone design of growth cell for reducing the warpage of 6”-SiC wafer. Mater. Sci. Forum 1004 , 32–36 (2020).

Xianglong, Y. et al. 2019 16th China International Forum on Solid State Lighting & 2019 International Forum on Wide Bandgap Semiconductors China (SSLChina: IFWS) (2019).

Yang, X. et al. Basal plane bending of 4H-SiC single crystals grown by sublimation method with different seed attachment methods. CrystEngComm 20 , 6957–6962 (2018).

Xie, X. et al. Characterization of the three-dimensional residual stress distribution in SiC bulk crystals by neutron diffraction. CrystEngComm 19 , 6527–6532 (2017).

Ambacher, O. et al. Two-dimensional electron gases induced by spontaneous and piezoelectric polarization in undoped. J. Appl. Phys. 87 , 334–344 (2000).

Jain, S. C., Willander, M., Narayan, J. & Overstraeten, R. V. Iii–nitrides: growth, characterization, and properties. J. Appl. Phys. 87 , 965–1006 (2000).

Wang, Q. et al. Fabrication and characterization of AlGaN/GaN HEMTs with high power gain and efficiency at 8 GHZ. J. Semiconductors 42 , 8 (2021).

Xiao, L. et al. Effect of electron avalanche breakdown on a high-purity semi-insulating 4H-SiC photoconductive semiconductor switch under intrinsic absorption. Appl. Opt. 57 , 2804–2808 (2018).

Luan, C. et al. A new phenomenon in semi-insulating 4H-SiC photoconductive semiconductor switches. IEEE Trans. Electron Devices 65 , 172–175 (2018).

Ywa, C. et al. Flexible graphene-assisted van der waals epitaxy growth of crack-free AlN epilayer on SiC by lattice engineering. Appl. Surface Sci. 520 , 146358 (2020).

Yu, Y. et al. Demonstration of epitaxial growth of strain-relaxed GaN films on graphene/SiC substrates for long wavelength light-emitting diodes. Light Sci. Appl. 10 , 8 (2021).

Sun, L. et al. The effect of the surface energy and structure of the SiC substrate on epitaxial graphene growth. Rsc Adv. 10 , 1039.C6RA21858J (2016).

Yu, W., Chen, X., Hu, X. & Xu, X. Wafer-scale graphene on 4-inch SiC. Mater. Sci. Forum 858 , 1133–1136 (2016).

Zhang, F. et al. High mobility and large domain decoupled epitaxial graphene on SiC (0001¯) surface obtained by nearly balanced hydrogen etching. Mater. Lett. 195 , 82–85 (2017).

Yu, C. et al. Uniform coverage of quasi-free standing monolayer graphene on SiC by hydrogen intercalation. J. Mater. Sci.: Mater. Electron. 28 , 3884–3890 (2017).

Yang, X. et al. Growth and device application of high quality N-type SiC single crystals. J. Synth. Cryst. 44 , 1427–1431 (2015).

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant No. 52022052 and No. 51902182, the Shandong Province Natural Science Foundation of China under grant No. ZR2019JQ01, ZR2019BEM030 and ZR2019BEM011, Key R & D project of Shandong Province under grant No. 2019JMRH0901and 2019JMRH0201.

Author information

Authors and affiliations.

State Key Laboratory of Crystal Materials, Institute of novel semiconductors, Shandong University, Jinan, 250100, China

Xiufang Chen, Xianglong Yang, Xuejian Xie, Yan Peng, Longfei Xiao, Chen Shao, Huadong Li, Xiaobo Hu & Xiangang Xu

You can also search for this author in PubMed   Google Scholar

Corresponding authors

Correspondence to Xianglong Yang or Xiangang Xu .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Chen, X., Yang, X., Xie, X. et al. Research progress of large size SiC single crystal materials and devices. Light Sci Appl 12 , 28 (2023). https://doi.org/10.1038/s41377-022-01037-7

Download citation

Received : 02 April 2022

Revised : 16 September 2022

Accepted : 09 November 2022

Published : 24 January 2023

DOI : https://doi.org/10.1038/s41377-022-01037-7

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Mathematical Modeling of Czochralski Type Growth Processes for Semiconductor Bulk Single Crystals

• Published: 22 July 2012
• Volume 80 , pages 311–332, ( 2012 )

Cite this article

• W. Dreyer 1 ,
• P. -É. Druet 1 ,
• O. Klein 1 &
• J. Sprekels 1  

416 Accesses

5 Citations

Explore all metrics

This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e. g., silicon (Si) or gallium arsenide (GaAs) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Modeling Semiconductor Crystal Growth Under Electromagnetic Fields

A model for crystal growth of solid solutions in the inas–gaas system by a modified floating-zone technique.

Z. A. Agamaliyev, M. A. Ramazanov & G. Kh. Azhdarov

Modeling of the effect of the presence of a free surface on transport structures and mixing during the dissolution process of silicon into germanium melt

Farid Mechighel, Neil Armour & Sadik Dost

Bossavit A.: Electromagnétisme en vue de la Modélisation. Springer, Berlin-Heidelberg- New York (2004)

Google Scholar  

E. Bänsch. Simulation of instationary, incompressible flows , Acta Mathematica Universitatis Comenianae, vol. LXVII (1998), pp. 101 –114.

S. Clain, J. Rappaz, and M. Swierkosz, Coupling between nonlinear Maxwell and heat equations for an induction heating problem: Modeling and numerical methods , Krizek, M. (ed.) et al., Finite element methods. 50 years of the Courant element. Conference held at the Univ. of Jyvaeskylae, Finland, 1993. New York, NY: Marcel Dekker, Inc. Lect. Notes Pure Appl. Math. 164, 163-171 (1994).

Druet P.-É.: Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right-hand side in L p . Math. Meth. Appl. Sci. 32 , 135–166 (2008)

Article   MathSciNet   Google Scholar  

P.-É. Druet, Existence of weak solutions to the time-dependent MHD equations coupled to the heat equation with nonlocal radiation boundary conditions , Nonlin. Anal. RWA 10 (2009), 2914–2936.

P.-É. Druet, Analysis of a coupled system of partial differential equations modeling the interaction between melt flow, global heat transfer and applied magnetic fields in crystal growth , PhD Thesis, Humboldt-Universität zu Berlin, 2009.

Druet P.-É.: Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects. Cz. Math. J. 59 , 791–825 (2009)

Article   MathSciNet   MATH   Google Scholar  

P.-É. Druet, Weak solutions to a model for crystal growth from the melt in changing magnetic fields , in: (K. Kunisch, G. Leugering, J. Sprekels and F. Tröltzsch, eds.), ”Optimal Control of Coupled Systems of PDE”, International Series of Numerical Mathematics 158 (2009), Basel, Birkhäuser, 123–137.

P.-É. Druet, Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary p-summable right-hand side , Appl. of Math. 55 (2010), 111–149.

P.-É. Druet, O. Klein, J. Sprekels, F. Tröltzsch, and I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects , SIAM J. Control Optim. 49 (2011), 1707–1736.

Druet P.-É., Philip P.: Noncompactness of integral operators modeling diffuse-gray radiation in polyhedral and transient settings, Integr. Equ. Oper. Theory 69 , 101–111 (2011)

C. Frank-Rotsch, et al. Vorrichtung und Verfahren zur Herstellung von Kristallen aus elektrisch leitenden Schmelzen (Device and method for producing crystals from electroconductive melt) , July, 17th, 2009, Patentschrift (patent specification) of granted german patent 10 2007 028 548, German Patent and Trade Mark Office, December, 21st, 2011, patent specification of granted european patent EP 2 162 571 B1, European Patent Office.

J. Fuhrmann, T. Koprucki, and H. Langmach, pdelib: An open modular toolbox for the numerical solution of partial differential equations. design patterns , In W. Hackbusch and G. Wittum, Editors, Proceedings of the 14th GAMM Seminar on Concepts of Numerical Software (University of Kiel, 2001), pp. 121 – 132.

O. Klein, P. Philip, and J. Sprekels, Modelling and simulation of sublimation growth in SiC bulk single crystals , Interfaces Free Bound. 6 (2004), 295–314.

O. Klein, Ch. Lechner, P.-É. Druet, P. Philip, J. Sprekels, Ch. Frank-Rotsch, F. M. Kiesling, W. Miller, U. Rehse, and P. Rudolph, Numerical simulation of Czochralski crystal growth under the influence of a traveling magnetic field generated by an internal heater-magnet module (HMM) , J. Crystal Growth 310 (2008), 1523–1532.

O. Klein, C. Lechner, P.-É. Druet, P. Philip, J. Sprekels, C. Frank-Rotsch, F.-M. Kießling, W. Miller, U. Rehse, P. Rudolph, Numerical simulations of the influence of a traveling magnetic field, generated by an internal heater-magnet module, on liquid encapsulated Czochralski crystal growth , Magnetohydrodynamics 45 (2009), 557–567.

O. Klein, P. Philip, Correct voltage distribution for axisymmetric sinusoidal modeling of induction heating with prescribed current, voltage, or power , IEEE Transactions on Magnetics 38 (2002), 1519–1523.

Klein O., Philip P.: Transient conductive-radiative heat transfer: Discrete existence and uniqueness for a finite volume scheme, Math. Models Methods Appl. Sci. 15 , 227–258 (2005)

M. Laitinen, T. Tiihonen, Conductive-radiative heat transfer in grey materials , Quart. Appl. Math. 59 (2001), 737–768.

C. Lechner, O. Klein, P.-É. Druet, Development of a software for the numerical simulation of VCz growth under the influence of a traveling magnetic field , J. Crystal Growth 303 (2007), 161–164.

C. Meyer, P. Philip, and F. Tröltzsch, Optimal control of a semilinear PDE with nonlocal radiation interface conditions , SIAM J. Control Optim. 45 (2006), 699–721.

C. Meyer and I. Yousept, Regularization of state-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions , SIAM J. Control Optim. 48 (2009), 734–755.

J. Rappaz and M. Swierkosz, Modelling in numerical simulation of electromagnetic heating , Modelling and optimization of distributed parameter systems (Warsaw, 1995), Chapman & Hall, New York, 1996, 313–320,

Rudolph P.: Travelling magnetic fields applied to bulk crystal growth from the melt:The step from basic research to industrial scale, J. Crystal Growth 310 , 1298–1306 (2008)

Article   Google Scholar  

P. Rudolph, Ch. Frank-Rotsch, F.-M. Kiessling, W. Miller, U. Rehse, O. Klein, Ch. Lechner, J. Sprekels, B. Nacke, H. Kasjanov, P. Lange, M. Ziem, B. Lux, M. Czupalla, O. Root, V. Trautmann, G. Bethin, Crystal growth in heater-magnet modules – From concept to use , in: (E. Braake, B. Nacke, eds.), ”Proceedings of the International Scientific Colloquium Modelling for Electromagnetic Processing (MEP2008), Hannover, October 26-29, 2008”, Leibniz University of Hannover (2008), 26–29.

O. Schenk and K. Gärtner, Solving unsymmetric sparse systems of linear equations with pardiso . Journal of Future Generation Computer Systems 20 (2004), no. 3, pp. 475–487.

J. Shewchuk. Triangle: Engineering a 2d quality mesh generator and delaunay triangulator. In First Workshop on Applied Computational Geometry (Philadelphia, Pennsylvania ) (ACM, 1996), pp. 124–133.

Download references

Author information

Authors and affiliations.

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

W. Dreyer, P. -É. Druet, O. Klein & J. Sprekels

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to W. Dreyer .

Rights and permissions

Reprints and permissions

About this article

Dreyer, W., Druet, P.É., Klein, O. et al. Mathematical Modeling of Czochralski Type Growth Processes for Semiconductor Bulk Single Crystals. Milan J. Math. 80 , 311–332 (2012). https://doi.org/10.1007/s00032-012-0184-9

Download citation

Received : 21 February 2012

Published : 22 July 2012

Issue Date : December 2012

DOI : https://doi.org/10.1007/s00032-012-0184-9

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Mathematics Subject Classification (2010)

• Czochralski method
• crystal growth
• traveling magnetic fields
• radiative heat transfer
• nonlinear PDE systems
• Navier-Stokes equations
• MHD equations
• Maxwell’s equations
• well-posedness
• optimal control
• first-order necessary optimality conditions
• numerical simulation
• Find a journal
• Publish with us
• Track your research

Physical Chemistry Chemical Physics

Phase field crystal modeling of graphene/hexagonal boron nitride interfaces.

Two-dimensional (2D) materials such as graphene and hexagonal boron nitride (h-BN) are an important class of materials that have enhanced structural and electronic properties in comparison to their bulk counterparts. The phase field crystal (PFC) model can reach diffusive time scales (relevant e.g. in nucleation and growth of crystallites, relaxation of strain-driven 2D monolayers, and thermal conduction) that are much larger in comparison to molecular dynamics (MD) and quantum mechanical density functional theory (QMDFT) methods while retaining atomic resolution. The model also incorporates an atomic length scale and elastic and plastic deformations in a natural manner. We simulate the morphological transition of the crystal growth of various equilibrium crystal shape. In this work, we generalize the one-mode PFC model to study graphene/h-BN interface heterostructure by using the conserved dynamics to describe the dynamics of the model. The model was used to find the equilibrium shape of crystal of the h-BN crystal embedded in a graphene monolayer.

Supplementary files

• Supplementary information PDF (156K)
• Supplementary information PDF (14824K)

Article information

Download citation, permissions.

S. S. channe, Phys. Chem. Chem. Phys. , 2024, Accepted Manuscript , DOI: 10.1039/D3CP05265F

To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page .

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page .

Read more about how to correctly acknowledge RSC content .

Social activity

Search articles by author.

This article has not yet been cited.

Advertisements

• Share full article

Advertisement

Supported by

A Critical Eye

Watch Fair Opens in a Time of Uncertainty

Brands hope the new models unveiled at Watches and Wonders Geneva will attract buyers despite the tough retail climate.

By Robin Swithinbank

Just what sort of shape is the luxury watch industry in?

Globally, the sector has been stuttering as political and economic uncertainty persists (hasn’t it always?), while reports from the front line of luxury watch retail suggest that times are tougher now that the Covid-era bounce has bottomed out.

And yet last year, Swiss watchmakers reported record export values — again. Watches and Wonders Geneva, the world’s premier luxury watch show, opens today and typically is a fair barometer of the industry climate, even though most of the big releases will have been dreamed up some years ago.

Many of the big players will be there, including Rolex, Cartier and Patek Philippe, while others, including Omega and Audemars Piguet, continue to stay away. Yet the event now has more than 50 exhibitors for the first time, including eight new names. Here are some of the showstoppers landing in Geneva.

At the Top of the Hour

One trend that shows no signs of slowing is the high-end watchmakers’ enthusiasm for the “low volume, high value” business model. Brands have logged that the industry’s growth point is at the top end as wealthy clients continue to spend big, so it comes as little surprise that Watches and Wonders booths are awash with hyperwatches stretching the limits of micromechanics, design and aesthetics (as well as price) to spectacular new heights.

Piaget Altiplano Ultimate Concept Tourbillon

After a brief hiatus, the battle for the thinness crown has resumed. Bulgari this week introduced what it called the world’s thinnest mechanical watch, a seemingly impossible 1.7-millimeter sliver of mechanical ingenuity. That was followed almost immediately by Piaget, in its 150th anniversary year, issuing what it identified as the world’s thinnest tourbillon: the Altiplano Ultimate Concept Tourbillon, which at two millimeters all but sucks the third dimension out of the whirring anti-gravitational tourbillon device so loved by elite watchmakers. Six years ago, the original Altiplano Ultimate Concept slipped into the record books at two millimeters (the obsession with that measurement started in 1957 with the 9P caliber, which was two millimeters). But it contained neither the tourbillon cage that surrounds the watch’s oscillating escapement nor the 30 percent additional power required to fuel it. Somehow, Piaget has squeezed those into the new watch’s 41.5-millimeter blue cobalt alloy case without fattening it up. A watch that will be remembered long after the fair doors have closed.

Estimated at $650,000

IWC Portugieser Eternal Calendar

The luxury watch industry continually touts the fact that mechanical watches will significantly outlast their quartz and “smart” cousins, as long as they are well maintained. This year, IWC is stretching that maxim with the Portugieser Eternal Calendar, a watch said to indicate the correct date until the year 3999 without adjustment, even accounting for the vagaries of the 400-year leap-year cycle. Added to that, its moon-phase indication is said to be accurate to one day every 45 million years, a figure so intergalactic it barely registers. Why “only” to the year 3999? Because those who decide such things have yet to determine whether 4000 will be a leap year or not. One for the grandchildren to the power of 100 to worry about. Despite its time-bending complexity, the Eternal Calendar sits inside a very modest 44.4-millimeter platinum Portugieser case and has just one crown to adjust its legion time and date displays.

TAG Heuer Monaco Split-Seconds Chronograph

TAG Heuer’s early 21st-century flirtations with haute horlogerie produced some memorable watches that were not always mechanically infallible. The madcap belt-driven Monaco V4 and the Carrera Mikrogirder, with its exposed linear coupling beam, spring to mind. But the watchmaker best known for its consumer-favorite Carrera and Monaco chronographs insists that its latest venture into high-end complications is no hurried concept, but rather heralds a new era of experimental fine watchmaking. The new watch’s signature function is its rattrapante, or split-seconds chronograph, which can time two events that start simultaneously but finish independently, such as two cars in a race. It is powered by a new movement — cast in titanium and produced in collaboration with the specialist Vaucher Manufacture Fleurier — said to be TAG Heuer’s lightest automatic chronograph movement, at 85 grams (slightly less than three ounces). Wrapped in a 41-millimeter version of the Monaco’s square case that is half grade 5 titanium and half sapphire crystal, the model is available in either red or blue colorways.

A. Lange & Söhne Datograph Perpetual Tourbillon Honeygold “Lumen”

This year marks the 25th anniversary of Lange’s highly collectible Datograph and to celebrate, the German maker has thrown the kitchen sink at this new model. The spec sheet lists a revamped in-house movement offering a flyback chronograph (which requires the single push of a button to stop, zip back to zero and restart), a perpetual calendar that adjusts for leap years and a tourbillon with Lange’s celebrated stop-seconds mechanism, all gathered around the brand’s hallmark oversize date window. For the first time, the Datograph case has been cast in Lange’s patented warm Honeygold and a translucent dial features elements finished in what the company calls Lumen, or luminous detailing. Just a run of 50 for this new model.

Price on application

In the Eye of the Beholder

Following the fashion world, some in watchmaking have moved away from gendered watches — for fear of alienating men who might choose to wear women’s smaller watches as much as women who might choose men’s larger ones. But some brands are staying the course, saying that reports indicate that many women still want watches designed with their tastes and wrist shapes in mind.

When Hermès released its H08 model in 2021, it tiptoed around the description. Was it a sports watch? Yes, it was sporty, but not strictly a sports watch because that might involve sweating. Either way, the H08 drove sales and in its wake comes another sports watch of sorts, this time unequivocally labeled feminine. Named Cut, for the polished slices taken from the flanks of its case, the 36-millimeter model has a shape that defies conventional description, a bespoke typeface on the dial and elegant echoes of its shape artfully woven into the design of, for example, its numerals. Pure Hermès, and another hit in the making.

Van Cleef & Arpels Lady Arpels Brise d’Été

The latest twinkle-toe circus act watch to emerge from Van Cleef’s ateliers is another mechanical marvel, this time an automaton that springs into life at the push of the button found between 7 and 8 o’clock. Two plique-à-jour enamel butterflies then flit around the dial to indicate the time, while background flowers in bluish vallonné enamel sway as if caught in the wind. The look is enhanced with precious stones and materials and métiers d’art decoration. Another Van Cleef spectacle.

Estimated at $177,000

Chopard Impériale

Daintiness, exquisite artisanry and the promise of a handsome mechanical movement have become the trademarks of Chopard’s women’s watches, thanks in no small part to the influence of the winsome Impériale collection. In its latest guise, the Impériale is sugarcoated in white gold and diamonds, and displays a deep blue-green enamel dial overlaid with a raised lattice that is decorated with pink and white enamel flowers set with diamonds and rare pinkish Padparadscha sapphires. Behind it, naturally, a slim-line Chopard automatic movement.

Oris Aquis Date 36.50 mm Upcycle

It seems unreasonable to say that a brand entering its 120th year is punching above its weight, but Oris remains an outlier in an industry dominated by groups and privately owned superbrands. The independent has reworked its Aquis collection of sporty, dive-ready, relatively inexpensive mechanical watches this year, so that it now includes this women’s design, complete with a slinky H-shape bracelet and a pared-back bezel design. The Upcycle part of the name refers to the dial, said to be cut from sheets of recycled PET (polyethylene terephthalate) plastic that is unique in every watch.

On Another Level

Of the eight brand newcomers to Watches and Wonders this year, five are exhibiting in a new area of the show called La Mezzanine, half a floor above the mainstays. Up the same flight of stairs is the British brand Bremont, returning to a Swiss fair for the first time in years under Davide Cerrato, its new chief executive who is a former Tudor and Montblanc man.

Bremont Terra Nova 38

Mr. Cerrato joined Bremont almost a year ago but waited until now to introduce a new logo, new branding and a new product line, based on three product categories: air, land and sea. Of equal note is that, unlike many of his industry peers, he has reduced Bremont’s entry-level price in a bid to capture a market all but abandoned by many establishment players. The hardy Terra Nova 38 field watch embodies all this, coming in at a price that might grab the attention of at least one of Cerrato’s former employers, both of which compete in this price segment.

Gerard Charles Masterlink

Bringing a watch to market is said to take years, and in this case it has. Despite its familiar blueprint of a stainless steel sports watch with an integrated bracelet, the new Masterlink was conceived almost four years ago by Octavio Garcia, Gerald Charles’s experienced creative director. It is an evolution of the brand’s Maestro model, which the legendary watch designer and company founder Gerald Genta created almost two decades ago. The new design keeps the “smile” at 6 o’clock, but it spreads it to the bracelet, exaggerating the watch’s asymmetry.

Norqain Wild ONE of 1

For all the talk of how much watch buyers want personalization , Swiss watch brands have been reluctant to offer customized watches in large volumes, leaving the niche to third parties that charge hefty premiums for their services. All the more remarkable then that the company set to offer a possible 3.5 million iterations of the same watch is Norqain, the six-year-old independent. Buyers using an online configurator will be invited to fiddle to their hearts’ content and, once the order is placed, wait a brief-ish three months for their Wild ONE of 1 to arrive.

From $17,600

Nomos Glashütte Tangente 38 Datum Sportbunt 175 Years

A decade or so ago, much of the watch industry’s oxygen was created by a cohort of so-called accessible luxury brands that were making mechanical watches priced in the low thousands, even hundreds, of dollars. Inflation and premiumization, a focus on high-end products, have stunted that movement, taking with them some of the glow attached to the German watchmaker Nomos Glashütte. That always seemed a shame. Nomos’s minimalist designs, beautiful in-house movements and Berlin-infused creativity gave it a place. Its watch fair return is therefore welcome, as is this colorful expression of its signature Tangente, one of 31 iterations landing this week, each in a run of 175 pieces to mark 175 years of watchmaking in the German town of Glashütte .