DOI:
10.1039/D5TA03784K
(Review Article)
J. Mater. Chem. A, 2025, Advance Article
The role of single-crystal substrates in synthesis of low-dimensional materials by CVD and their applications in electrocatalysis
Received
12th May 2025
, Accepted 13th August 2025
First published on 8th September 2025
Abstract
Single-crystal substrates have significant influence on the chemical vapor deposition (CVD) method for preparing low-dimensional materials. This review summarizes recent advancements in CVD synthesized low-dimensional materials using single-crystal substrates. First, growth parameters of the CVD growth process such as temperature, time, carrier gas flow, and substrate are introduced. In particular, the growth mechanism of CVD is explained to show the importance of single crystal substrates. Then, this review discusses in detail the important role of single-crystal substrates in the preparation of low-dimensional materials such as aligned CNT arrays, graphene nanoribbons, graphene films, hexagonal boron nitride (h-BN), and transition metal dichalcogenides (TMDCs). This is the key section that elaborates on the preparation methods of single-crystal substrate materials and their significant role in the growth of low-dimensional materials. Many research results have shown that the lattice structures of the substrates affect the growth direction, morphology, quality and properties of low-dimensional materials. In particular, the step structures of high-index single-crystal substrates are helpful to the study of growth mechanisms for low-dimensional materials. The growth mechanisms are of guiding significance for the large-scale synthesis and practical application of high-quality, single-crystal low-dimensional materials. Furthermore, this review summarizes the applications of low-dimensional materials in electrocatalysis to elucidate structure–function relationships in catalytic processes. The findings demonstrate that microenvironmental catalytic systems utilizing CVD-synthesized low-dimensional materials offer an optimal platform for probing catalytic behavior. Finally, the review discusses the potential and challenges of single-crystal substrates in the large-scale, low-cost preparation of high-quality low-dimensional materials. By developing the preparation techniques of single-crystal substrates and optimizing CVD growth parameters, it is expected to improve the application prospects of low-dimensional materials in electronics, optoelectronics, and energy conversion fields.
 Li Li | Li Li is a special-term associate research fellow at the Institute for Advanced Study, Chengdu University. She obtained her PhD in Condensed Matter Physics from the National Center for Nanoscience and Technology in 2018. After that, she was a Research Fellow at the Department of Chemistry, National University of Singapore (NUS). Subsequently, she served as an Assistant Research Fellow at the Suzhou Institute of Nano-Tech and Nano-Bionics (SINANO), Chinese Academy of Sciences (CAS). Her research focuses on controllable synthesis of low-dimensional materials via CVD, growth mechanism investigation, and performance modulation and device engineering in optoelectronics. |
 Jiaqi Chen | Jiaqi Chen received her PhD degree in Materials Science from the National Center for Nanoscience and Technology in 2020. On December 1st, she joined the Department of Materials Engineering, School of Mechanical Engineering, Chengdu University, as an associate professor. Her research interests include the thiolated ligand-regulated synthesis, mechanistic investigation, the optical and catalytic properties, and the related applications in biosensors of chiral plasmonic nanomaterials. |
 Tao Sun | Tao Sun is a full professor at the School of Chemical Engineering, Northwest University, China. His research focuses on the design of nanostructured materials applied in energy conversion technologies and pollutant degradation, such as fuel cells, water-splitting devices and metal–air batteries, as well as photocatalysis in hydrogen generation and pollutant decomposition. He has published over 100 high-profile SCI papers, and more than 50 papers as the first and corresponding author have been reported in high-level journals, such as Nature Nanotechnology, Advanced Materials, ACS Nano, ACS Catalysis, etc. Citations received are >7000, and his H-index = 38. He is also a youth editor in EcoEnergy, Advanced Powder Materials and Carbon Energy journals. |
1. Introduction
Low-dimensional materials are defined as materials confined in at least one spatial dimension (typically at the nanoscale), exhibiting quantum confinement effects in electrons or phonons due to reduced dimensionality. This dimensional constraint leads to fundamentally distinct mechanical, electronic, optical, and thermal properties compared to their bulk counterparts. Based on the degree of dimensional restriction, they are categorized into zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D) materials. Chemical vapor deposition (CVD) is one of the most common processes for thin films, wherein materials are synthesized by initiating chemical reactions in either gases or mixtures of gases on a heated surface.1–3 CVD has many advantages in the semiconductor industry and hence finds wide utilization in semiconductor processes and material surface treatments. Another material preparation method is physical vapor deposition, referred to as a physical coating technique under vacuum conditions, where the material source is vaporized into gaseous molecules or atoms, partially ionizes them into ions, and deposits a special functional thin film on the surface of the substrate through a low-pressure gas process.4 This review paper focuses on the CVD method for the preparation of low-dimensional materials. The CVD process has high coating uniformity. The growth controllability of low-dimensional materials can be effectively improved by regulating the growth conditions to obtain the low-dimensional materials with required specific properties. In addition to CVD growth conditions, there is an increasingly large number of research studies on the importance of the growth substrate. It not only provides a template for material growth but also acts as a catalyst, influencing the growth characteristics of the material.
The commonly used substrate materials for preparing low-dimensional materials fall into two categories according to their conductivity: insulating and metal substrates. The insulating substrates include silicon dioxide/silicon (SiO2/Si), sapphire, mica, h-BN, silicon nitride, quartz, aluminum nitride, etc.5–11 The SiO2/Si substrate is one of the most commonly used materials, especially in the semiconductor industry. Its advantages include excellent crystal quality, superior surface flatness, and exceptional stability.12,13 Working as a substrate materials, it has anti-high temperature, chemical corrosion, and mechanical stress. Good insulation performance is suitable for the substrate of electronic devices to prevent current leakage. The sapphire substrate has excellent optical performance and chemical stability, which can provide stable substrate conditions for low-dimensional materials.14–20 Moreover, the symmetry of sapphire substrates in different directions of cutting angles is different, which could facilitate regulating the material growth. Mica is a layered structured material, presenting excellent electrical insulation performance with low dielectric constant and low thermal expansion coefficient.21 In particular, the synthetic fluorophlogopite has excellent heat resistance, corrosion resistance, and chemical resistance, which is commonly applied to growing TMDCs as substrates.22 Metal substrates mainly include copper, nickel, gold, silver, germanium, molybdenum, ruthenium, platinum, cobalt, iridium, etc.23–35 The metal substrates can be used for thin film materials. For example, large-area and high-quality graphene films and h-BN films have been synthesized on copper foils and nickel films, which can be used as electrodes, functional materials, or dielectric materials in electronic devices and optoelectronic devices, etc.36–40 Additionally, high-index copper foil can also help elucidate the relationship between copper atomic configurations and electrocatalysis.41,42 Here, this review presents a general introduction to the role of single crystal substrates in the CVD growth of low-dimensional materials, further deepening the understanding of the importance of single crystal substrates (Fig. 1). Section 2 takes graphene as an example to show the CVD process and illustrate the growth mechanism in detail. In Section 3, application examples, namely aligned CNT arrays, graphene nanoribbons, graphene films, h-BN, and TMDCs, are introduced to show the effect of these single-crystal substrates (copper, gold, and Al2O3) on material growth. Section 4 summarizes the applications of low-dimensional materials in electrocatalysis. Finally, we discuss the future and challenges about the single crystal preparation and low-dimensional material synthesis, considering the practical applications of single crystal substrates.
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| Fig. 1 The preparation and applications of single crystals in the synthesis of low-dimensional materials. | |
2. CVD method
In addition to the top-down preparation method, the bottom-up preparation method is conducive to the controllable synthesis of large-area low-dimensional materials. For bottom-up synthesis, there are two vapor phase growth methods, physical vapor deposition (PVD) and chemical vapor deposition (CVD). In the process of vapor phase growth, first of all, by means of processes such as high-temperature sublimation, evaporation, sputtering, or decomposition, the desired crystal material is transformed from the bulk into the vapor phase. Under appropriate conditions, the crystal material is deposited onto a solid film. The film can either be single crystalline or non-single crystalline. PVD is a physical process where the source material is transferred to the substrate by vacuum evaporation or sputtering. Ultra-high vacuum conditions are essential in PVD. Metal films are commonly prepared by this method as well as the copper films deposited on sapphire or silicon substrates can be obtained by e-beam evaporation and magnetron sputtering.43,44 While CVD is the decomposition or reaction of gaseous precursors through a chemical reaction to form a solid film on a substrate. Gaseous precursors undergo surface-mediated chemical reactions on the substrate to deposit the target thin film materials.
Herein, we offer a comprehensive overview of the thermal chemical vapor deposition (CVD) method for growing low-dimensional materials, excluding plasma-enhanced CVD, photo-CVD, microwave plasma CVD, and metal–organic chemical vapor deposition (MOCVD). This discussion covers the process fundamentals, underlying principles, key advantages, and practical applications of conventional thermal CVD. Take the example of growing graphene on Cu(111) using the CVD method.45 Copper foil (Cu) is one of the most commonly used substrates for material preparation. The minimal carbon content in Cu enables precise control and high repeatability in graphene growth. And high-index copper foil as a substrate shows more possibilities in the epitaxial growth of graphene and other low-dimensional materials. The growth process is described as follows (Fig. 2a). First, the growth substrate (copper) is placed in the center of the furnace. Then, the quartz tube is vacuumed to remove air. The furnace starts to run heating program (Fig. 2b). And during the heating up process, the tube is filled with hydrogen and argon gas to protect copper from oxidation. Once the temperature reaches the growth temperature, hydrocarbon gases (such as methane, ethylene, or acetylene) are introduced into the CVD chamber to provide the carbon source for graphene nucleation and growth. The growth period finishes until the temperature control program is over. The heating procedure diagram is shown in Fig. 2c.
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| Fig. 2 Cartoon drawing of a CVD furnace from perspective (a) and sectional top views (b). (c) Heating program diagram of the furnace. | |
CVD involves chemical reactions and transport reactions of gaseous substances on a solid substrate, resulting in the deposition of materials.2 Taking the CVD growth of graphene on copper or dielectric substrates using methane as an example, the process can be roughly divided into three steps, as shown in Fig. 3.46 First, the gaseous reactants are transported to the surface of the substrate through the carrier gas flow (Fig. 3(i)). Then, these gaseous reactants will diffuse on the substrate surface and initiate nucleation once the critical concentration is reached (Fig. 3(ii)). This nucleation process is influenced by factors such as temperature, gas flow rate, and substrate properties.47 Once nucleation occurs, the carbon atoms continue to deposit and form graphene islands. These islands grow laterally across the substrate surface. As the graphene islands grow, they eventually coalesce to form a continuous graphene film (Fig. 3(iii)). Commonly, graphene islands merge and can form grain boundaries, which may affect the electrical and mechanical properties of graphene. One of the key research directions is to develop new methods and growth mechanisms to avoid grain boundary formation. Currently, there are two methods: one is to grow a single graphene sheet as large as possible and the other is to achieve seamless connections between multiple graphene grains through oriented growth.
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| Fig. 3 Schematic illustration of the CVD method taking the growth mechanism of graphene film as an example. The blue balls represent carbon atoms and the black balls represent hydrogen atoms. (i) Adsorption of precursors (methane) onto the substrate, followed by (ii) nucleation and (iii) growth of graphene. | |
During the material growth process, experimental parameters – including the amount of precursor, growth temperature, carrier gas flow rate, growth duration, substrate type, and chamber pressure – can be adjusted to effectively control the composition, morphology, crystal structure, and grain size of the thin film. This flexibility highlights the high controllability of CVD growth.48 Among them, it is worth noting that the substrate plays a significant role in the nucleation and growth of low-dimensional materials. First of all, the surface state of the substrate directly affects the nucleation and growth uniformity of low-dimensional materials. For example, the rough surface will lead to uneven nucleation, so electrochemical polishing or annealing treatment can optimize the surface of Cu substrates and improve the uniformity of graphene.49–52 Furthermore, the interactions between substrates and desired growth materials determine the growth modes and final structures of the films. For instance, Kaicheng et al. developed a facile method to grow large-area superclean graphene films. They identified the pretreatment of the copper substrates as a critical factor for improving the material's crystallinity and domain size.53 The growth behavior of low-dimensional materials is fundamentally determined by key surface structural characteristics, including surface symmetry, termination type, reconstructed step, and crystalline plane.
3. Low-dimensional material growth on single crystal substrates
In the following, we will introduce examples of how single-crystal substrates are used to prepare low-dimensional materials by the CVD method. The discussion will be structured according to the dimensional confinement of materials at the nanoscale, specifically into one-dimensional and two-dimensional materials.
3.1 1D materials
In 2005, single-walled carbon nanotubes (SWNTs) were successfully CVD grown on sapphire substrates using methane as the precursor, with the grown nanotubes exceeding 100 micrometers in length.54 Fig. 4a shows the surface structures of sapphire with the R-, A-, and C-face surfaces. The red and blue atoms indicate Al and O, respectively. Fig. 4b is the SEM image of SWNTs grown on the R-face sapphire substrate. The aligned SWNTs were guided by Al arrays due to the strong interaction between the Al atoms and nanotubes. Then, the atomic lattice-oriented growth (also named atomic arrangement-programed, AAP) and step-edge template growth were used to successfully grow aligned SWNTs on sapphire in 2007.55 The researchers found that there was a competition between two growth modes. The surface geometry of sapphire determines the choice of growth mode. As shown in Fig. 4c, the SWNTs are grown on the inclined sapphire surface in the presence of single-atomic and double-atomic steps. At single-atomic step heights, SWNTs follow the AAP growth mode, aligning perpendicular to copper step edges. For heights greater than a single atomic step, SWNTs grow parallel to the step edges via a step-templated mechanism. The lattice-oriented growth and step-templated growth of SWNTs co-occur at the edge of a sapphire substrate (Fig. 4d). It demonstrates that the SWNTs can align along specific crystal directions by means of the interaction forces between the nanotubes and the substrate. And this method does not require electric fields or rapidly flowing gases to align the nanotubes. It has low requirements for the growth equipment and low energy consumption, making it suitable for large-scale production. However, the step height variation has a significant impact on the growth mode of aligned SWNTs. Uneven height of the steps will result in uncontrollable density of the grown carbon tubes. Similarly, unidirectional graphene nanoribbons were grown on the (001) surface of transition metal germanium (Ge) using the CVD method (Fig. 4e).56 The miscut angle of a metal substrate refers to the slight inclination angle between the crystal surface and its ideal crystal planes (such as (001), (111), etc.). This tilt causes the formation of a periodically arranged terrace-step structure on the surface, thereby significantly influencing the morphology and atomic arrangement of the metal surface. The relationship between the step spacing (L) and the inclination angle can be described by the formula L = h/tan
θ, where h represents the height of a single step (that is the vertical distance between adjacent crystal planes). The larger the miscut angle (θ), the higher the density of surface steps. In the growth of graphene nanoribbons (GNRs) on Ge(001) substrates, a miscut angle of 12° leads to the synthesis of unidirectional GNRs aligned along a single orientation (Fig. 4f). In contrast, for substrates with smaller miscut angles (0°, 4°, and 8°), the GNRs adopt dual orientations – parallel and perpendicular to the miscut direction. Notably, as the miscut angle increases, the proportion of GNRs aligned perpendicular to the miscut direction becomes dominant. And based on the formula L = h/tan
θ, the larger the miscut angle (θ), the smaller the step spacing, meaning the higher the density of surface steps. Thus, the synthesis of unidirectional GNRs aligned along a single orientation on Ge(001) substrates with 12° miscut angle results from stepped substrates, which is similar to the growth of aligned SWNTs based on the step-templated mechanism. Yang et al. developed a universal synthesis strategy for fabricating unidirectionally aligned monolayer TMDC ribbons (including MoS2, WS2, MoSe2, WSe2, and MoSxSe2−x) by high-index Au facets as growth substrates.57 These monolayer TMDC ribbons follow step-edge-guided growth mode and can be merged to wafer-scale TMDC single crystals. This research not only deepens the understanding of the epitaxial growth mechanism but also opens up a new path for the single-crystal growth of 2D materials at the wafer scale.
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| Fig. 4 (a) Surface structures of sapphire (Al2O3) with the R-, A-, and C-face surfaces. Reproduced with permission.54 Copyright 2005 Elsevier B.V. (b) SEM images of SWNTs grown on the R-face sapphire substrate. Reproduced with permission.54 Copyright 2005 Elsevier B.V. (c) Schematic illustrations of the SWNTs grown on the inclined sapphire surface in the presence of single-atomic a and double-atomic b steps. Reproduced with permission.55 Copyright 2007 American Institute of Physics. (d) SEM image of the AAP growth and step-templated growth of SWNTs at the edge of a sapphire substrate. Reproduced with permission.55 Copyright 2007 American Institute of Physics. (e) AFM friction images of GNRs grown on vicinal Ge(001) surfaces with 0°, 4°, 8° and 12°, respectively. Reproduced with permission.56 Copyright 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (f) The change in the distribution ratio of GNRs as a function of miscut angle. Reproduced with permission.56 Copyright 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | |
3.2 2D materials
2D materials refer to atomically thin substances with lateral dimensions (in-plane) extensively exceeding their thickness (out-of-plane). In these materials, electrons are confined to move only within the 2D plane, while they are affected by the quantum confinement effect in the vertical direction, resulting in significantly different physical and chemical properties from three-dimensional bulk materials. Common two-dimensional materials include graphene, h-BN, and two-dimensional transition metal dichalcogenides (TMDCs), phosphorene, MXenes, and other elemental 2D materials. This section will classify and discuss the growth of graphene, h-BN, TMDCs, and vdW heterostructures on single-crystal substrates in detail.
There are two mainstream strategies to synthesize large-crystal 2D materials. One is based on an induvial nucleus and enlarge into a large-size domain. Another is a multinucleation strategy, which involves the alignment of nucleation domains and the seamless stitching of these domains into a continuous film. The primary strategy involves controlling the orientation alignment of multi-nucleation domains, as this method offers key advantages such as high production rate, high material quality, favorable controllability, and good compatibility with the integration process for future 2D electronic devices. Notably, single-crystal substrates have essential advantages in the growth of two-dimensional materials (such as sapphire, mica, Cu(111), etc.) since they can provide growth templates with atomically ordered lattice arrangements, guiding two-dimensional materials to nucleate along specific crystal directions through surface steps. Additionally, the matched lattice parameters help minimize interfacial strain, facilitating the directional merging of single-crystal domains and reducing the grain boundary defects.
3.2.1 Graphene. Monolayer graphene was fabricated in 2004 by Andre Geim and Konstantin Novoselov by using a mechanical exfoliation method.58 It ushered in the era of two-dimensional material research. Subsequently, single-layer graphene films were grown on 25-micron pieces of copper foil using the CVD method, in 2009, with a single-layer coverage exceeding 95%.59 This marked the beginning of using copper as a substrate for graphene growth. The CVD method for growing graphene on copper foil has become one of the most promising and widely used techniques for producing large-area, single-layer graphene films, owing to copper's low carbon solubility and excellent catalytic properties. Advances in graphene growth research revealed that the copper substrate's crystal structure critically influences graphene's growth orientation. For example, graphene grown on Cu(111) exhibits a single orientation, whereas graphene grown on Cu(100) displays a multidomain structure with two dominant orientations. This difference arises from the mismatch between the six-fold lattice symmetry of graphene and the four-fold lattice symmetry of Cu (Fig. 5).60 In addition, researchers found that graphene preferentially grew from the surface step edges onto the lower terraces of fcc and hcp metal surfaces. The findings indicate that an epitaxial lattice match between graphene and the metal step-edge enhances the stability of graphene and reduces the critical size required for graphene nucleation.61 And the local crystal structure of copper impacts the growth rate of graphene. At high temperatures, the copper surface reconstructs to form (n10) facets, which plays a role in directing the initial stages of graphene growth.62 Recognizing the strong correlation between graphene's growth direction and its interaction with the substrate, researchers have developed methods to produce highly oriented graphene using single-crystal copper substrates. In 2014, Jiwoong Park's group demonstrated that annealing copper at high temperatures (1030 °C) for extended periods (12 hours) could produce 16 cm-long single-crystal Cu(111), as shown in Fig. 5a.63 To confirm the successful preparation of Cu(111), electron backscatter diffraction (EBSD) maps were analyzed from three 200 × 200 μm2 regions across a 12 cm annealed copper foil. By using this substrate and optimizing growth parameters, they reduced the nucleation density and suppressed the bilayer growth, achieving continuous, large-area single-crystal graphene films (Fig. 5b). In recent years, there has been significant work using this strategy to prepare large-area, single-crystal graphene, continuously expanding the size of single-crystal Cu(111) and delving deeper into the mechanisms of its recrystallization. In 2017, Xu et al. achieved the preparation of (5 × 50) cm2 single-crystal Cu(111) using temperature-driven annealing techniques.37 On these substrates, they grew continuous graphene films with crystal domain orientations exceeding 99% within 20 minutes. This rapid process for producing quasi-single-crystal graphene films spanning tens of centimeters offers significant potential for the large-scale, cost-effective production of ultra-large, high-quality graphene films, opening new avenues for industrial applications.64 In 2018, Jin et al. conducted an in-depth study on the formation mechanism of single-crystal Cu(111).65 They prepared ultra-large single-crystal Cu(111) using a “contact-free annealing” method. The growth of large grains (up to 32 square centimeters) was achieved by minimizing contact stress, resulting in preferred in-plane and out-of-plane crystal orientations (Fig. 5c and d). The minimization of surface energy during the crystal lattice rotation process drives the preferred crystal orientation to “consume” adjacent grains, thereby achieving the growth of large single-crystal Cu(111). Transforming ordinary polycrystalline copper foil into single-crystal copper foil can be achieved not only through high-temperature annealing but also by using molten copper recrystallization methods. For example, Yunqi Liu's and Fuqiang Huang's research groups have reported using molten copper as a substrate to prepare highly oriented graphene domains, ultimately obtaining continuous single-crystal graphene films, as shown in Fig. 5e and fe.66,67
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| Fig. 5 (a) EBSD maps acquired from three 200 × 200 μm2 regions on a 12 cm piece of annealed Cu foil, illustrating the large-scale Cu alignment. Reproduced with permission.63 Copyright 2014 American Chemical Society. (b) Optical image of the post-annealed Cu foil (top) and the corresponding dark-field optical images of graphene grown on the foil (below), with green dotted lines marking the graphene edge orientations at the indicated locations. Reproduced with permission.63 Copyright 2014 American Chemical Society. (c) Schematic of the quartz holder to enable contact-free annealing of Cu foil. (d) Photograph of the annealed single-crystal Cu foil up to 32 square centimeters. Reproduced with permission.65 Copyright 2018 AAAS. (e) Schematic illustration of the growth procedure for a single-crystal graphene film by using resolidified copper foil on a molybdenum substrate. (f) SEM image of single-crystal graphene growth with 2 sccm CH4 for 3 min. Reproduced with permission.66 Copyright 2019 The Royal Society of Chemistry. | |
In addition to low-index single-crystal metals, recent years have seen increasing research on the preparation of large-size high-index single-crystal copper substrates. In 2020, Kaihui Liu's research group conducted an in-depth study on the preparation and formation mechanism of high-index single-crystal copper foil.24 They found that pre-oxidizing polycrystalline copper foil followed by high-temperature annealing in a reducing atmosphere enabled the growth of high-index copper foil. As shown in Fig. 6a, Cu(112) foil of 39 × 21 cm2 size was annealed from a piece of polycrystalline foil. However, the crystal plane characteristics of high-index copper foil were not fixed; the choice of crystal plane was randomly determined by the largest grain's crystal plane before annealing (Fig. 6b). Therefore, they developed a method for seed-controlled growth of high-index single-crystal copper foil, thereby achieving controllable preparation of large-size high-index single-crystal copper foil (Fig. 6c). Subsequently, Professor Zhongfan Liu's research group developed another method to prepare large-size high-index single-crystal copper foil based on the abnormal grain growth mechanism using strain, as shown in Fig. 6d.68 The specific growth behaviors of graphene were studied using this high-index single-crystal copper foil, deepening the understanding of its growth mechanism and simultaneously providing new preparation approaches and material bases for graphene's large-scale applications.
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| Fig. 6 Single crystal copper foil with high-index. (a) Optical image of a piece of single-crystal Cu(112) foil. Reproduced with permission.24 Copyright 2020 Springer Nature. (b) Optical image of the eight representative types of single-crystal Cu foil with a typical size of 35 × 21 cm2. Reproduced with permission.24 Copyright 2020 Springer Nature. (c) Photographs of the front surface of Cu foil after seed-guided annealing for 60 min and the back surfaces of Cu foil after seed-guided annealing for 60 min, 200 min, and 300 min, respectively. Reproduced with permission.24 Copyright 2020 Springer Nature. (d) Schematics of anomalous grain growth of Cu foil during annealing without (route I) and with (route II) contact with the susceptor, respectively. Photograph of the batch-transformed high-index Cu foil on graphite susceptors. Reproduced with permission.68 Copyright 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | |
Additionally, the formation of graphene with atypical geometries was observed on stepped surfaces of high-index single-crystal substrates. Yingying Zhang's research group discovered that pentagonal graphene grew on high-index Cu(114) surfaces (Fig. 7a).69 This occurred because the steps on the high-index copper surface promoted graphene growth perpendicular to these steps, causing one side of the hexagonal graphene to disappear and form a pentagon. Moreover, higher H2 partial pressure accelerated the anisotropic etching of graphene domains, promoting the formation of pentagonal graphene. The directional growth characteristic was found to be independent of the airflow direction. In addition, Li et al. found that there is hetero-epitaxial growth of graphene on several high-index copper surfaces, (Cu(234), Cu(455), Cu(326), and Cu(355)) as shown in Fig. 7b.70 The nucleation density of graphene on high-index copper is higher than that of Cu(111), which provides a fast way to grow high-quality graphene films. Specifically, high-index copper surfaces reconstructed to crystal faces with a larger inter-plane distance indicate the strong interaction between the copper substrate and graphene. The lattice structure of copper determines the growth mode of graphene, and the graphene growth process affects the lattice structure of copper in turn. The above studies further illustrate the significant impact of the substrate's lattice structure on the growth of two-dimensional materials. In addition to Cu, other metals such as Ni, Pt, Au, Al, Ga, Ge, Ag, Ir, and Ru have been employed for the growth of 2D materials. When assessing key performance indicators such as substrate affordability, resultant 2D material quality, and manufacturing scalability, copper demonstrates superior potential compared to alternative substrates.
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| Fig. 7 (a) Pentagonal graphene flakes grown on Cu(114). Reproduced with permission.69 Copyright 2016 Tsinghua University Press and Springer-Verlag Berlin Heidelberg. (b) SEM images of CVD graphene on copper foil with various crystallographic planes, such as Cu(234), Cu(455), Cu(326), Cu(355), and Cu(111), respectively. Reproduced with permission.70 Copyright 2021 IOP Publishing Ltd. | |
3.2.2 h-BN. h-BN has a hexagonal crystal structure formed by alternating nitrogen and boron atoms, similar to graphene. h-BN possesses excellent thermal conductivity, outstanding insulating properties, and chemical stability, making it highly promising for applications in the semiconductor industry.71 As early as 2011, the controlled preparation of large-size h-BN films was achieved by introducing AlN as a buffer layer on sapphire, paving the way for h-BN's applications in the electronics field.72 And then, Lu et al. developed a new strategy to grow large-area h-BN grains, where the synthesized single-crystal h-BN grains up to 7500 mm2 with a nucleation density of 60 per mm2 by using the Cu–Ni alloy as a catalytic substrate in the CVD process.73 As shown in Fig. 8a, the Cu–Ni alloy was prepared by annealing in H2 for 2 hours, and then ammonia borane was introduced into the tube as the precursor to initiate the nucleation of h-BN. The experiment demonstrated that incorporating 10 to 20% Ni in the Cu–Ni alloy can effectively reduce the nucleation density and improve the catalytic capacity of the substrate and promote the decomposition of the precursor. This work provides a deep understanding of h-BN nucleation and growth mechanisms. Sapphire is another substrate which is used for the epitaxial growth of h-BN. Vuong et al. systematically investigated the growth behavior of h-BN on different oriented sapphires, including a-, c-, and m-planes.74 Their findings revealed that the increased surface energy of m-plane sapphire, caused by its distinct atomic arrangement, led to misoriented h-BN growth. Tokarczyk et al. further studied the influence of the sapphire substrate off-cut angle on the graphene of h-BN. For off-cut angles larger than 0.3°, the crystal structure of the sapphire substrate no longer influenced the growth orientation of h-BN.75 Following the developmental trajectory observed in graphene growth, the objective for h-BN growth has evolved from pursuing large-area deposition to achieving large-area single-crystalline films. Chen et al. discovered a new, relatively inexpensive method for the large-scale production of h-BN films.36 They found the existence of top-layer Cu step edges solved the problem of twin boundary caused by the high symmetry of Cu(111). As shown in Fig. 8b, confining h-BN flakes in a unidirection was achieved. These step edges disrupted the symmetry of the Cu(111) surface, thereby suppressing the formation of twinned domains during growth. Then they showed how to prepare 2-inch h-BN films and transfer the synthesized films to new target substrates. They sputtered a 500 nm thick layer of copper and performed high-temperature annealing to obtain Cu(111)/sapphire, where 2-inch c-plane sapphire was used as a template. The 2-inch h-BN film was transferred onto another Si substrate by electrochemical delamination (Fig. 8c). In the same year, a 100 cm2 single-crystal hexagonal boron nitride monolayer on Cu(110) is based on epitaxial growth induced by the coupling of Cu〈211〉 step edges with h-BN edges.76 The interactions between the substrates and h-BN result in a mono-orientation alignment and seamless coalescence of h-BN domains into a continuous film with several centimeters in length (Fig. 8d). The 4 inch single-crystal h-BN film was successfully synthesized on Cu0.8Ni0.2(111)/sapphire wafers (Fig. 8e).23 This work further verifies the strong coupling between the substrate and h-BN, which is the key point for the wafer-scale.
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| Fig. 8 (a) Schematic illustration showing the procedure of h-BN growth by using the Cu–Ni alloy. Reproduced with permission.73 Copyright 2020 Springer Nature. (b) Optical image of unidirectionally aligned h-BN flakes on a single-crystalline Cu(111) film. Reproduced with permission.36 Copyright 2020 Springer Nature. (c) Process schematic for wafer-scale hexagonal boron nitride (h-BN) transfer via electrochemical polymer-assisted techniques. Reproduced with permission.36 Copyright 2020 Springer Nature. (d) SEM image of unidirectionally aligned h-BN domains grown on the Cu(110) substrate. Reproduced with permission.76 Copyright 2019 Springer Nature. (e) Schematic illustration of single-crystal h-BN growth on the Cu–Ni substrate. Reproduced with permission.23 Copyright 2024 Springer Nature. | |
3.2.3 TMDCs. TMDCs are layered materials consisting of transition metal atoms sandwiched between chalcogen atoms. TMDCs have attracted significant attention due to their potential applications in fields such as electronics and optoelectronics.77 MoS2 was the first material to be discovered and investigated. And how to synthesize large-scale, high-quality MoS2 films is the crucial point for practical application of materials. Guangyu Zhang's research group has achieved a great deal in this field. In 2015, they found that the introduction of oxygen during the CVD growth process could effectively reduce the nucleation density of MoS2, and the lateral size of the MoS2 domains was up to ∼350 μm, as shown in Fig. 9a.78 Then, batch fabrication of MoS2 films was done using the strategy of step engineering, where the commercial C-plane sapphire substrates with a miscut angle were annealed to produce atomically flat steps along the 〈11
0〉 direction (Fig. 9b).79 By utilizing these step edges, monolayer MoS2 was epitaxially grown on sapphire substrates (Fig. 9c).80 Recently, 2-inch and 8-inch single-crystal monolayer MoS2 were successfully synthesized on sapphire substrates.81,82 These large-scale high-quality MoS2 films were achieved by controlling the MoO3/S precursor ratio or by using a tailor-made vertical CVD system. The key point is that the interaction between sapphire substrates and MoS2 could induce a lattice alignment. However, these large-scale high-quality MoS2 films are not single crystal films in a true sense as antiparallel domain appearance leads to the twin boundaries. Besides sapphire, researchers found single-crystal gold as a good substrate to eliminate the evolution of antiparallel domains.83 It is also the steps on Au(111) that guide the nucleation of MoS2, which further leads to unidirectional growth of MoS2 along the 〈110〉 step edges (Fig. 9d).84 Researchers discovered that low-symmetry Au(101) can be the substrate for the epitaxial growth of MoS2 due to the perfect lattice constant alignment of MoS2 with Au(101) along the high-symmetry directions of the substrates.85 Beyond MoS2, Chen et al. also demonstrated the growth of highly oriented ReS2 on Au(111), where the alignment was governed by step edges along the [01(−)1(−)] crystallographic direction.86 While the step-directed growth mechanism is well recognized, alternative explanations for the growth dynamics have been proposed. Fu et al. reported that a single atomic plane configuration of c-plane sapphire is sufficient to facilitate the epitaxial growth of TMDCs, independent of step-edge aid. As shown in Fig. 9e, mono-oriented MoS2 flakes are grown on periodic, aligned step edges.87 Chen et al. demonstrated that the epitaxial alignment of MoS2 on sapphire arises from a van der Waals epitaxy mechanism, where a molecularly ordered MoO3 interlayer serves as the structural template.88 The presence of MoO3 enhances interfacial interactions and creates a distinctive atomic arrangement with 1-fold symmetry on the sapphire surface, promoting the unidirectional alignment of MoS2. With the development of scientific investigation, the synthesized types of TMDCs are expanding. For example, in 2015, it was discovered that aligned growth of 2D WSe2 could be successfully realized on sapphire substrates, guided by step edges on the sapphire surfaces.89 Another example is 2-inch single-crystal WS2 monolayer films on a-plane sapphire substrates, as shown in Fig. 9f.90 The interactions between the sapphire substrates and WS2 lead to parallel and antiparallel orientations of WS2 domains, and the interactions between sapphire step edges and WS2 avoid the appearance of WS2 nucleation with antiparallel orientation. Therefore, unidirectional aligned WS2 domains stitch into a continuous film. Later, a new approach was discovered to inhibit the formation of twin boundaries. The steps on the sapphire surface coupled with growth conditions could facilitate surface diffusion, lateral domain growth, and merging of the aligned domain structure. A fully covered monodirectional WS2 monolayer on a 2-inch c-plane sapphire substrate is shown in Fig. 9g.91 With the unremitting improvement and innovation of the synthesized method, the application prospect of TMDC materials in electronics, optoelectronics, and integrated circuits is more promising.
 |
| Fig. 9 (a) Optical images of 350 μm MoS2 grown on sapphire. Reproduced with permission.78 Copyright 2015 American Chemical Society. (b) Schematic illustration of the strategy of step engineering. Reproduced with permission.79 Copyright 2023 Tsinghua University Press. (c) Optical image of MoS2 domains grown on a C/A (αA = 0.89°) substrate. Reproduced with permission.80 Copyright 2024 Springer Nature. (d) Schematic illustration of the Au(111) formation and MoS2 growth process. Reproduced with permission.84 Copyright 2020 American Chemical Society. (e) Mono-oriented MoS2 flakes are distributed uniformly across the periodic and aligned step edges. Reproduced with permission.87 Copyright 2023 Springer Nature. (f) Photograph of a two-inch WS2 monolayer film on sapphire. Reproduced with permission.90 Copyright 2022 Springer Nature (g) False-colour SEM image of WS2 films after O2 etching. The etched holes have similar shapes and the same orientation. Reproduced with permission.90 Copyright 2023 Springer Nature. | |
The reports on CVD growth modes of low-dimensional materials on the single-crystal substrates are summarized in Table 1. The step-edge-guided growth mechanism is widely accepted as accounting for the oriented growth behavior observed in CNTs, graphene, h-BN, and TMDCs, fully exploiting the step characteristics of the single-crystal substrate material. In addition, AAP growth mode of CNTs presents the complexity and diversity of aligned growth behavior. Recent studies have revealed a novel growth mechanism for MoS2 synthesized on Al2O3 substrates. By precisely controlling growth parameters including the Mo
:
S precursor ratio and substrate–MoS2 interfacial interactions, researchers have demonstrated that these factors critically govern the aligned nucleation and subsequent growth of large-area, single-crystal MoS2 films. These findings significantly advance our theoretical understanding while establishing a robust framework for controllable fabrication of 2D materials.
Table 1 Summaries of modes of growth for low-dimensional materials on single-crystal substrates
Nature of substrates |
Low-dimensional materials |
Modes of growth |
Reference |
h-BN |
MoS2 |
Lattice alignment epitaxial growth mode |
10 |
c-Plane Al2O3 |
MoS2 |
Step-edge-guided growth |
14 |
a-Plane Al2O3 |
MoS2 |
Anisotropic MoS2–substrate interaction |
17 |
c-Plane Al2O3 |
MoS2 |
Epitaxial growth |
50 |
c-Plane Al2O3 |
MoS2 |
Step-edge-guided growth |
79 |
c-Plane Al2O3 |
MoS2 |
Step-edge-guided growth |
80 |
c-Plane cc |
MoS2 |
Step-edge-guided growth |
20 |
c-Plane Al2O3 |
MoS2 |
Controlling the MoO3/S precursor ratio |
82 |
Au(111) |
MoS2 |
Step-edge-guided growth |
84 |
Au(101) |
MoS2 |
Step-edge-guided growth |
85 |
c-Plane Al2O3 |
MoS2 |
Strong interactions |
87 |
α-Al2O3 |
MoS2 |
MoO3 interlayer |
88 |
High-index Au |
MoS2 nanoribbons |
Step-edge-guided growth |
57 |
c-Plane Al2O3 |
WSe2 |
Step-edge-guided growth |
89 |
a-Plane Al2O3 |
WS2 |
Dual-coupling-guided growth |
90 |
c-Pane Al2O3 |
WS2 |
Step-edge-guided growth |
91 |
Au(111) |
ReS2 |
Step-edge-guided growth |
86 |
Fluorphlogopite |
α-In2Se3 |
Quasi-equilibrium growth |
22 |
Cu0.8Ni0.2 |
hBN |
Strong interactions |
23 |
Cu(110) |
hBN |
Step-edge-guided growth |
76 |
Cu(111)/Al2O3 |
hBN |
Step-edge-guided growth |
36 |
Cu(111) |
hBN |
Step-edge-guided growth |
40 |
High-index Cu |
Graphene and hBN |
Epitaxial growth |
24 |
Liquid Cu/W |
Graphene |
Minimum energy |
67 |
High-index Cu |
Graphene |
Epitaxial growth |
68 |
High-index Cu |
Graphene |
Step-edge-guided growth |
69 |
High-index Cu |
Graphene |
Step-edge-guided growth |
70 |
Cu(111) |
Graphene |
Step-edge-guided growth |
37 |
Ge(001) |
Graphene nanoribbons |
Step-edge-guided growth |
56 |
r-, a-, and c-plane Al2O3 |
SWNTs |
AAP |
54 |
a-Plane Al2O3 |
SWNTs |
AAP and step-edge-guided growth |
55 |
Ag(111) |
Blue phosphorene |
Step-edge-guided growth |
81 |
4. Applications in electrocatalysis
Electrocatalysis is considered as one of the most promising solutions to the world's energy dilemma and environmental degradation. In energy conversion, low-dimensional materials have been extensively investigated as effective catalysts for hydrogen production.92–95 Compared to their bulk counterpart, low-dimensional materials possess more vacancy-type defects, topological defects, and exposed edges, facilitating the improvement of electrocatalytic performance.96,97 In addition, low-dimensional materials have shown many advantages and unique characteristics in the applications of electrocatalysis due to their variety richness, atomic-level thickness, high specific surface area, adjustable electronic structure, facile structural modification, and abundant active sites. Low-dimensional materials prepared by the hydrothermal method, solvothermal method, liquid exfoliation, electrochemical exfoliation, and so on have demonstrated excellent catalytic performance such as high catalytic activity, superior stability and selectivity.98–106 The wet chemical methods can produce low-dimensional materials with abundant catalytic sites in large quantities at a low cost, demonstrating better catalytic performance and practical applicability than that of CVD. Although the CVD low-dimensional materials possess fewer active sites, resulting in a lower catalytic efficiency, as model catalysts they can be used to investigate the catalytic behavior at the atomic level. For example, Liu et al. synthesized 1T′ MoS2 monolayers and 1T′/2H heterophase bilayers by the potassium-assisted CVD method.107 The introduction of potassium lowered the formation energy of 1T′ MoS2, leading to successful growth of 1T′ MoS2 monolayers with high phase purity. In particular, 1T′ MoS2 showed higher hydrogen evolution reaction (HER) performance than its 2H counterpart due to its metallic nature and increased catalytic active sites (Fig. 10a). Besides the 1T′ MoS2 monolayer, Yu et al. reported the CVD growth of 1T′ MoS2 and 1T′ MoSe2 bulk crystals and phase transformation from 1T′ MoS2 to 2H MoS2 achieved by laser irradiation (Fig. 10b).108 By means of the collimation of laser radiation, local phase patterning was carried out on a 1T′ MoS2 flake. And Raman and photoluminescence results proved the controlled phase transformation before and after laser irradiation. Furthermore, electrochemical microcells were fabricated to investigate the phase-dependent electrocatalysis. Consistent with the above experimental results, 1T′ MoS2 had excellent HER performance compared to 2H MoS2 due to the higher catalytic effect on the basal flake and better charge transport ability of 1T′ MoS2, which further proved the phase-dependent electrocatalysis of low-dimensional materials. In addition to phase, morphology also affects the catalytic efficiency. Yang et al. showed a general approach for CVD grown arrays of orientated monolayer TMDC ribbons on gold substrates with high-index facets.57 These unidirectional aligned MoS2 ribbons with straight edges were synthesized on Au(223) facets, following a step-edge-guided growth mechanism and stitched into a continuous MoS2 film. In order to demonstrate the influence of morphology on catalytic ability, the 1D monolayer MoS2 ribbons and 2D monolayer MoS2 flakes grown on Au/W substrates as HER electrocatalysts are explored (Fig. 10c). Thanks to more abundant active sites, 1D MoS2 ribbons showed better catalytic performance such as ∼194 mV overpotential and 56 mV dec−1 Tafel slope over 2D MoS2 flakes (∼220 mV overpotential and 71 mV dec−1 Tafel slope) (Fig. 10d). Similar strategies to single-atom catalysis, where metal is dispersed in the form of isolated single atoms on a low-dimensional material host, atomic-modified or defect-engineered two-dimensional materials can also enhance the catalytic efficiency. Duan et al. reported CVD grown Fe locally doped MoS2 monolayer with an in-plane heterostructure that functions as a bifunctional electrocatalyst for water splitting (Fig. 10e).109 As shown in Fig. 10f and g, the microelectrochemical cell based on Fe-doped MoS2 showed an overpotential of 351 mV in the HER and an overpotential of 220 mV in the OER (both at a current density of 10 mA cm−2), which benefited by defective MoS2 in the inside core region and the in-plane heterostructure with Fe-doping in the outside ring. Liu et al. synthesized a monolayer MoS2–MoS2xTe2(1−x) lateral heterostructure (LHS) with Mo vacancies and Te doping. On-chip electrochemical microcells based on MoS2, Mo-vacancy-deficient MoS2 (α), Mo-vacancy-rich MoS2 (β), and Mo-vacancy + Te-doped MoS2 (γ) were fabricated to investigate the structure–activity relationship between the material structure and catalytic performance (Fig. 10h). The results showed LHS achieving higher reaction kinetics than MoS2 (Fig. 10i–k). The creation of metal vacancies exposed additional unsaturated S atoms, enhancing proton adsorption, while Te doping adjusted the band alignment. Synergistic effects enable optimized HER performance with accelerated kinetics.110 Recently, entropy engineering is adopted in 2D monolayers via the CVD method. Jia et al. achieved epitaxial growth of 2-inch 1T′′ monolayer ReaWbMocIndSxSey. X-ray photoelectron spectroscopy, scanning transmission electron microscopy, energy dispersive X-ray spectroscopy and electron energy loss spectroscopy were used to characterize the atomic structure and chemical composition of this hexanary medium-entropy alloy monolayer. The uniform distribution of the six elements enabled ReaWbMocIndSxSey to achieve a wide-spectrum optical response (from the visible to NIR light). With the aid of optical sensitivity, on-chip electrochemical micro-devices based on ReaWbMocIndSxSey showed photo-enhanced electrocatalytic HER performance, where the alloy exhibited significantly reduced HER overpotentials, decreasing from 176.6 mV (dark) to 92.8 mV (1550 nm) and 43.7 mV (520 nm) at 10 mA cm−2. Correspondingly, the Tafel slopes change from 96.1 to 67.8 and 51.9 mV dec−1 (Fig. 10l and m). This study indicates that the rich defects of medium-entropy alloys imply more active sites, thus making it a way to enhance the electrocatalytic activity.111 In summary, the microenvironmental catalytic system based on CVD-synthesized TMDCs establishes an ideal model for investigating the relationship between catalytic behavior and its structure. This platform not only enables the systematic optimization of catalytic properties (activity/selectivity/stability) but also provides a critical theoretical understanding for mechanism-directed performance improvement.
 |
| Fig. 10 (a) Polarization curves and the corresponding Tafel plots of 1T′ and 2H MoS2 flakes grown on highly oriented pyrolytic graphite. Reproduced with permission.107 Copyright 2018 Springer Nature. (b) (b1) Schematic and photograph of the fabrication of an electrochemical microcell (EM-1, EM-2 and EM-3). (b2) Polarization curves obtained with EM-1, EM-2 and EM-3. (b3) Tafel plots obtained from the polarization curves in (b2). Reproduced with permission.108 Copyright 2018 Springer Nature. (c) Schematic illustration of the HER process of MoS2 ribbons. Reproduced with permission.57 Copyright 2022 Springer Nature. (d) Tafel plots of the as-grown monolayer MoS2 triangles and monolayer MoS2 ribbons on Au/W electrodes. Reproduced with permission.57 Copyright 2022 Springer Nature. (e) HER and OER activities of an Fe locally doped MoS2 monolayer. Their corresponding Tafel plots in the HER (f) and OER (g), respectively. Reproduced with permission.109 Copyright 2025 Youke Publishing Co., Ltd. (h) The schematic illustration of the structure diagram of the three regions (α, β, and γ) of the patterned defective LHS domain. (i–k) Linear sweep voltammograms and the corresponding Tafel slope diagrams comparing the electrochemical behavior of exposed graphene contact, pristine MoS2 and different regions of defect-patterned MoS2. Reproduced with permission.111 Copyright 2025 Wiley-VCH GmbH. (l and m) Polarization curves and (f) Tafel plots of ReS2 and the ReaWbMocIndSxSey alloy under different light conditions. Reproduced with permission.105 Copyright 2025 Wiley-VCH GmbH. | |
5. Summary and outlook
How to obtain large-area, high-quality single-crystal substrates is crucial for the growth of low-dimensional materials. In the past few years, greater attention has been focused on developing new methods for preparing large-area single-crystal substrates and leveraging their unique crystal surface morphology to enhance the growth quality of materials. However, certain issues still require further investigation and exploration. At present, the preparation of large-area single-crystal substrates is based on high temperature annealing or large-scale equipment, which means high cost or harsh preparation conditions. So, the lower cost of mass production of needed single-crystal substrates should be a priority with respect to energy consumption, which will ultimately redound to the advantage of the future industrial production of materials.
For the CVD growth of low-dimensional materials, single-crystal substrates can help reduce the appearance of grain boundaries and defects, thus improving the quality of synthesized materials. Meanwhile, single-crystal substrates usually have high purity, which helps to avoid impurity contamination during the CVD process, ensuring that the prepared materials have high purity and quality. The ultimate goal is to realize mono-orientation nucleation to control the morphology of synthesized materials. In particular, for the growth of large-area single crystal 2D materials, the strategy of stitching of unidirectional nuclei would reduce the growth time and energy as it grows concurrently into a continuous film. This would be the mainstream development direction of CVD growth of single-crystal two-dimensional materials with large area and high quality, satisfying industrial application.
Because of the complexity of the growth mechanism and the difficulty of direct observation about the effect of single-crystal substrates on the growth of low-dimensional materials, it mainly relies on theoretical calculation to explain the strong coupling between the substrates and the synthesized materials. We expect more efforts could be developed to guide the preparation of single-crystal substrates and the synthesis of low-dimensional materials. The gap between materials synthesis and industrial production could be solved in the future. In addition, microcells fabricated based on CVD low-dimensional materials provide an original platform to investigate the catalytic behavior at the atomic level. Microenvironmental catalysis can precisely control the local reaction environment, enabling synergistic optimization of catalytic activity, selectivity, and stability. This approach holds significant promise for application in energy catalysis and related fields.
Conflicts of interest
The authors declare no competing financial interest.
Data availability
The original contributions presented in this study are included in the article; further inquiries can be directed to the corresponding authors.
Acknowledgements
The National Natural Science Foundation of China (22378326), Basic Science Research Program of Shaanxi Basic Sciences Institute (Chemistry, Biology, 23JHQ081), Qin Chuangyuan project of Shaanxi Province (QCYRCXM-2022-213), Key Research and Development Program of Shaanxi Province (2024GX-YBXM-449) and Initial Scientific Research Fund of Northwest University (S. Tao) are acknowledged for the financial support of this work. The Initial Scientific Research Fund of Chengdu University (L. Li) provided financial support for this work.
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