A detailed review of the literature for the last 5-10 years on epitaxial growth of graphene is presented. Both experimental and theoretical aspects related to growth on transition metals and on silicon carbide are thoroughly reviewed. Thermodynamic and kinetic aspects of growth on all these materials, where possible, are discussed. To make this text useful for a wider audience, a range of important experimental techniques that have been used over the last decade to grow (e.g. CVD, TPG and segregation) and characterize (STM, LEEM, etc.) graphene are reviewed, and a critical survey of the most important theoretical techniques is given. Finally, we critically discuss various unsolved problems related to growth and its mechanism which we believe require proper attention in future research.
The complete mechanism behind the thermal decomposition of ethylene (C 2 H 4 ) on Ir(111), which is the first step of graphene growth, is established for the first time employing a combination of experimental and theoretical methods. High-resolution x-ray photoelectron spectroscopy was employed, along with calculations of core level binding-energies, to identify the surface species and their evolution as the surface temperature is increased. To understand the experimental results, we have developed a reaction sequence between the various C n H m species, from ethylene to C monomers and dimers, based on ab initio density functional calculations of all the energy barriers and the Arrhenius prefactors for the most important processes. The resulting temperature evolution of all species obtained from the simulated kinetics of ethylene decomposition agrees with photoemission measurements. The molecular dissociation mechanism begins with the dehydrogenation of ethylene to vinylidene (CH 2 C), which is then converted to acetylene (CHCH) by the removal and addition of an H atom. The C-C bond is then broken to form methylidyne (CH), and in the same temperature range a small amount of ethylidyne (CH 3 C) is produced. Finally methylidyne dehydrogenates to produce C monomers that are available for the early stage nucleation of the graphene islands. * Physics Department, King's College London, London, WC2R 2LS, United Kingdom. ‡ The Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
The growth of graphene by molecular beam epitaxy from an elemental carbon precursor is a very promising technique to overcome some of the main limitations of the chemical vapour deposition approach, such as the possibility to synthesize graphene directly on a wide variety of surfaces including semiconductors and insulators. However, while the individual steps of the chemical vapour deposition growth process have been extensively studied for several surfaces, such knowledge is still missing for the case of molecular beam epitaxy, even though it is a key ingredient to optimise its performance and effectiveness. In this work, we have performed a combined experimental and theoretical study comparing the growth rate of the molecular beam epitaxy and chemical vapour deposition processes on the prototypical Ir (111) surface. In particular, by employing high-resolution fast X-ray photoelectron spectroscopy, we were able to follow the growth of both single- and multi-layer graphene in real time, and to identify the spectroscopic fingerprints of the different C layers. Our experiments, supported by density functional theory calculations, highlight the role of the interaction between different C precursor species and the growing graphene flakes on the growth rate of graphene. These results provide an overview of the main differences between chemical vapour deposition and molecular beam epitaxy growth and thus on the main parameters which can be tuned to optimise growth conditions.
By combining high-resolution photoelectron spectroscopy and ab initio calculations, we show that different carbon clusters can be formed on Ir(111) upon low temperature molecular beam epitaxy using a solid state carbon source. Besides carbon monomers, also dimers, trimers and larger clusters are detected through C 1s core levels measurements. The spectroscopic signal of carbon monomers is then used as a fingerprint to detect their presence during the early stages of graphene growth by ethylene chemical vapor deposition at high temperature. We demonstrate that our spectroscopic approach can be employed to investigate the role of carbon monomers and dimers in the nucleation and growth of graphene on different metal surfaces. 3 IntroductionThe interest of the material's science community in carbon monomers (C1) and dimers (C2) has grown considerably in the last years because of their role in the synthesis of high-quality graphene (Gr) monolayers on solid surfaces 1-3 . Carbon clusters, especially those formed by a small number of atoms, play an important role in determining the different atomistic mechanisms for the epitaxial growth of graphene by means of chemical vapor deposition (CVD). The carbon monomers' concentration and the rate at which adatoms are generated from the hydrocarbon feedstock are relevant quantities for understanding the non-linear growth kinetics of Gr experimentally observed on different surfaces 4 . The control of monomer supersaturation is an effective approach to modify not only the growth rate, but also the morphology and orientation of the Gr islands 5 . In addition, C monomers are predicted to be essential for the growth of the graphene islands both through direct attachment to the Gr edges and through the formation and attachment of larger C clusters 6 .Apart from monomers, also dimers play an important role in the formation of high-quality Gr monolayers characterized by a low density of defects such as mono-and di-vacancies, disclinations, dislocations, and domain boundaries 7 . For example, according to theoretical calculations, in the case of copper surfaces, where dimers represent the dominant feeding species for Gr growth 8,9 , they have either a diffusion-or an attachment-limited aggregation behavior depending on the crystallographic surface orientation 10,11 . More specifically, while the rate determining step for Gr growth on Cu(111) is the energy barrier for dimer surface diffusion, in the case of Cu(100) the limit is given by the energy barrier for the attachment of C2 to both zig-zag and arm-chair terminated Gr edges. On the other hand, it has been predicted that the formation of dimers is energetically unfavorable on ideal and flat transition metal Besides their relevance for graphene epitaxial growth, C2 species are extremely important for the formation of all carbon-based three-dimensional materials 19 , for the synthesis of carbon quantum dots, and as building blocks for metal-alkynide and alkynide complexes 20,21 .
It is widely accepted that the nucleation of graphene on transition metals is related to the formation of carbon clusters of various sizes and shapes on the surface. Assuming a low concentration of carbon atoms on a crystal surface, we derive a thermodynamic expression for the grand potential of the cluster of N carbon atoms, relative to a single carbon atom on the surface (the cluster work of formation). This is derived taking into account both the energetic and entropic contributions, including structural and rotational components, and is explicitly dependent on the temperature. Then, using ab initio density functional theory, we calculate the work of formation of carbon clusters C on the Ir(111) surface as a function of temperature considering clusters with up to N = 16 C atoms. We consider five types of clusters (chains, rings, arches, top-hollow, and domes), and find, in agreement with previous zero temperature studies, that at elevated temperatures the structure most favoured depends on N, with chains and arches being the most likely at N<10 and the hexagonal domes becoming the most favourable at all temperatures for N>10. Our calculations reveal the work of formation to have a much more complex character as a function of the cluster size than one would expect from classical nucleation theory: for typical conditions, the work of formation displays not one but two nucleation barriers, at around N = 4-5 and N = 9-11. This suggests, in agreement with existing LEEM data, that five atom carbon clusters, along with C monomers, must play a pivotal role in the nucleation and growth of graphene sheets, whereby the formation of large clusters is achieved from the coalescence of smaller clusters (Smoluchowski ripening). Although the main emphasis of our study is on thermodynamic aspects of nucleation, the pivotal role of kinetics of transitions between different cluster types during the nucleation process is also discussed for a few cases as illustrative examples.
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