Molecular dynamics simulation of graphene sinking during chemical vapor deposition growth on semi-molten Cu substrate

Graphene, a single layer of sp2-bonded carbon atoms, has attracted significant attention due to its exceptional properties. The chemical vapor deposition (CVD) method is a promising approach for synthesizing large-area, high-quality graphene, particularly using copper as a catalyst. At the growth temperatures used in CVD (~1000 °C), the copper substrate exhibits semi-molten behavior, meaning it is in a state between solid and liquid. This semi-molten state significantly influences the growth process. Previous studies have highlighted the importance of graphene island formation during nucleation, with their coalescence being crucial for the final quality of the graphene. These islands can act as nucleation seeds or building blocks, and their seamless stitching on single-crystal substrates like Cu(111) is vital for producing large single-crystal graphene (SCG). Before graphene island formation, various intermediates like carbon dimers, nanoarches, and carbon clusters exist. The coronene-like cluster (C24) is considered an ideal precursor due to its structure and symmetry. While the movement and coalescence of these carbon islands are crucial, the dynamics at the atomic level remain unclear. Recent static DFT calculations have suggested an "embedded" growth mode where graphene islands sink into softer metals like copper. Unlike nickel, graphene growth on copper is a surface-mediated process because of the low solubility of carbon in bulk copper. This research aims to address the open questions regarding graphene island sinking into the semi-molten copper surface, the alignment of these islands, and the impact of sinking on the stitching mechanism and overall graphene quality. Molecular dynamics (MD) simulations, utilizing a self-developed C-Cu potential and density functional theory (DFT) methods, are employed to study this process.

The literature review extensively covers existing research on graphene synthesis, particularly CVD growth on transition metals. It highlights previous studies on graphene nucleation, the role of metal step edges in graphene growth, and the various intermediate species involved in the initial stages of graphene formation, including carbon clusters, nanoarches, and polycyclic aromatic hydrocarbons (PAHs). The review includes studies exploring the impact of copper morphology on graphene nucleation, the importance of controlling the orientation and edge geometry of graphene islands for high-quality graphene synthesis, and the role of substrate lattice symmetry in directing island alignment. Several papers focusing on the coalescence of graphene islands and the formation of grain boundaries are also reviewed. The "embedded" growth mode, where graphene islands sink into soft metals, is introduced and discussed as a key concept in understanding the observed phenomena. The discussion also includes the influence of the semi-molten state of copper at typical growth temperatures on the overall growth process.

The study employs classical molecular dynamics (MD) simulations and density functional theory (DFT)-based molecular dynamics simulations to investigate the behavior of graphene on a semi-molten copper substrate. A self-developed C-Cu empirical potential, combining REBO2 for carbon-carbon interaction and considering carbon-metal and metal-metal interactions, was used. The simulations used four-layer Cu(111) slabs with periodic boundary conditions, keeping the bottom layer fixed to simulate a semi-infinite surface. The velocity Verlet algorithm and the Berendsen thermostat were used. Different sized carbon nanoclusters (C24, C54, C96) and graphene nanoribbons were simulated at various temperatures. The Lindemann index was used to characterize the state of the copper substrate. The average heights of the carbon clusters and surrounding copper atoms were tracked to quantify the sinking process. DFT-MD simulations were performed to validate the results from classical MD simulations. The orientation of the C24 cluster was analyzed by tracking its rotation angle over time. Periodic graphene nanoribbons were used to model the stitching process, and simulations involved adding carbon atoms to the gap between the ribbons to study their merging behavior. The simulations allowed for observing and analyzing the sinking behavior of graphene islands, their orientation on the substrate, and the stitching of individual graphene ribbons to form larger graphene domains.

The MD simulations revealed two distinct sinking modes: (i) Sunken-mode I, where smaller graphene islands like C24 sink into the first layer of the semi-molten copper substrate at temperatures above 1350 K. (ii) Sunken-mode II, observed with larger islands (C54, C96), where the islands float on the surface, and surrounding copper atoms diffuse upwards to surround them. The sinking of smaller islands leads to a unidirectional alignment of the islands, controlled by the underlying unmolten copper lattice. This unidirectional alignment is less pronounced on a fully liquid copper surface. The simulations showed that the orientation of C24 on the semi-molten surface has a narrow distribution around 0° and 60° due to the interaction with the unmolten subsurface. Surprisingly, the metal steps formed during the sinking process do not hinder the stitching of graphene nanoribbons. Instead, they actively assist in defect healing. The merging of nanoribbons resulted in a near-perfect graphene sheet with minimal defects. This is in contrast to the graphene stitching observed on Nickel where more defects were present. The overall results suggest that the semi-molten copper surface is advantageous for creating large, high-quality single-crystal graphene due to the described sinking and stitching behaviors. The classical MD results were consistent with DFT-MD simulations, validating the accuracy of the developed C-Cu potential.

The findings address the research questions by providing a detailed mechanistic explanation for the growth of large single-crystal graphene on semi-molten copper substrates. The observation of two distinct sinking modes, coupled with the defect-healing nature of the metal steps during stitching, explains how large, high-quality graphene can be produced. The results highlight the significance of the semi-molten state of the copper substrate in achieving the observed unidirectional alignment and seamless stitching of graphene islands. This study clarifies how the interplay between the size of graphene islands, the semi-molten nature of the substrate, and the resulting atomic-scale dynamics lead to the formation of large, high-quality graphene films. The consistency between classical MD and DFT-MD simulations reinforces the reliability of the developed potential and the validity of the interpretations. The study provides a deeper understanding of the atomic-level processes governing graphene growth and offers valuable insights for optimizing the synthesis of high-quality graphene.

This study systematically investigated graphene island sinking on semi-molten Cu(111) substrates using MD simulations. Two sinking modes were identified, influencing island alignment and stitching. The metal steps formed during sinking facilitate defect healing during the stitching process, resulting in high-quality graphene. These findings provide crucial insights into CVD graphene growth on semi-molten copper and offer theoretical guidance for controlled synthesis of large, single-crystal graphene. Future work could focus on investigating the influence of other growth parameters, such as precursor concentration and pressure, and extending the simulations to larger graphene domains.

The simulations are limited by the computational cost of DFT-MD, necessitating the use of simplified models for some simulations. The developed C-Cu potential, while validated against DFT-MD, may not be perfectly transferable to all situations and could be refined further. The simulations primarily focus on idealized systems and might not perfectly capture the complexity of real CVD growth conditions, which can include imperfections and impurities in the substrate and a more complex distribution of carbon species.