Epitaxial Graphene Growth and Shape Dynamics on Copper: Phase-Field Modeling and Experiments

Abstract

The epitaxial growth of graphene on copper foils is a complex process, influenced by thermodynamic, kinetic, and growth parameters, often leading to diverse island shapes including dendrites, squares, stars, hexagons, butterflies, and lobes. Here, we introduce a phase-field model that provides a unified description of these diverse growth morphologies and compare the model results with new experiments. Our model explicitly accounts for the anisotropies in the energies of growing graphene edges, kinetics of attachment of carbon at the edges, and the crystallinity of the underlying copper substrate (through anisotropy in surface diffusion). We show that anisotropic diffusion has a very important, counterintuitive role in the determination of the shape of islands, and we present a "phase diagram" of growth shapes as a function of growth rate for different copper facets. Our results are shown to be in excellent agreement with growth shapes observed for high symmetry facets such as (111) and (001) as well as for high-index surfaces such as (221) and (310).

Growth Study and Characterization of Single-Layer Graphene Structures Deposited on Copper Substrate by Chemical Vapour Deposition

“…After the heating up to 1040°C and posterior cooling, the domains increase significantly in size. According to these observations, graphene domains grow forming different morphologies which depend on the copper lattice orientation, in accordance to previous theoretic and experimental results [45]. In concrete, we have observed how graphene domains with a four-lobe morphology grow over the Cu (100) plane, while graphene domains with a butterfly-like morphology grow over the Cu (221) plane.…”

“…The different shapes of the domains that can be seen in Figure 2a are a result of the different copper orientation. As it has been explained [45] domains with four cusps grow over Cu (221) and domains with six cusps over Cu (310). The Raman spectra in the inset of Figure 2b ensures us about the single-layer nature of the graphene film.…”

Rapid Growth of Large Single‐Crystalline Graphene via Second Passivation and Multistage Carbon Supply

“…Notably, the shape of the as-formed graphene grains can be both hexagonal and square, which is determined by the orientation of underlying substrates. [ 32 ] In addition, such graphene grains possess a narrow size distribution compared to those without second passivation (Figure 1 d). It is worth noting that the broad distribution of grain size is quite typical for the observation of graphene domains formed at different periods, which, in our case, can be easily explained by the new nucleation introduced by the oversupply of CSS after the fi rst nucleation stage.…”

Polycrystalline graphene and other two-dimensional materials

“…This indicates weak interaction between graphene and Cu surfaces with no clear epitaxial relationship 76,77 . On the other hand, such interactions still exist, and Cu crystal orientation can still have some influence on the growth of the graphene overlayer [78][79][80][81][82][83] . Imperfections (defects, GBs and surface steps) and impurities in the Cu substrate can provide the nucleation centres for growth 79,84 .…”