Single crystalline electronic structure and growth mechanism of aligned square graphene sheets

Graphene, a unique single-layer carbon sheet with a honeycomb lattice, has attracted enormous research interests in the past decade due to its elegant structural and electronic properties as well as great potentials in applications.^1–5 Recently, chemical vapour deposition (CVD) has emerged as a promising, efficient, and inexpensive method to realize scalable production of large-scale graphene films.^6,7 Nonetheless, the quality of such films has been suspected to be inferior to the exfoliated thin films due to defects during growth and boundaries between different graphene domains.^8–12 Such inhomogeneity not only adversely affected device applications but also made the conventional angle-resolved photoemission spectroscopy (ARPES) a powerful tool for the study of electronic structures^13–15 unsuitable for studying CVD thin films, as which typically is composed of single-crystalline individual and merged graphene grains of tens of micro-meters, much smaller than the conventional ARPES photon beam spot size (usually 0.5–1.0 mm). Consequently, conventional ARPES will only give the averaged band structure from many individual graphene grains with various crystalline orientations.

Recently, the situation has been greatly improved from both aspects. On one hand, the development of ARPES with very high (e.g., sub-micron) spatial resolution (i.e., micro-ARPES) in the past few years^16–18 provides a new powerful tool to directly probe the electronic structures of low-dimensional materials down to atomic thickness and sub-micrometer lateral size,^19–22 which enables us to investigate individual graphene grains and merged regions as well as the inhomogeneity of these films and gain valuable information about growth mechanism. On the other hand, low-pressure CVD growth methods^23,24 were developed and oxygen was introduced to reduce the nucleation density and increase the quality of graphene grains as well as the growth rate.^25–27 Interestingly, besides the usual hexagonal shape, graphene can also be grown into large aligned square-shape grains, despite its hexagonal honeycomb lattice.^28–30 If the orientations of such individual graphene grains can be aligned to enable seamless merging and then form a larger sheet, the quality of the CVD graphene films can be further improved.^31,32 Under this circumstance, an effective method that can investigate the electronic structures of these graphene films with precise spatial information and study their inhomogeneity is urgently needed.

In this work, we applied micro-ARPES to study the electronic structures and lattice orientation of square graphene grains grown on commercially available Cu foil substrate, as well as their growth mechanism. Taking advantage of the excellent spatial resolution of micro-ARPES, we were able to measure individual square graphene grains (and even different locations within one grain) to set up a direct link between the square grains’ geometric shape and their lattice orientation. Furthermore, with the capability of simultaneously collecting photoelectrons from both graphene grains and the Cu substrate underneath, we could study their electronic structures and investigate their correspondence, which can shed light on the growth mechanism that results in their high quality and unusual square shape.

Figure 1(c) shows the principle of micro-ARPES technique. Complementary to other commonly used characterization methods [e.g., low energy electron diffraction (LEED), Raman, and transmission electron microscope (TEM)], micro-ARPES can directly visualize the electronic band structures of individual graphene grains and study their uniformity, as well as the grain-to-grain evolution with submicron spatial resolution. Furthermore, given the advantage that photoelectrons from both graphene and substrate Cu foil can be simultaneously collected and analyzed [see Fig. 1(c) and the supplementary material for details], the correlation between electronic structures of graphene grains and the Cu substrate can be investigated, leading to important information for understanding the growth mechanism. In addition, as a surface sensitive probe (supplementary material), micro-ARPES can provide information about what happened to topmost layers of Cu substrate which are directly involved in the CVD growth (instead of the bulk counterpart).

The square graphene grains in our study were grown on Cu foils by a low-pressure CVD method at a high growth rate (the maximum can reach 300 μm min⁻¹).³⁰ In particular, two Cu foils were stacking together (with a gap of around tens of microns) and inside molecular move in a molecular-flow-mode³⁰ [Fig. 1(b)]. From the optical image [Fig. 1(a)], individual graphene square grains can be easily identified and some of them even merge to form larger sheets (up to millimeter scale). The larger size and the smoother sides of individual square graphene grains from our synthesis³⁰ show the improvement over some previous studies that typically yield smaller grains with jagged edges.^28,29

In order to investigate both individual graphene grains and their merged regions, we chose an area marked by the orange rectangle in Fig. 1(a) (optical image). The corresponding photoemission intensity map in real space obtained by micro-ARPES is illustrated in Fig. 1(d), showing excellent correspondence to Fig. 1(a).

In order to check if each square graphene grain is single layer and single crystalline, we first focused the photon beam onto different grains to measure their band dispersions in momentum space, which can be compared with the theoretical band structure of mono-layer graphene as schematically shown in Fig. 1(e–i). Indeed, the measurement in Fig. 1(e–ii) [stacking plot of constant energy contours of the photoemission spectral intensity from grain G2 in Fig. 1(d)] shows excellent agreement with that in Fig. 1(e–i). Besides the constant energy contours, we can also obtain band dispersions across the Dirac points from different grains, as shown in Fig. 1(f). All grains exhibit clear single linear dispersions around the K point in momentum space, indicating the single-layer and electron-doped nature of these grains [note that the variation of doping level at different positions can be mainly ascribed to the local Cu-graphene separation variation (considering the corrugated nature of Cu foil, Fig. S1 of the supplementary material) that influences the extent of charge transfer and doping level^21,33].

Interestingly, as these square graphene grains are apparently well-aligned [their sides are parallel aligned; Figs. 1(a) and 1(d)], we can compare the band structures of different grains and their merged region to check if this is indeed the case (lattice structures are aligned). Figure 2 summarizes various measurements on graphene grains from two different samples labeled as Sample A and Sample B (from different growth batches). The real-space spectral intensity maps of Sample A and B are displayed in Figs. 2(a) and 2(e), respectively, while the constant energy contours cutting through the Dirac points in momentum space are shown in Figs. 2(b) and 2(f), respectively. Evidently, from each graphene domain, only a single set of Dirac points are observed [Figs. 2(b) and 2(f)] as expected [Fig. 2(d)], again proving their single-layer nature.

Remarkably, in Fig. 2(b) or Fig. 2(f), one can easily find that the measurements from different grains of the same sample are almost identical in momentum space, which can be verified by overlapping these measurements for comparison [see Fig. 2(c) for Sample A and Fig. 2(g) for Sample B]. The slight variation of the Dirac point positions in Figs. 2(c) and 2(g) is due to the experimental uncertainty resulting from the surface unevenness of the Cu foil (corrugation is common in commercial Cu foils used in CVD growth; see Fig. S1 of the supplementary material) and the angle variation due to the rotation of the electron analyzer of micro-ARPES. Since the orientation of the band structure in momentum space is reciprocal to the lattice orientation in real space [see Fig. S7(a) and S7(b) in the supplementary material for details], the good agreement of the band structures [Figs. 2(c) and 2(g)] shows that the lattice orientation of different graphene grains in each sample is also well aligned, which is consistent with reported selected-area electron diffraction measurements.³⁰ 

Besides the individual grains, we find that the merged regions between different grains also show high crystalline quality with the same lattice orientation as individual grains. As examples, measurements at points A1 [in Sample A, see Fig. 2(a)] and B2 residing at the merged area of two graphene grains BG1 and BG2 [in Sample B, see Fig. 2(e–ii)], both show matched orientation to their neighboring grains. This observation suggests that the individual graphene grains can merge into a larger sheet with similar crystalline orientation, making our CVD growth a promising method to grow large-scale graphene sheets with high quality.

After establishing that the square-shaped grains are indeed single-layer graphene sheets with aligned orientation, we can further investigate if and how their electronic structures, shape, and lattice orientation are related to those of the Cu foil underneath, which may help understand the role of the Cu substrate in the CVD growth that is still under debate.^34–41 

We first measured the electronic and lattice structures of bare Cu foil by focusing the photon beam to the Cu substrate next to the graphene grain under investigation [Fig. 3(a)]. The constant energy contour of the Cu d band [Fig. 3(b)] clearly shows four-fold symmetry with the periodicity (∼2.5 Å⁻¹) consistent with the Cu (001) surface. We then moved the photon beam to the adjacent graphene grain [see Fig. 3(c–i)] where we can simultaneously measure the band structures of graphene and Cu substrate. The results on graphene covered regions of both Samples A and B are displayed in Fig. 3(d). In addition to the square-shaped band contours (from the Cu substrate) shown in Fig. 3(b), Fig. 3(d) clearly shows additional triangular band contours centered at the K points from the Dirac cone of the graphene grains. In order to further check the uniformity of the Cu substrate, an unfocused photon beam (>50 μm beam spot size) was used [see Fig. 3(e); 100 eV photons were used to enhance the Cu sp band near E_F]. Remarkably, the sharp single-domain Fermi-surface in Fig. 3(e) (also see Fig. S6 in the supplementary material for more details) with four-fold symmetry clearly demonstrates the single crystalline nature of the Cu (001) substrate in a large area that was also confirmed by electron back-scatter diffraction (EBSD) measurements.³⁰ 

With both band structures from graphene grains and the Cu substrate, we can examine their relative orientation, which we define as the angle α [Fig. 3(f)] between the K–K direction of the graphene Brillouin zone (BZ) and the X–M direction of the Cu (001) BZ. Interestingly, after comparing different graphene grains from Samples A and B, we find that [Fig. 3(f)] although in each sample the α values are consistent for different graphene grains [considering the substrate corrugation (see Fig. S1 of the supplementary material) and experimental uncertainty], between different samples, α is clearly different [Fig. 3(f)] which indicates that the relative crystalline orientation between graphene grains and the Cu substrate may not be critical for the formation of the square graphene grains.

Instead, we now consider if the geometrical shape of the square grains in both samples is correlated to the Cu substrate. As the electronic structure’s orientation in momentum space is reciprocal to the lattice orientation in real space, we can also investigate how the sides of the square grains are aligned with the lattice directions of the Cu (001) surface underneath from the measurements in Fig. 3.

In Fig. 4, the reconstructed graphene lattice orientation, the geometrical grains’ side orientation, and the high-symmetry directions in reciprocal space of the Cu (001) surface (with which lattice orientation of Cu can be deduced) are plotted together and then compared. Figure 4(a) shows that the zigzag and armchair edges are roughly aligned with the sides of the graphene grain in Sample A [panel (i)], while in Sample B [panel (ii)] they are clearly misaligned, again confirming our above discussions [the correspondence between the BZ in momentum space and the lattice in real space is illustrated in Figs. 4(b) and S7 in the supplementary material]. Despite this difference, in Fig. 4(a), both samples show that the sides of the graphene grains (blue dashed lines) determined from the real-space maps are significantly parallel to the X–M direction of the Cu substrate [i.e., the Cu ⟨110⟩ direction, marked as the yellow dashed lines in the insets of Figs. 4(a-i) and 4(a-ii)].

This correspondence in both samples suggests that certain Cu atomic direction plays an important role during the growth of the square graphene grains. Figure 4(c) shows a possible picture where graphene grains preferentially nucleate and extend along the Cu ⟨110⟩ step edge (since atomic steps on Cu foils were revealed by atomic force microscope measurements³⁰). In this regard, the shape and orientation of graphene grains are highly influenced by the Cu (001) crystalline surface structure.

In summary, we successfully applied the state-of-the-art micro-ARPES technique in the systematic study of spatially resolved electronic structures of aligned square graphene sheets grown on commercially available Cu foil. We confirmed the graphene sheets’ high quality and well-aligned orientation and furthermore revealed that the crystalline surface structure of Cu foils plays an essential role in the formation of their square shape during CVD growth. In addition, our work demonstrates the potential of this new experimental technique in the study of low-dimensional materials down to atomic thickness and sub-micrometer lateral size (e.g., besides graphene, it can also be applied to transition metal dichalcogenides,⁴² various van der Waals heterostructures,⁴³ and black phosphorus⁴⁴) and even in situ study of the active materials used in functional devices.

See supplementary material for detailed experimental description and data.

Y. L. Chen acknowledges the support from the EPSRC (UK) Grant No. EP/K04074X/1 and a DARPA (USA) MESO Project (No. N66001-11-1-4105). H. F. Yang acknowledges the financial support from the Bureau of Frontier Sciences and Education, Chinese Academy of Sciences. C. Chen and H. Peng acknowledge the support from China Scholarship Council—University of Oxford. S. A. Ekahana acknowledges the support from Indonesia Endowment Fund for Education (Lembaga Pengelolaan Dana Pendidikan, LPDP). N. B. M. Schröter acknowledges the support from Studienstiftung des deutschen Volkes.