Nanofaceting as a stamp for periodic graphene charge carrier modulations

The exceptional electronic properties of monatomic thin graphene sheets triggered numerous original transport concepts, pushing quantum physics into the realm of device technology for electronics, optoelectronics and thermoelectrics. At the conceptual pivot point is the particular two-dimensional massless Dirac fermion character of graphene charge carriers and its volitional modification by intrinsic or extrinsic means. Here, interfaces between different electronic and structural graphene modifications promise exciting physics and functionality, in particular when fabricated with atomic precision. In this study we show that quasiperiodic modulations of doping levels can be imprinted down to the nanoscale in monolayer graphene sheets. Vicinal copper surfaces allow to alternate graphene carrier densities by several 1013 carriers per cm2 along a specific copper high-symmetry direction. The process is triggered by a self-assembled copper faceting process during high-temperature graphene chemical vapor deposition, which defines interfaces between different graphene doping levels at the atomic level.


Energy-dependent LEED
Position-dependent LEED showed that these patterns are quite homogeneous over millimeter scales on the copper foil. Three energy-independent specular reflections define the three facet normals n 1 , n 2 , and n 3 aligned perpendicular to the [110] direction (intensity maxima at the centers of the specular reflections are cut for better visibility of remaining LEED pattern). They correspond to (111), (110), and (221), respectively, where (111) has by far the largest intensity and thus dominates the surface area. The assignment of crystal orientations to the specular reflections was done according to the distance of the three specular spots n 1 , n 2 , and n 3 on the LEED screen. Knowing the geometry of the LEED instrument the relative inclination angles with respect to n 1 Cu[111] can be estimated with good accuracy.
Additionally to the graphene spots, a p(2 × 2) superlattice is visible, 30 • rotated with respect to the Cu (111)  Core level X-ray photoemission spectroscopy Independently of the LEED studies, the presence of oxygen is directly evident from XPS data summarized in Fig. 2. Fig. 2a shows XPS scans over a wide energy range for regions with (red circle) and without (white circle) graphene. C 1s core level spectra in panel Fig. 2b reveal a sharp carbon peak on graphene, which is much larger in intensity compared 2 to that on the bare Cu foil, and is located at a higher binding energy E B ≈ 284.7 eV typical for graphene 2 . Oxygen O 1s spectra presented in Fig. 2c evidence higher oxygen amounts on bare Cu foil and less on the graphene covered areas. Partly oxidized surfaces underneath graphene are expected from the observed oxygen p(2 × 2) superlattice on Cu(111) in LEED.
Copper oxides with O 1s core levels at E B ∼ 531 eV represent only minor contributions, whereas the main oxygen peak at E B ∼ 533 eV can be mostly attributed to adsorbed H 2 O and to lesser extend to any C-O related bonds 2,3 . Comparing Cu 3p and 2p 3/2 core level XPS spectra in Fig. 2d-e to the literature, they resemble those of clean copper.

Derivation of carrier modulations
Hereby, A c is the graphene unit cell area of 0.051 nm 2 . With v F = (0.95 ± 0.05) × 10 6 m/s we get D 0 = (0.085 ± 0.009) per (eV 2 and graphene unit cell area), a value similar to the one found e.g. by Giovannetti et al. 5 for graphene on Pt (111).
A simple integration of D(∆E) over energy finally gives the number of transferred carriers per unit cell area: Since within the error bar the Fermi velocity was found the same for all facets n 1 , n 2 , and n 3 this relation can be used in all three cases. Scaling the area to 1 cm 2 the respective doping levels ∆E = (0.44 ± 0.10), (0.63 ± 0.10), and (0.82 ± 0.10) eV correspond to carrier densities of n = 1.6 × 10 13 cm −2 , 3.3×10 13 cm −2 , and 5.7×10 13 cm −2 , respectively. We estimate the according relative errors to 60%, 45%, and 35%. These errors are not to be added when calculating relative changes ∆n.

Dark-field microscopy statistics
In Fig. 4 additional dark field measurements on further example islands are presented. It is worth to note that large islands occasionally host patches of 2nd and 3rd layer graphene (see Fig. 4c and d). They can be straightforwardly identified in energy-filtered PEEM, where multiple graphene layer areas appear darker due to the change in work function contrast.
Interestingly, the growth of the 2nd layer changes the roof-top modulation in a similar way as the triangular shaped rotational domain seeds within single layer graphene. Also for 2nd layer areas the periodicity of the roof-top structure is larger. Indeed, this supports recent reports of the 2nd layer of graphene growing below the 1st layer 6 , where it can restructure the copper surface by direct contact. Unfortunately, the 2nd layer graphene orientation ϕ could not be identified without doubt.  (a) small single-domain island without DF contrast and with homogeneous stripe structure, (b) small island with rotational domain and non-homogeneous stripe structure visible also after sputtering, (c)-(d) larger coalescing islands with dark field contrast. 2nd layer graphene areas are visible as darker patches due to the work function contrast in energy filtered bright field PEEM.