Structure and local variations of the graphene moiré on Ir(111)

We have studied the incommensurate moiré structure of epitaxial graphene grown on iridium(111) by dynamic low-energy electron diffraction [LEED $I$($V$)] and noncontact atomic force microscopy (AFM) with a CO-terminated tip. Our LEED $I$($V$) results yield the average positions of all the atoms in the surface unit cell and are in qualitative agreement with the structure obtained from density functional theory. The AFM experiments reveal local variations of the moiré structure: The corrugation varies smoothly over several moiré unit cells between 42 and 56 pm. We attribute these variations to the varying registry between the moiré symmetry sites and the underlying substrate. We also observe isolated outliers, where the moiré top sites can be offset by an additional 10 pm. This study demonstrates that AFM imaging can be used to directly yield the local surface topography with pm accuracy even on incommensurate two-dimensional structures with varying chemical reactivity.

Figure 1

(a) LEED pattern of graphene on iridium (78 eV) showing the moiré spots. The illustrated indexed spots correspond to the first-order substrate spots. (b) Comparison of the experimentally measured (blue) and calculated (red) $I$($V$) curves for the best fit (7886 eV, $R_{\mathrm{P}}=0.39$).

Figure 2

(a) The topographic structure of the moiré unit cell obtained from LEED $I$($V$). (b) Cross section through the moiré unit cell of the LEED $I$($V$) model along the white dashed line marked in (a). The color scales of the $z$ positions of the atoms are relative to the mean height of the layer, given on the left side of the image. (c) Magnification of the area marked with the dashed box in (b). The vertical scale in (c) is magnified fivefold to better illustrate the shape of the graphene layer.

Figure 3

(a) Constant frequency shift AFM image of the graphene moiré ($\Delta f=0$ Hz, $\text{bias}=0$ V). (b) AFM line profile over the moiré unit cell marked with a white dashed line in (a).

Figure 4

(a) The moiré corrugation as a function of graphene island size excluding the outliers. The solid line is the average of the set and the dotted lines the standard deviation. (b) Distribution of all the individual top site heights extracted from the AFM images (including outliers). (c) Overview STM scans of the islands in the plot in (a). The scale bar is 50 nm in all images.

Figure 5

(a) Constant frequency shift AFM image over a larger area ($\Delta f=0$ Hz, $\text{bias}=0$ V, $24\times 24$ nm${}^2$). (b) Same AFM image as in (a) but with the contrast adjusted to the top sites. (c) Heights of the top sites with respect to the neighboring hcp sites. (d) Distribution of the top site heights in (c).