Three-fold diffraction symmetry in epitaxial graphene and the SiC substrate

The crystallographic symmetries and spatial distribution of stacking domains in graphene films on 6H-SiC(0001) have been studied by low-energy electron diffraction and dark-field imaging in a low-energy electron microscope. We find that the graphene diffraction spots from two and three atomic layers of graphene have three-fold symmetry consistent with $AB$ (Bernal or rhombohedral) stacking of the layers. On the contrary, graphene diffraction spots from the buffer layer and monolayer graphene have apparent six-fold symmetry, although the three-fold nature of the satellite spots indicates a more complex periodicity in the graphene sheets.

Figure 1

(Color online) (a) A LEED image (43 eV) of an epitaxially grown graphene sample. The region of intensity to the left of center is due to secondary electrons. (b) A cartoon of the LEED image in (a) that shows the relevant sets of diffraction spots more clearly. In both panels, two SiC spots are marked with stars, two graphite spots are marked with triangles, two $6\times 6$ spots are marked with squares, and the (0,0) spot is marked with a circle.

Figure 2

(Color online) $2\times 2\mu \text{m}$ LEEM images, taken at the same place on sample 1. (a) A bright-field image (3.7 eV) where the buffer layer is light gray and single-layer graphene is medium gray. (b) Dark-field image (53.0 eV) for the SiC LEED spot labeled “A” in Fig. 1. (c) Dark-field image (also 53.0 eV) for the SiC LEED spot labeled “B” in Fig. 1. (d) Dark-field contrast between the two 53.0 eV SiC LEED spots shown; panel (d) is a subtraction of panel (c) from panel (b). In panel (d), positive and negative contrast are given by the black and white regions of the image, and regions of zero contrast are gray. (e) Cartoon illustrating two ways to stack one layer above another in a closest-packed configuration; $AB$ stacking differs from $AC$ stacking by a $60°$ rotation.

Figure 3

(Color online) $2\mu \text{m}\times 2\mu \text{m}$ LEEM images. (a,b) Bright-field images of two different samples. The gray scale of (a) is different from (b); (a) was taken at 3.7 eV, where the buffer layer is light gray, and single-layer graphene is medium gray. (b) was taken at 5.4 eV, where single-layer graphene is light gray or white (rippled looking), bilayer graphene is medium gray, and three-layer graphene is black. The buffer layer would be a bright white. (c,d) Dark-field contrast images from two graphite LEED spots (labeled “C” and “D” in Fig. 1), taken at 49.2 and 55.7 eV, respectively. Positive and negative contrasts are given by the black and white regions of the image, and regions of zero contrast are gray. Outlines [red (darker gray) for monolayer graphene, green (lighter gray) for bilayer] are drawn to help the comparison. (e) Cartoon that shows the two types of stacking domains in panel (d).

Figure 4

(Color online) $2\times 2\mu \text{m}$ LEEM images. (a) and (b) Bright-field images of two samples [the same images as panels (a) and (b) of Fig. 3]. (a) was taken at 3.7 eV, where the buffer layer is light gray, and single-layer graphene is medium gray. In (b), taken at 5.4 eV, single-layer graphene is light gray or white (rippled looking), bilayer graphene is medium gray, and three-layer graphene is black. (c) and (d) Dark-field contrast of two $6\times 6$ LEED spots (labeled “E” and “F” in Fig. 1), taken at 39.6 and 14.5 eV, respectively. Positive and negative contrasts are given by the black and white regions of the image, and regions of zero contrast are gray. Outlines [red (darker) for monolayer graphene, green (lighter) for bilayer] are drawn to help the comparison.