Role of structure of C-terminated $4H$-SiC($000\overline{1}$) surface in growth of graphene layers: Transmission electron microscopy and density functional theory studies

The principal structural defects in graphene layers, synthesized on a carbon-terminated face, i.e., the SiC(000$\overline{1}$) face of a $4H$-SiC substrate, are investigated using microscopic methods. Results of high-resolution transmission electron microscopy (HRTEM) reveal their atomic arrangement. The mechanism of such defects’ creation, directly related to the underlying crystallographic structure of the SiC substrate, is proposed. The connection between the $4H$-SiC(000$\overline{1}$) surface morphology, including the presence of the single atomic steps, the sequence of atomic steps, and also the macrosteps, and the corresponding emergence of planar defective structure (discontinuities of carbon layers and wrinkles), is revealed. It is shown that the disappearance of the multistep island leads to the stress-related creation of wrinkles in the graphene layers. The density functional theory (DFT) calculation results show excess carbon atoms convert a topmost carbon layer to the sp${}^2$-bonded configuration, liberating Si atoms in the barrierless process. The DFT results show that the diffusion of carbon atoms is essentially impossible at the C-terminated SiC surface. On the contrary, DFT results prove that diffusion of the silicon atoms is possible on the C-terminated SiC surface at a high temperature close to 1600 °C. Because, according to TEM studies, at the carbon-terminated SiC surface, the buffer layer is absent, that creates a channel for effective horizontal diffusion of both silicon atoms under the graphene layer. Ultimately the silicon atoms escape could be facilitated by the channels created at the bending layer defects (wrinkles). The sp${}^2$-bonded carbon atoms are incorporated into the growing graphene layers, which contribute to stress in the growing layers, detachment from SiC support, and partial contribution to the creation of wrinkles. These results explain the phenomenon of the growth of thick undulated graphene layers by subsequent creation of the new layer underneath the existing graphene cover and also the creation of the principal defects in graphene at the C-terminated SiC(000$\overline{1}$) surface.

Figure 1

Atomic structure of silicon carbide C-terminated surface and the energy surface of the adsorbed Si and C atoms derived from DFT results: (a) the atomic structure of an SiC surface, (b) the energy surface of the silicon atom, (c) the energy surface of the carbon atom, at the (000$\overline{1}$)SiC surface. On the right-hand side (d) and (e), the energy profiles along the black line correspond to the distances shown in the diagrams.

Figure 2

Side view of silicon carbide Si- and C-terminated surfaces, with similar adatoms in the equilibrium positions. The grey and black balls correspond to Si and C atoms, respectively.

Figure 3

Morphology of the SiC(000$\overline{1}$) surface containing graphene layers observed by optical microscope with Nomarski contrast (a) and AFM image of magnified part of surface (b).

Figure 4

Cross-sectional HRTEM images of graphene layers observed in the [11$\overline{2}$0] SiC orientation, showing the arrangement of 15 carbon layers (a) and filtered image of a few C layers associated with SiC substrate (b).

Figure 5

Cross-sectional TEM image of the graphene structure on the SiC substrate containing a macrostep. Contact of two thick carbon layers originated from two terraces (a) with diffraction pattern from a flat part of graphene (b). Magnified part of a macrostep (marked by arrow) with inset showing details of transition of the planes from SiC to C (c) and diffraction pattern from area includes the step (d). The magnified areas used in the analysis are shown beside the entire diffraction patterns. Diffraction patterns are negatives. Images are in the [$\overline{1}$100] SiC substrate orientation.

Figure 6

TEM images of discontinuities and bendings of the graphene multilayers created near a macrostep (a) and at the small steps (b). Graphene with bending layers is marked by dashed lines.

Figure 7

Examples of various arrangements of anchoring of graphene layers to the SiC planes: (a) the (0001)C planes almost perpendicular to the surface, (b) the (0001)C planes are parallel to the edge of the macrostep, and (c) C planes are located along the (0001)SiC planes. Sketch showing the mutual position of the graphene layers and SiC planes (d). Dashed lines denote position of the planes.

Figure 8

TEM images of a pair of graphene multilayers having a different thickness: (a) a general view of the graphene structure on the SiC islands, (b) and (c) magnified parts of the carbon layers located at the edge of the two SiC islands.

Figure 9

TEM images of the disappearing SiC islands: (a) a few bending graphene multilayers and (b) coalescence of a pair ofbending layers.

Figure 10

TEM images showing detachment of the multilayer graphene: (a) as a result of disappearance of the SiC island, marked by the arrow, (b) and (c) wrinkles with different sizes of channels on the flat surface, and (d) wrinkle on the islands.