Formation of graphene atop a Si adlayer on the C-face of SiC

The structure of the SiC($000\overline{1}$) surface, the C-face of the {0001} SiC surfaces, is studied as a function of temperature and of pressure in a gaseous environment of disilane ($\mathrm{S}{\mathrm{i}}_2{\mathrm{H}}_6$). Various surface reconstructions are observed, both with and without the presence of an overlying graphene layer (which spontaneously forms at sufficiently high temperatures). Based on cross-sectional scanning transmission electron microscopy measurements, the interface structure that forms in the presence of the graphene is found to contain 1.4–1.7 monolayers (ML) of Si, a somewhat counter-intuitive result since, when the graphene forms, the system is actually under C-rich conditions. Using ab initio thermodynamics, it is demonstrated that there exists a class of Si-rich surfaces containing about 1.3 ML of Si that are stable on the surface (even under C-rich conditions) at temperatures above ∼400 K. The structures that thus form consist of Si adatoms atop a Si adlayer on the C-face of SiC, with or without the presence of overlying graphene.

Figure 1

Possible terminations of the SiC($000\overline{1}$) surface: (a) full SiC bilayer together with <1 monolayer of Si adatoms atop the bilayer, and (b) full bilayer plus a monolayer (adlayer) of Si plus additional Si adatoms on top of the adlayer. Structures of the type shown in (b) are referred to as “adatom on adlayer” (AOA) structures.

Figure 2

(a) High-angle annular dark-field (HAADF) imaging and (b) annular bright-field (ABF) imaging of graphene on C-face SiC. Four layers of graphene are observed for this region of the sample surface. These four layers show very low contrast in the HAADF image whereas they have clear contrast in the ABF image, consistent with the low atomic number of C compared with Si. (c) Another region of the sample, now displaying three layers of graphene. (d) EDS and (e) EELS measurements along the line indicated in (c).

Figure 3

Overview of experimental LEED results, showing the symmetry of the observed patterns. Each data point represents a surface prepared by five minutes of heating at the temperatures and disilane pressures indicated. LEED patterns to the right of the dashed line contain graphene spots (indicating the presence of graphene on the surface), while those to the left of the dashed line do not contain graphene spots. The “0” disilane pressure (vertical axis) indicates experimental results obtained in vacuum, with no disilane introduced.

Figure 4

LEED patterns of (a) 3 × 3, (a) 2 × 2, and (c) 4 × 4 surfaces. Pattern (a) was obtained from a sample heated at 1070 °C for 10 min in vacuum (without any disilane), whereas patterns (b) and (c) were obtained from samples prepared under nominally identical conditions: heating in $5\times {10}^{-5}$ Torr disilane at 1180 °C for 5 min. Patterns (a) and (c) were acquired at an electron energy of 100 eV, and pattern (b) at 96 eV.

Figure 5

Total energy, including vibrational free energies, for select surface structures on SiC($\overline{111}$) (intended to model SiC($000\overline{1}$) surfaces), as a function of the coverage of Si adatoms. Results are shown in the C-rich limit, and for temperatures of 0, 1000, and 1500 K. The dashed lines for coverages near 1.3 ML are drawn to match the minimum-energy models there, for each temperature.

Figure 6

Schematic views of the surface structures whose energies are labeled in Fig. 5. The surface arrangements sit on a SiC bilayer, with Si atoms (open orange circles) at the bottom of the bilayer and C atoms (filled gray circles) at the top. Above the bilayer are Si adatoms (solid orange circles), which in many cases form a complete adlayer. Above these adatoms, for certain structures, are additional Si adatoms (brown filled circles). Unit cells are shown by a light blue trapezoid. The black triangle in (c) indicates a biaxial distortion in the location of the three orange adlayer atoms at its corners, whereas the triangle in (d) shows a predominantly twisting distortion.

Figure 7

Vibrational free energies for graphite, Si, and 3C-SiC, with all results shown per atom (for SiC, the result shown is 1/2 the free energy per Si + C unit). Solid lines show free energies obtained using a complete spectrum of vibrational modes, whereas dashed lines show results using only a single Einstein mode for Si and graphite, and two such modes for SiC. All mode energies are obtained from ab initio computations.

Figure 8

Computed phase diagrams, showing regions of minimum free energy for various SiC($000\overline{1}$) surface structures, at temperatures of 0, 1000, and 1500 K. Vibrational free energy is included, leading to the temperature dependence of the Si-rich and C-rich limits (dashed lines) as well as the temperature-dependent shifts in the positions of boundaries between phases. Structures A, B, and C are shown in Figs. 6, 6, and 6, respectively. Structures D and E are shown in the schematic views, using the same color scheme as in Fig. 6 and with red filled circles representing H (these two structures are the only ones in the phase diagram that contain any H). Structure F is the one proposed in Ref. [30].