Self organization of a hexagonal network of quasi-free-standing monolayer graphene nanoribbons

We investigated the H desorption process and the surface structure after H desorption in quasi-free-standing monolayer graphene (QFMLG) on silicon carbide (SiC). In situ scanning tunneling microscopy observations revealed that H adatoms preferentially desorb at SiC step edges. We found self-organization of a hexagonal network of QFMLG nanoribbons during H desorption. The surface structure on the nanoribbons indicates that electron scattering occurs at the boundary between the QFMLG and H-desorbed regions. The configuration of the network is determined by the formation energy of the boundary and by the surface stress energy.

Figure 1

(a) STM image of a 4$H$-SiC(0001) sample at room temperature after H intercalation (scan size = $500\times 500{\mathrm{nm}}^2$, bias voltage = −0.14 V, tunnel current = 0.5 nA, height range = 0.66 nm). Inset: Line profile along the solid line. (b) Magnified image around the edge of a SiC hole indicated by a square in (a) ($10\times 10{\mathrm{nm}}^2$, −0.13 V, 0.6 nA, 0.41 nm). The left side of the image is inside the hole. A unit cell of graphene is indicated by the rhombus.

Figure 2

(a) STM image at 540 °C after annealing at 670 °C for 2 h in a vacuum (500 × 500 nm${}^2$, −0.14 V, 0.5 nA, 0.40 nm). (b) STM image at 590 °C around the edges of a SiC hole ($50\times 50$ nm${}^2$, −0.14 V, 0.5 nA, 0.25 nm). The left side is inside the hole. (c) STM image of an H-desorbed patch at room temperature ($50\times 50$ nm${}^2$, −0.13 V, 0.5 nA, 0.20 nm). (d) Line profile along the solid line in (b).

Figure 3

(a)–(c) Series of time-lapsed STM images at 590 °C, with elapsed times of (a) 0, (b) 10, and (c) 64 min. The arrows point to QFMLG nanoribbons intruding into H-desorbed patches (182 × 250 nm${}^2$, −0.14 V, 0.5 nA, 0.25 nm). (d)–(f) Series of time-lapsed STM images at 630 °C, with elapsed times of (d) 0, (e) 37, and (f) 69 min. The arrow points to the nucleation of an H-desorbed patch on a flat terrace. There is a SiC step at the upper right corner (273 × 341 nm${}^2$, −0.13 V, 0.5 nA, 0.25 nm).

Figure 4

(a)–(c) STM images at room temperature after H desorption [(a) and (b) 200 × 200 nm${}^2$, −0.002 V, 0.07 nA, 0.40 nm; (c) 30 × 30 nm${}^2$, −0.002 V, 0.5 nA, 0.62 nm]. (d) Magnified image of the square in (c) (10 × 10 nm${}^2$, −0.05 V, 0.5 nA, 0.52 nm). (e) Magnified image at the center of the nanoribbon in (d) (2.5 × 2.5 nm${}^2$, −0.05 V, 0.5 nA, 0.46 nm). The rhombus shows a graphene $\sqrt{}$3 × $\sqrt{}$3-$R$30° unit cell.

Figure 5

(a) Coverages of QFMLG regions at 630, 650, and 670 °C are plotted as squares, triangles, and circles as a function of time, with straight line fits as red, green, and blue dashed lines, respectively. (b) Arrhenius plot of desorption rates in (a).

Figure 6

Average spacings as a function of coverage of H-desorbed patches are plotted as squares. The solid curve is the minimum energy configuration of the model in the inset described by Eq. (1) when $E_{\mathrm{wall}}/C=0.38$.