Strain in Epitaxial Graphene Visualized by Intercalation

Intercalation of Eu under graphene on Ir(111) results in patterns oriented along the graphene moiré and quantized in size by its unit mesh. The patterns are formed by stripes, compact islands, and channels. Over a wide range of intercalated amounts the step concentration of the pattern has a rather constant saturation value. These findings are explained by the chemically modulated binding of graphene to the substrate and the preexisting strain in graphene due to its cooldown from the growth temperature. Local variations in the intercalation step density appear to reflect local variations in the preexisting strain.

Figure 1

(a)–(d) STM topographs (image size $80\mathrm{nm}\times 80\mathrm{nm}$) after intercalation of Eu resulting in successively larger intercalation coverages of (a) 18% ML, (b) 39% ML, (c) 72% ML, and (d) 89% ML. The arrow in (b) indicates the [$\overline{1}\overline{1}2$] direction.

Figure 2

(a) STM topograph ($21\mathrm{nm}\times 21\mathrm{nm}$) after intercalation of 50% ML Eu at 720 K. Based on the different local symmetries of C rings with respect to the substrate, the moiré unit cell (black rhomboid) is tiled. White: atop area; green (light gray): fcc area; red (dark gray): hcp area (see text). The arrow indicates the Ir[$\overline{1}\overline{1}2$] direction. (b) Schematic sketch of (a) redrawn into the tiled moiré pattern.

Figure 3

Intercalation step density $\rho$ as a function of intercalated Eu amount $\theta$. Blue solid line: expected $\rho (\theta )$ if $t$ stripes are energetically preferred (no strain). Red dashed line: expected $\rho (\theta )$ taking only strain relaxation of Gr into account (no binding inhomogeneity and edge energy).

Figure 4

Height profile over a single $t$ stripe taken along the blue line in the STM image ($43\mathrm{nm}\times 10\mathrm{nm}$). The moiré periodicity of $\sqrt{3}{a}_m$ in path direction is displaced by $\Delta s_m$ due to the $t$ stripe (see text). Because of the inverted moiré contrast atop areas are imaged now as dark spots. The imaging contrast (regular or inverted) depends on tip state and tunneling resistance [26].

Figure 5

(a) STM topograph ($195\mathrm{nm}\times 160\mathrm{nm}$) after intercalation of 72% ML Eu. (b) STM topograph ($70\mathrm{nm}\times 130\mathrm{nm}$) after Eu deposition on Ir(111) covered with 40% ML Gr.