Diffraction paradox: An unusually broad diffraction background marks high quality graphene

The realization of the unusual properties of two-dimensional (2D) materials requires the formation of large domains of single-layer thickness, extending over the mesoscale. It is found that the formation of uniform graphene on SiC, contrary to textbook diffraction, is signaled by a strong bell-shaped component (BSC) around the (00) and G(10) spots (but not around the substrate spots). The BCS is also seen on graphene grown on metals, because a single uniform graphene layer can be also grown with large lateral size. It is only seen by electron diffraction but not with x-ray or He scattering. Although the origin of such an intriguing result is unclear, its presence in the earlier literature (but never mentioned) points to its robustness and significance. A likely mechanism relates to the the spatial confinement of the graphene electrons, within a single layer. This leads to large spread in their wave vector which is transferred by electron-electron interactions to the elastically scattered electrons to generate the BSC.

Figure 1

Diffraction pattern for mixture of BL and SLG at energy $E=194$ eV. The BSC forms around the (00) and G(10) but not the SiC(10) spots. Several spots are marked including the 5/13 spot and the two neighboring spots forming a three-spot cluster. Its evolution tracks the transition from BL to SLG.

Figure 2

(a) 1D scan of the specular spot along the SiC direction $\left[1\overline{2}10\right])$, at $E=148$ eV. The FWHM of the narrow component is 0.5% BZ and of the BSC is 33% BZ which corresponds to a distance $\sim 3a_{\mathrm{g}}$. The ratio of the integrated narrow component to the sum of narrow and BSC areas is ∼0.65. (b) 1D scan of the specular along the graphene direction, and $E=132$ eV. The FWHM of the G(10) narrow component is 2.25% BZ and of the BSC component is 80% of the FWHM of the (00) spot at the center of the scan. The integrated areas ratio of the narrow to the sum of the areas of both components is 0.5.

Figure 3

(a) 1D profiles of the 00 spot collected every 4 eV from 100 to 200 eV. The color range is shown to the right (from $2\times {10}^6$ to ${10}^3$). (b) 1D profiles of the G(10) spot collected every 4 eV from 100 to 200 eV. The color range is shown to the right (from $1\times {10}^5$ to $5\times {10}^2$). The maxima are shifted with respect to the maxima of the (00) in (a), because of the contribution of the nonzero parallel wavevector component of the G(10) spot. For both spots the maxima of the narrow and BSC components follow each other which is not consistent with scattering interference from adjacent terraces as the origin of BSC. [The initial bending of the Gr(10) spot is related to the nonlinearity of SPA-LEED at the edge of BZ and at lower energy.]

Figure 4

Integrated areas of the narrow component (cyan) and the BSC (blue) plotted as a function of the scaled momentum transfer $s=\left(\mathrm{\Delta }{k}_z\right)/(2\pi /d_{\mathrm{g}})$ (shown at the bottom, with the corresponding energy at the top). The two areas have the same variation with energy while they should be anticorrelated if the origin of BSC was textbook scattering. The fraction of the narrow component defined by the ratio $R_{00}=\frac{A_{\mathrm{nar}}}{A_{\mathrm{nar}}+A_{\mathrm{bro}}}$ is plotted in black with the maxima close to half-integer values of $s=5.5,6.5,7.5$. Maxima are expected for integer values of $s$ if the BSC was originating from interference between adjacent terraces.