Diffraction paradox reveals perfection in graphene

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(top) 2-d diffraction pattern of graphene grown on SiC shows sharp spots on a very broad background around the (00) and G(10) spots. (bottom) 1-d scan of the (00) spot along [12 ̅10] shows the broad component with unusually large FWHM  that  unexpectedly correlates to forming a highly uniform film.
(top) 2-d diffraction pattern of graphene grown on SiC shows sharp spots on a very broad background around the (00) and G(10) spots.
(bottom) 1-d scan of the (00) spot along [1210] shows the broad component with unusually large FWHM  that  unexpectedly correlates to forming a highly uniform film.

In order to realize 2-d quantum materials potential, it is important to establish the best growth conditions so they are uniform, defect-free and extend over large domains. Paradoxically, we found that the growth of high quality graphene is characterized by very unusual electron diffraction profiles. Contrary to conventional understanding that uniform films should have only very narrow spots, graphene shows a very broad Bell Shaped Component (BSC) with Full-Width-Half-Maximum nearly 50% of the Brillouin Zone. Energy dependent profile measurements do not follow the standard variation from constructive to destructive interference,as the scattering phase changes between adjacent terraces on the surface. Such BSC have been in the graphitization literature for at least 25 years but its significance has been ignored. The features are present in all studies where characterization of key graphene properties,such as band structure and transport properties, have been performed. Here we show that it is related to electron confinement in graphene, with single layer precision over the mesoscale. Therefore, BSC is a key indicator of the perfection of the 2-d growth, regardless of the material. Quantifying these phenomena will provide a straightforward diagnostic to determine optimal growth conditions for other 2-d materials such as hex-BN, silicene, germanene, and borophene.

S Chen, MH von Hoegen, PA Thiel, MC Tringides, “A diffraction paradox: An unusually broad diffraction background signals high quality graphene” Phys. Rev. B 100, 155307 2019; DOI: 10.1103/PhysRevB.100.155307