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Due to the need of integrated circuit in the current silicon technology, the formation of graphene on Si wafer is highly desirable, but is still a challenge for the scientific community. In this context, we report the direct growth of graphene on Si(111) wafer under appropriate conditions using an electron beam evaporator. The structural quality of the material is investigated in detail by reflection high energy electron diffraction, Auger electron spectroscopy, X-ray photoemission spectroscopy, Raman spectroscopy, high resolution scanning electron microscopy, atomic force microscopy, and scanning tunneling microscopy. Our experimental results confirm that the quality of graphene is strongly dependent on the growth time during carbon atoms deposition.