2.1 Formation mechanism of graphene directly synthesized on arbitrary substrate by C-ion implantation
Figures 1a1-1a3 schematically illustrate our graphene growth processes. A 100 nm-thickness Ni layer was evaporated on arbitrary substrates and then implanted under room temperature with 70 keV C ions with the pre-determined fluences, as presented in Figure 1a1 . According to the Monte Carlo stopping and range of ions in matter (SRIM) code, the projected area of the implanted C ions in Ni is about 80 nm with a range of ~46 nm (standard deviation). The fluence of implanted C ions and the lateral uniformity could be accurately controlled by means of a 4-corner Faraday cup assembly, and the fluences of 4×1015 and 8×1015atoms/cm2 are selected to achieve uniform single and double graphene layer, respectively. Following the C ion implantation, 150 nm Cu film was placed on top of the Ni layer by e-beam evaporation where the substrate was kept at room temperature (Figure 1a2 ). The graphene with the expected thickness is obtained at the interface of the Cu-Ni alloy and the objective substrate after the thermal treatment (1000 ℃ for 10 min under 10-5 mbar) of the Cu/Ni dual metal substrates (Figure 1a3 ). Afterward, the Cu-Ni alloys are easily removed using thermal release tape, leaving the graphene on the arbitrary substrate. The current strategy can directly synthesize graphene on arbitrary substrates, bypassing the undesired post-synthesis transfer process for further device fabrication. Besides, considering C ions are pre-implanted into the Ni layer on the objective substrate before the thermal treatment, the experimental conditions, especially the gas sources operated for the annealing process, become less critical as compared in other graphene synthesis processes where hydrogen capture of oxygen from metal oxides is needed to facilitate graphene formation at metal surfaces.
To investigate the forming process of graphene on an arbitrary substrate (in this case, SiO2) through ion implantation, secondary ion mass spectrometry (SIMS) is employed to evaluate the depth distributions of C, Cu, and Ni in the Cu/Ni dual metal on SiO2 substrates, as exhibited in Figures 1b1-1b3 . After the C ion implantation into the Ni layer, the implanted C ions present a Gaussian-like distribution in the Ni layer (Figure 1b1 ).[23,34-35] The implantation energy is selected to keep the implanted C ions within the Ni layer based on their projected ranges, as schematically illustrated in Figure 1c1 . Note that the Si signal corresponding to SiO2 substrates is also shown while the O signal is omitted to show better clarity for the interested species. Figure 1b2 represents the SIMS result of the deposition of 150 nm Cu film on top of the Ni layer, showing that Cu, Ni, and C signals emerge at their respective locations in reference to the surface (as schematically shown in Figure 1c2 ). As the top Cu film is thicker compared to the bottom Ni layer of ~100 nm, when Cu/Ni inter-diffusion proceeds during the thermal annealing, the thinner Ni is diluted by Cu and eventually disappears entirely into the Cu-dominant Cu-Ni alloy. Development of Cu-Ni alloy is verified through Ni showing up near the surface (Figure 1b3 ) after 10 min under 1000 ℃. As is well-known that Ni has a neutral C solubility of 0.4~2.7 at% at 600~1300 ℃,[12] while the solubility of C in Cu is more than two orders of magnitudes smaller and thus negligible (<0.003 at%) at 1000 ℃.[13] Hence, the C solubility in the afresh formed Cu-dominant Cu-Ni alloy is expected to decrease significantly when inter-diffusion of Ni and Cu proceeds to form the Cu-Ni alloy. Therefore, C atoms are driven towards the interface of the Cu-Ni alloy and the objective substrate, and finally converted into graphene structure promoted through the catalysis impact of the Cu-Ni alloy,[23,32,34,36] as illustrated schematically in Figure 1c3 .[7,23,31] The optimal growth conditions of monolayer and bilayer graphene films synthesized by C ion implantation into the Cu/Ni dual metal substrates were investigated systematically and are detailed in SupplementaryFigures S1-S2 .