From the success of graphene growth on Ni or Cu by chemical vapor deposition (CVD) 1 2 , some variations were introduced to CVD to avoid the use of metallic catalysts 3 4 5 6 7 8 . However, the growth of carbon by chemical methods involves a complex mechanism due to the presence of carrier gases. For example, hydrogen acts as an etching reagent as well as a co-catalyst 9 . In contrast, physical deposition methods such as molecular beam epitaxy (MBE) are useful to understand the growth mechanism of carbon because of the relatively simple kinetics 10 11 12 13 . Experimentally, it has been shown that nanocrystalline graphite (NCG) could be formed on crystalline and amorphous oxides by direct sublimation of carbon 14 15 16 . Although first-principles calculations partly explained that the strong bonding between carbon and oxygen limited the cluster size 14 16 , the growth mechanism is yet to be understood.

So far, carbon MBE has been tried on substrates containing elements from group IV 10 11 12 13 , group V 17 , and group VI 12 14 15 16 . Here, we present the results of carbon MBE on fluorides (where the anion belongs to group VII) and compare them with similar studies on oxides to understand the effect of the anion on the quality of NCG. Since the bonding between carbon and fluorine is much stronger than the bonding between carbon and oxygen, we expected the carbon film to be more amorphous. On the contrary, NCG of good crystallinity was formed on MgF₂, and the cluster size deduced from Raman spectra was even larger than those of NCGs on MgO and sapphire 18 19 . These results show that the quality of NCG does not simply depend on the bond strength of carbon and substrate anion, and imply that the carbon growth mechanism could be more complex than previously thought.

Figure 1 shows the Raman spectra from 3- to approximately 5-nm-thick carbon films grown on various fluorides by MBE. The characteristic peaks of graphitic carbon are well identified in all films: the D peak at approximately 1,350 cm⁻¹ and the G peak at approximately 1,590 cm⁻¹. These and previous studies show that MBE is an effective method for graphitic carbon growth on a wide range of substrates 14 15 16 17 . The degree of graphitization is, however, quite different depending on the cation. In fact, graphitic carbon refers to a wide range of disordered graphite, from NCG to mainly sp ² amorphous carbon. As clarified by Ferrari 20 , the relative strength of D and G peaks alone cannot determine the degree of disorder, and it is the 2D peak at approximately 2,700 cm⁻¹ which distinguishes NCG from amorphous carbon. As shown in Figure 1, the Raman spectra of the carbon film on MgF₂ show a clear 2D peak, indicating that successful NCG growth was accomplished on MgF₂ by carbon MBE. In contrast, the carbon films grown on CaF₂ and BaF₂ can be ascribed to amorphous carbon. As far as we know, carbon MBE on a family of substrates having the same anion has not been reported. Clear understanding of this cation dependence is yet to come, but our results will stimulate systematic studies on other series of substrates and further theoretical investigations.

We will focus on the growth on MgF₂ from now on and compare the results with NCGs on oxides. For a quantitative comparison, the Raman spectra of NCG on MgF₂ were fit by several Lorentzian functions as in 15 (Table 1). Interestingly, the intensity ratios of the D peak and 2D peak to the G peak (I _D/I _G and I _2D/I _G) are larger than those from NCG on MgO. Furthermore, all the peaks are narrower, implying a better crystallinity on MgF₂ (from the comparisons of the full width at half maximum (FWHM) in Table 1 and those in 15 ). The average cluster size, L _a, can be calculated from the relation I _D/I _G = C L _a ², where C = 0.0055 and L _a in Å 20 . From I _D/I _G = 2.7 (Table 1), we get L _a = 22 Å, a slight increase from those on oxides 15 16 . Figure 2 shows a Raman map of the intensity ratio of I _D/I _G over 10 μm². Most regions have I _D/I _G = 2.7 ± 0.1, thus showing a high degree of uniformity. The uniformity is also better than that of NCG on MgO 16 .

Lorentzian functions are used to fit D, G, and 2D peaks. FWHM, full width at half maximum.

All these results indicate that NCG on MgF₂ is less disordered than those on oxides. This is quite surprising if we consider the bond strength of the C-F bond, which is larger than the C-O bond strength 18 19 . The high electronegativity of fluorine even makes the C-F bond partially ionic. From first-principles calculations, we have known that the strong C-O bond limits the cluster size of NCG on sapphire and MgO 14 16 . If that is the whole story, the stronger C-F bond should lead to smaller clusters on MgF₂. Our results against this imply that an important factor is missing in the theoretical understanding of the NCG growth mechanism. Recently, models such as the catalytic role of step edges or the migration of cyclic carbons are good examples of pertinent suggestions 4 21 .

Figure 3 presents XPS results to clarify the carbon bonding characteristics. Similar to previous studies 14 16 , 284.7 ± 0.2 and 285.6 ± 0.2 eV components in C1s spectra are attributed to sp ² and sp ³ bonds 22 , namely, sp ² hybridization of carbon atoms and sp ³ hybridization of C-C or C-H bonds, respectively 23 . The fitting results show that the fraction of the sp ² bond is more than 80%, confirming the NCG formation on MgF₂.

Finally, Figure 4 shows AFM images before and after the NCG growth on MgF₂. Unlike crystalline and amorphous oxide substrates, the mean roughness parameter, R _a, of the MgF₂ substrate is large. The R _a of NCG (2.45 nm over 1 × 1 μm scan) is even larger by an order of magnitude than those NCGs on oxide substrates 14 15 16 . It is not clear why the surface morphology is worse while the Raman spectra indicate a better crystallinity. We hope that the understanding of NCG growth on MgF₂ can lead to better NCG or possibly graphene growth on other (flat) dielectrics.

In summary, we have grown graphitic carbon on fluoride substrates, expanding the application of carbon MBE into group VII anions. While amorphous carbons were formed on CaF₂ and BaF₂, nanocrystalline graphite of good crystallinity was formed on MgF₂ despite the strong bonding between carbon and fluorine. In comparison to similar studies on MgO, the effect of the substrate anion on the quality of NCG contradicts the expectation based on the bond strength between carbon and the anion. Further systematic studies and theoretical investigations are encouraged to understand the carbon growth mechanism by MBE.

AFM: Atomic force microscopy; CVD: Chemical vapor deposition; FWHM: The full width at half maximum; MBE: Molecular beam epitaxy; NCG: Nanocrystalline graphite; XPS: X-ray photoelectron spectroscopy.

The authors declare that they have no competing interests.

SKJ carried out the carbon molecular beam epitaxy experiments and X-ray photoelectron spectroscopy. JHL carried out the atomic force microscopy measurements. YSK characterized the thin films by Raman spectroscopy. SHC designed the experiments and wrote the manuscript. All authors read and approved the final manuscript.