## 3 Direct ALD on Pristine Epitaxial Graphene  
Early studies on thermal ALD of high-k insulators (like Al\({}_{2}\)O\({}_{3}\) or HfO\({}_{2}\)) on pristine EG samples typically resulted in a non-uniform coverage, with poor or no oxide nucleation in the vicinity of the step edges [34; 38]. As an example, [PERSON]. et al. [38] investigated direct thermal ALD of Al\({}_{2}\)O\({}_{3}\) on EG grown at 1650 \({}^{\circ}\)C in Ar (p = 900 mbar) [3]. Figure 4 illustrates the morphologies of the Al\({}_{2}\)O\({}_{3}\) films obtained after 500 ALD cycles (corresponding to 50 nm Al\({}_{2}\)O\({}_{3}\)) at different deposition temperatures of 200 \({}^{\circ}\)C (a), 300 \({}^{\circ}\)C (b) and 350 \({}^{\circ}\)C (c), using trimethylaluminum (TMA) as the aluminum source, and water as the oxidant. Poor or no oxide nucleation was observed in the vicinity of the step edges. As discussed in the Section 2, samples with 1 L EG on the (0001) terraces typically exhibit 2 L or few layers EG stripes at the step edges between terraces [3]. Hence, the Al\({}_{2}\)O\({}_{3}\) uncovered areas were associated by the authors to the presence of 2 L or few layer EG underneath. However, no clear explanation of the different ALD nucleation and growth behavior on 1 L and 2 L EG was provided. Similarly, [PERSON] et al. [34] reported that the direct thermal ALD of Ta\({}_{2}\)O\({}_{5}\), and TiO\({}_{2}\) results in non-uniform coverage of EG up to a maximum deposition temperature (300 \({}^{\circ}\)C). More recently, [PERSON] et al. [21] employed highly uniform 1 L EG samples (>98% monolayer coverage) as substrates for direct thermal ALD of Al\({}_{2}\)O\({}_{3}\) at a temperature of 250 \({}^{\circ}\)C with TMA and H\({}_{2}\)O precursors. Figure 5 shows the morphological and structural characterization of an Al\({}_{2}\)O\({}_{3}\) film obtained after 190 deposition cycles, corresponding to a nominal film thickness of 15 nm, evaluated from the 0.08 nm/cycle deposition rate on a reference silicon substrate. Figure 5a depicts a representative morphological image by AFM on a 20 \(\upmu\)m \(\times\) 20 \(\upmu\)m scan area. The Al\({}_{2}\)O\({}_{3}\) film is conformal with the topography of the EG/4H-SiC surface, except for some small depressions showing the same elongated shape of the 2L graphene patches (see, for comparison, Figure 3). A high resolution cross-sectional TEM image of the as-deposited Al\({}_{2}\)O\({}_{3}\) film is reported in Figure 5b, where the 1 L EG plus the underlying BL can be clearly identified, and the amorphous Al\({}_{2}\)O\({}_{3}\) layer shows uniform contrast, indicating a uniform Al\({}_{2}\)O\({}_{3}\) density. The measured Al\({}_{2}\)O\({}_{3}\) thickness was 12 nm, which is thinner than the nominal one and was ascribed to a lower growth rate of Al\({}_{2}\)O\({}_{3}\) on EG surface in the early stages of the deposition process. Raman spectroscopy measurements were carried out both on the virgin EG sample and after the Al\({}_{2}\)O\({}_{3}\) deposition, in order to evaluate the changes induced by the thermal ALD process at 250 \({}^{\circ}\)C on the structural quality and doping/strain of the underlying EG. Two representative Raman spectra for the two cases, respectively, are reported in Figure 5c. The characteristic G and 2D peaks of graphene exhibit single Lorentzian shape, and the FWHM of the 2D peaks in these representative spectra are consistent with the 1 L nature of EG [52]. The small changes in the positions of the G and 2D peaks after the Al\({}_{2}\)O\({}_{3}\) deposition indicate that the ALD process did not significantly affect the doping and strain of the EG. The features in the 1200-1500 cm\({}^{-1}\) range were related to the interfacial BL, whereas  
Figure 4: AFM images of Al\({}_{2}\)O\({}_{3}\) grown directly on the pristine EG surface by 500 thermal ALD cycles of TMA/water (i.e., 50 nm Al\({}_{2}\)O\({}_{3}\)) at different temperatures: (**a**) 200 \({}^{\circ}\)C, (**b**) 300 \({}^{\circ}\)C and (**c**) 350 \({}^{\circ}\)C. Images adapted with permission from Ref.