## 3 Results and Discussion  
Figure 1 shows SEM images of h-BN monolayers on copper foils with and without ECP treatment. In both cases, h-BN monolayer fully covered the copper foils after 90 s' growth (Figure 1a,b). In these samples, wrinkles were commonly observed for thermal stress minimization. They could stem from the nucleation of defects on the step edges of Cu terraces during cooling process, and their presence is indirect evidence of the successful continuous growth of h-BN monolayer [20]. Once the copper foils were fully covered by h-BN monolayers, it was not possible to analyze the difference in the growth of h-BN monolayers on the two copper foil samples with and without ECP. To investigate how ECP influences the growth of an h-BN monolayer, we grew h-BN monolayers for a shorter time: 60 s (Figure 1c,d). At the initial stage of growth, we could detect small domains as well as large ones in both samples. The shape of the small domains was random, while that of the large domains was triangular. The areal number density of domains was noticeably different in the two cases; it was higher on copper foil without ECP than with ECP. The root-mean-square (RMS) roughness of the copper foils was measured by AFM (Figure S3). The RMS roughness of copper foils with ECP was measured to be 37 nm while that of copper foils without ECP was 78 nm, which is consistent with SEM images. It is well known that surface irregularities such as wrinkles,  
Figure 1: Scanning electron microscopic images of h-BN monolayers synthesized on copper foils (**a,b**) for 90 seconds and (**c,d**) for 60 seconds; (**a,c**) are without ECP treatment and (**b,d**) are with ECP treatment. steps, grain boundaries, and defects have much higher surface energy than a flat surface, and such features could serve as nucleation sites [21; 22; 23]. Hence, the higher irregularity of the surface of copper foils without ECP caused a higher areal nucleation density of h-BN monolayer than copper foils with ECP [7]. If the areal number density of initial domains is higher, it will lead to a higher defect density when the domains eventually merge as the growth proceeds [24; 25; 26]. As a result, h-BN monolayers grown on copper foils with ECP are expected to show better gas barrier performance owing to a lower defect density. Figure 2a shows Raman spectra of the h-BN monolayers grown on copper foils without ECP (black line) and with ECP (red line). The peaks observed at 1369.8 cm\({}^{-1}\) from both the samples are indicative of an h-BN monolayer [27; 28]. Typically, to compare the crystallinity of h-BN monolayers, the intensities of the spectra are compared. However, it would be hard to compare the crystallinity directly using this method because of the scattering of the laser spot by the surface roughness of the copper foils. Instead, we compared the crystalline quality of h-BN monolayers on copper foils based on the full width at half maximum (FWHM). The FWHM values of h-BN monolayer grown on copper foils without ECP and with ECP were \(\sim\)25.02 cm\({}^{-1}\) and \(\sim\)17.41 cm\({}^{-1}\) respectively, indicating that the crystallinity of h-BN monolayers on copper foils with ECP was higher than that of h-BN monolayers on copper foils without ECP. To further confirm the growth of the h-BN monolayers, we measured the 1s core level XPS spectra of boron and nitrogen in the h-BN monolayers on copper foils with and without ECP (Figure 2b,c). From both samples, peaks in the XPS spectra were observed at \(\sim\)190.8 eV, which corresponds to the binding energy of boron atoms [29; 30]. Peaks were also observed at \(\sim\)398.2 eV in both samples. This energy corresponds to the binding energy of nitride atoms [29; 30]. To investigate the spatial distribution of the defects, the surface morphology of h-BN monolayers on copper foils without ECP and with ECP was examined by AFM (Figure 3a,b). Before the measurements, a film-induced frustrated etching (FIFE) was completed to reveal the spatial distribution of the defects.