## 3 Results and Discussion
The etched fit densities for h-BN monolayers on copper foils without ECP and with ECP were estimated to be 1.3 \(\times\) 108/cm\({}^{2}\) and 3 \(\times\) 107/cm\({}^{2}\), respectively (Figure 3c). In addition, etched to total area ratios were obtained by an image processing program (Image J 1.52p, National Institute of Health, Bethesda, MD, USA) based on a randomly selected area (indicated by a white rectangle in Figure 3a,b) of the AFM images of both samples [31]. The etched to total area ratios of h-BN monolayers on copper foils without ECP and with ECP were 23% and 3%, respectively. It is obvious that the h-BN monolayer on copper foils with ECP had a lower etched pit density with a smaller etched area, indicating that the ECP methods significantly reduced the defect density. Figure 2: (**a**) Raman spectra of h-BN monolayers on copper foils without ECP (black line) and with ECP (red line). (**b,c**) show the 1s core level XPS spectra of boron and nitrogen of h-BN monolayers on copper foils without ECP and with ECP, respectively. We also evaluated contact angles of water on native copper foils, an h-BN monolayer on copper foil without ECP, and one with ECP, respectively (Figure 3d-f). Contact angle analysis is a fast and straightforward technique for estimating the defect density of 2D materials such as graphene and h-BN monolayers [32; 33; 34]. The measured contact angle of water on a native copper foil was 46.1\({}^{\circ}\), which was low due to the high surface energy between water and copper foil. The contact angles were higher in the other samples as the copper substrates were passivated by the h-BN monolayers; they were found to be 67.4\({}^{\circ}\) without ECP and 80.1\({}^{\circ}\) with ECP. It is well known that h-BN is totally charge neutral and nonpolar, satisfying the octet rule. However, when the defects are created, the resulting dangling bonds break the charge neutrality. Because of this, defects in h-BN monolayer contribute to a change in the contact angle by increasing the surface energy and surface polarities [35]. The h-BN monolayer on the copper foil without ECP had higher surface energy than that with ECP, implying that the defect density of h-BN monolayer was higher on the copper foil without ECP than that with ECP. This result is consistent with our discussion of defect density based on the results of SEM, Raman spectroscopy, and AFM analyses. WVTR was measured with varying time for bare polyethylene terephthalate (PET), an h-BN monolayer without ECP on PET, an h-BN monolayer with ECP on PET, and graphene on PET by a commercial MOCON's proprietary AQUATRAN model 3 WVTR analyzer (Figure 4a). Recently, we studied the gas barrier properties of graphene grown on copper foils with ECP treatment [7]. Here, we compare the gas barrier performance of h-BN monolayers and graphene. All four samples arrived at a steady state of WVTR within 1 day. The WVTR values of h-BN monolayers without and with ECP were measured to be, respectively, 0.798 and 0.774 g m\({}^{-2}\) day\({}^{-1}\). These values were slightly higher than that of graphene on PET (0.728 g m\({}^{-2}\) day\({}^{-1}\)), but significantly lower than that of bare PET (1.101 g m\({}^{-2}\) day\({}^{-1}\)). The gas barrier properties of h-BN are slightly lower than that of graphene, but after a long term, we believe that gas barrier properties of h-BN will be improved than that of graphene. This is because h-BN is not easily oxidized by the absence of itinerant electron. Between h-BN monolayers, the one with ECP showed a lower WVTR value than that without ECP. We expect that the lower WVTR value of the h-BN monolayer with ECP is associated with its reduced defects and grain boundaries. The results indicate that the h-BN monolayer with ECP successfully acted as a protective layer for PET against  
Figure 3: AFM images of the surface of h-BN monolayers on copper foils (**a**) without ECP and (**b**) with ECP after a film-induced frustrated etching. (**c**) Etched pit density observed from AFM images.