# Electrochemical Deposition of Copper on Epitaxial Graphene
## 4 Conclusions  
In this work, we have clarified the fundamental mechanisms behind the Cu electroreduction and kinetics at the epitaxial graphene/4H-SiC (0001) working electrode. We demonstrated and discussed the results of cyclic voltammetry, chronoamperometry, and DFT calculations in order to unravel the behavior of copper. The significant overpotential, typical of general faradaic phenomena, on epitaxial graphene yielded a bi-electronic reduction in copper ions bypassing Cu\({}^{1+}\) intermediates. The dynamic electrochemical measurements revealed an instantaneous nucleation mechanism, implying a limited number of active sites available for the deposit's growth, which seems to be akin to other metal (e.g., Pb, Hg and Li) electrodeposition on epitaxial graphene. In particular, it was revealed that the electrodeposition of metallic copper was possible only at two potentials (\(-0.39\) and \(-0.4\) V), as evidenced by the shape of the corresponding current transients. The estimated diffusion coefficient (\(-4.97\)-\(5.32\times 10^{-5}\) cm\({}^{2}\)/s) from the electrolyte to the EG electrode and the nuclei population density (\(-1.38\)-\(1.55\times 10^{6}\) cm\({}^{-2}\)) is consistent with data from the literature and indicates that the epitaxial graphene electrode is suitable for fast and Cu electroplating. By performing DFT calculations, we modelled the diffusion of the Cu on graphene and showed that, independently of the diffusion paths, there is a small barrier (35 meV) for the surface migration of Cu, which disappears in the presence of another Cu atom in close proximity to the first one. This favors the mass transfer within the diffusion zones and a fast nucleation process. The obtained results shed light on the nature of the copper electroreduction process at the epitaxial graphene and may facilitate the development of real applications based on copper-graphene nanohybrid materials.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/4/1405/s1](http://www.mdpi.com/2076-3417/10/4/1405/s1)]([http://www.mdpi.com/2076-3417/10/4/1405/s1](http://www.mdpi.com/2076-3417/10/4/1405/s1)), Figure S1: The decrease of the computed electron acceptor reactivity with the addition of the water molecules into the substrate.  
Figure 5: Potential energy curves for the movement of metallic copper atoms along the path #1 (**a**) and path #2 (**b**) in the presence and in the absence (marked by cross) of another copper atom. The height of the Cu atom was set to 2.723 Å. Note: the potential energy curve was normalized to the total energy of the system with a copper atom located at the top site of the graphene (energetically the most favorable site for copper adsorption); \(t_{1}\), \(b_{1}\) and \(h_{1}\) designate the possible sites (top, bridge and hollow, respectively) that are available for copper atom adsorption.  
the aquo complexes. Figure S2: The change in Hirshfeld charge on Cu species with the addition of the water molecules into the aquo complexes.  
Conceptualization, I.S. and M.V.; methodology, I.S. and M.V.; software, I.S.; validation, I.S., M.V. and R.Y.; formal analysis, I.S.; investigation, I.S. and M.V.; resources, I.S., M.V. and R.Y.; data curation, I.S.; writing--original draft preparation, I.S.; writing--review and editing, I.S., M.V. and R.Y.; visualization, I.S.; supervision, R.Y.; project administration, R.Y.; funding acquisition, I.S. and R.Y. All authors have read and agreed to the published version of the manuscript.  
The authors would like to thank the Swedish Foundation for Strategic research (SSF) for financial support through the grants GMT14-0077 and RMA15-024. I.S. acknowledges the support from Angpanneforeningens Forskningsstitles (Grant 16-541). R.S. acknowledges financial support via VR grant 2018-04962.  
The authors declare no conflict of interest.