# Electrochemical Deposition of Copper on Epitaxial Graphene
## 3 Results and Discussion
\tag{1}\]  
where \(t\) and \(t_{max}\) are the elapsed and maximum times, respectively; \(j_{inst}\), \(j_{prog}\) and \(j_{max}\) are the current densities for instantaneous and progressive nucleation, and maximum current density, respectively. The initial kinetics of the copper electrodeposition obeys the three-dimensional instantaneous nucleation model (Figure 3b), which is likely the general mechanism for the metal's electrodeposition on epitaxial graphene monolayer, since the same growth kinetics was observed during electrodeposition of lead [101] and mercury [80]. This implies that metal electrodeposition on epitaxial graphene happens on a limited number of active sites. The diffusion coefficient of copper ions as a reactant can be estimated from the current transients using the following relationship [102]:  
\[D=\frac{j_{max}^{2}\ t_{max}}{0.1629\cdot\left(z\text{-}F\text{-}C\right)^{2}} \tag{2}\]  
where the \(t_{max}\) is maximum time, corresponding to the maximum current \(j_{max}\), \(z\) is the valency of the metal ion (+2 in the case of divalent species), \(F\) is the Faraday constant (96 485 C/mol), \(C\) is the reactant concentration (\(10^{-7}\) mol/cm\({}^{3}\)). The values of the diffusion coefficient were \(4.97\times 10^{-5}\) cm\({}^{2}\)/s and \(5.32\times 10^{-5}\) cm\({}^{2}\)/s (at \(-0.39\) and \(-0.40\) V, respectively), which is higher than reported for glassy carbon (\(\sim\)0.4-\(0.8\times 10^{-5}\) cm\({}^{2}\)/s) [3]. The nuclei population density on epitaxial graphene monolayer was determined by using the following formula:  
\[N_{0}=0.065\Big{(}\frac{1}{8\pi CV_{m}}\Big{)}^{1/2}\Big{(}\frac{nFC}{I_{max}t _{max}}\Big{)}^{2} \tag{3}\]  
where \(n\) is the number of electrons involved, \(V_{m}\) is the molar volume. \(N_{0}\) was estimated to be as high as a \(1.55\times 10^{6}\) cm\({}^{-2}\) and \(1.38\times 10^{6}\) cm\({}^{-2}\) (at \(-0.39\) and \(-0.40\) V, respectively), which is comparable with data from the literature [3]. The change of the deposition potential towards more negative values led to the appearance of monotonous current transients (Figure 3a) assigned to the loss of the diffusion control and the appearance of chemisorption phenomena due to the double-layer effect at the electrode surface [103], which can be well described by the modified Elovich equation [103]:  
\[J=\frac{A}{B+t}+j_{L} \tag{4}\]  
where \(A\), \(B\) and \(j_{L}\) are fitting parameters. It was revealed that that the best fit can be achieved by using the following parameters as follows: \(A=-0.027\) mC/cm\({}^{2}\), \(B=0.3\) s and \(j_{L}=-0.05\) mA/cm\({}^{2}\) (Figure 3c). To better understand the nature of the interaction between electro-reduced species with graphene under realistic conditions, we then simulated the two-stage reduction process by (i) adding one electron directly to the Cu\({}^{2+}\) ion in the [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{2+}\) complex adsorbed on graphene to form [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{1+}\) and (ii) adding one more electron to the resulting [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{1+}\) complex in order to form the neutral complex [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\). The result of the structural optimization is shown in Figure 4a. As a direct consequence of the reduction process, the six-coordinated water complex is broken, and all complex's components become weakly bonded to each other. Having a positive charge (according to [PERSON] population analysis) of \(+0.29e^{-}\), the Cu atom tends to occupy the top site (directly above the C atom) of the graphene, with an adsorption height of 2.7 A. The results of the energy decomposition analysis,  
Figure 3: (**a**) Potentiostatic current transients recorded on epitaxial graphene recorded at the cathodic potential pulses of different amplitudes (resting potential 0.5 V; 0.1 M HCl\({}_{0}\), 0.1 mM Cu\({}^{2+}\)).