# Structural Modifications in Epitaxial Graphene on SiC Following 10 keV Nitrogen Ion Implantation
## 3 Results
### Raman Spectroscopy
At fluence of 1 \(\times\) 10\({}^{14}\) ions/cm\({}^{2}\), there is a significant broadening of FWHM of D and 2D peaks. This marks a clear indication of the onset of stage II [36]. [PERSON] et al. simulated phenomenological model and gave the relation between I(D)/I(G) and the average distance between defects represented as L\({}_{\text{D}}\) as shown below [39]. \[\frac{\text{I(D)}}{\text{I(G)}}=C_{\text{A}}\ \frac{\left(r_{A}^{2}-r_{S}^{2} \right)}{\left(r_{A}^{2}-2r_{S}^{2}\right)}\left[e^{-m_{S}^{2}/L_{\text{D}}^{ 2}}-e^{-\pi(r_{A}^{2}-r_{S}^{2})/L_{\text{D}}^{2}}\right] \tag{1}\]  
where r\({}_{\text{A}}\) = 3.1 nm and r\({}_{\text{S}}\) = 1 nm are the radii of the activated area and the structurally disordered area. Details of activated and disordered area are mentioned further by [PERSON] et al. [17]. The constant C\({}_{\text{A}}\) = 4.2 which depends on the laser excitation energy (in this work it is 2.33 eV) and the maximum possible value of I(D)/I(G). The I(D)/I(G) were estimated from the results obtained by Raman spectroscopy (Figure 2) and L\({}_{\text{D}}\) was calculated in graphene using the above equation. The Equation (2) below shows the relation between L\({}_{\text{D}}\) and defect density represented as n\({}_{\text{D}}\). \[n_{\text{D}}=10^{14}/\pi\,\text{L}_{\text{D}}{}^{2} \tag{2}\]  
The \(n_{\text{D}}\) was estimated using Equation (2). Table 2 tabulates the values of I(D)/I(G), L\({}_{\text{D}}\) and \(n_{\text{D}}\) at different fluences in the ion-implanted samples of EG/SiC. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{3}{c}{**N\({}^{+}\) Ion Implantation (10 keV)**} \\ \cline{2-4}  & **I(D)/I(G)** & **L\({}_{\text{D}}\) (nm)** & **\(n_{\text{D}}\times 10^{10}\) (cm\({}^{-2}\))** \\ \hline Pristine & 0.27 & 22.47 & 6.31 \\ Fluence & & & \\ \(1\times 10^{12}\) ions/cm\({}^{2}\) & 0.85 & 10.85 & 27.05 \\ \(5\times 10^{12}\) ions/cm\({}^{2}\) & 1.25 & 8.68 & 42.26 \\ \(1\times 10^{13}\) ions/cm\({}^{2}\) & 2.10 & 5.96 & 89.65 \\ \(5\times 10^{13}\) ions/cm\({}^{2}\) & 3.00 & 3.05 & 342 \\ \(1\times 10^{14}\) ions/cm\({}^{2}\) & 2.70 & 2.85 & 393 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intensity ratios of D and G peaks (I(D)/I(G)), mean distance between defects in graphene (L\({}_{\text{D}}\)) and defect density (\(n_{\text{D}}\)) in N\({}^{+}\) ion-implanted EG/SiC. Table 2 shows the rise in the defect density with the increase of fluence. Figure 2 shows that the 2D peak is positioned at \(\sim\)2730 cm\({}^{-1}\) in the pristine sample. Besides reduction in the 2D peak intensity with the increasing fluence, we also observed a red shift of the 2D peak (Figure 2) in the ion-implanted samples. The 2D peak is fitted with a Lorentzian curve and we observed that the 2D peak centered at 2730 cm\({}^{-1}\) in the pristine sample shifted to 2680 cm\({}^{-1}\) in the highest implanted fluence. This red shift of the 2D peak is because of relaxation of compressive strain following ion implantation as pristine EG is initially under compressive strain. Earlier studies showed that following electron beam implantation a red shift in the 2D peak is due to tensile strain or due to relaxation of compressive strain [40]. The structural modifications in the 4H-SiC substrate was explored using Raman spectroscopy. Defects in graphene appear due to a combination of direct collision of the incident ions with graphene atoms and due to the impact of indirect collision of the substrate atoms [6]. Thus, it is essential to investigate defects generated in SiC as well. Two prominent peaks in SiC Raman spectra are FTO (2/4) at 776 cm\({}^{-1}\) and LO at 965 cm\({}^{-1}\)[41]. Figure 3a shows the presence of these prominent SiC peaks in the Raman spectra. Figure 3a indicates a decrement in the intensity of FTO (2/4) and LO with the rise in fluence, which is similar to that reported earlier in ion irradiated SiC [42]. C sub lattices has displacement energy of 20 eV and Si has of 35 eV in the SiC lattice.