# Study of Implantation Defects in CVD Graphene by Optical and Electrical Methods
## 4 Discussion and Conclusions  
The probability of creating one defect by one implanted ion is relatively small. The fitting of the Raman \(I(D)/I(G)\) relation shows that this probability is 0.0025 for He\({}^{+}\) and 0.042 for N\({}^{+}\) ions. These small values suggest that defects have to be created by a direct collision of the falling ion with a carbon atom in the graphene lattice. This is supported by the \(I(D)/I(D^{\prime})\) ratio which is close to the value of 6-7. This value suggests that vacancy like defects play an essential role in the ion implantation process [21; 22]. The Stopping and Range of Ions in Matter (SRIM) code was used for simulation of vacancy generation in the graphene lattice under the assumption that removing one carbon atom requires 21 eV [9]. The number of carbon vacancies produced by direct ion collisions are 0.00246 for He\({}^{+}\) and 0.034 for N\({}^{+}\). Thus, the SRIM simulations are close to the experimental results. Therefore, it may be expected that as a result of such collisions vacancies are indeed created. The \(R_{D}\) value established by Hall measurements at 0.75 nm is larger than the size of monovacancy. However, a missing carbon atom with three dangling bonds from graphene of lattice will not be stable. Reconstruction of the whole area may lead to a formation pentagon and polygon structure with one dangling bond. The formation energy of such defect is about 7.5-7.7 eV [26; 27; 28] with relatively low migration barrier of about 1.3-1.5 eV. Hence, the reconstructed monovacancy can migrate creating divacancy. Reconstructed divacancy may form one octahedron and two pentagons in the so called 5-8-5 defect without dangling bonds. Formation energy of such defect is 7.28 eV [29; 30] with migration barrier about 7 eV [26]. Thus, such defect will be neutral and practically immobile. The diameter of such a defect is about 1 nm, which is of the order of the defect size determined in our experiments. Defect radius obtained from Hall measurements was about twice smaller than estimated on the basis of Raman experiments. However, it should be remembered that both methods are based on different physical phenomena and may probe different aspects of the same defect. Charge carrier mobility depends on low energy scattering associated with defect. Thus, the \(R_{D}\) may reflect the core of the defect. The Raman measurements are based on activation of the D mode which is generated in the unaffected graphene outside of the defect in close vicinity to its limit. So, the Raman is probing the graphene area outside the defect boundary and may provide another defect size than obtained from mobility measurements. On the other hand, the distance from the defect limit at which D mode is activated \(r_{A}\)-\(r_{S}\) was after [18] assumed to be 2 nm. However, modification of this distance may affect the defect radius \(r_{S}\) determined from Raman according to applied methodology [18]. The decrease of carrier mobility with the increase of defect density tends to zero for distances between defects of the order of 2 nm. This indicates that for such distances an overlap between defects takes place and leads to hopping transport. This observation supports the conclusion that the size of the ion induced defects is rather far larger than the size of a simple vacancy. Both applied methods Hall mobility and Raman gave basically the same defect size for both applied ions of helium and nitrogen despite a big difference of their atomic masses and very different probability of the defect generation in elastic collisions. It suggests that a certain preferred configuration of the structure of the ion induced defects is created and indicates that the size of this structure is larger than mono- or divacancy. The decrease of the carrier concentration with increasing ions fluences is probably caused by modification of the structure of SiC substrate by implantation. We have a strong experimental evidence that our data are reflecting electrical properties of damaged graphene and not SiC implanted layer.