# Study of Implantation Defects in CVD Graphene by Optical and Electrical Methods
## 3 Results
### Electrical Measurements  
The Hall measurements have been performed after each step of ion implantation. Carrier concentration (holes) versus defect density after implantation of both helium and nitrogen ions is shown in Figure 5. It should be noted that defect density was determined from ion fluencies and ND values estimated using Raman data as was presented in Figure 3. In addition to the points obtained from electrical measurements there are also points which were determined from Raman measurements presented in Figure 5. It can be seen that there is an agreement between electrical and optical measurements for both types of ions. The carrier concentration is affected by implantation and decreases by factor of 2 for the highest defect concentration. This suggest that the decrease of hole concentration versus defect density is probably connected with defects generated inside of SiC substrate, which acts as deep donors, and therefore create traps of holes from the graphene layer. The dependence of inverse of carrier mobility versus defect density is a linear function as shown in Figure 6. This is an indication that the main scattering mechanism is connected to defects generated by ion implantation. The slope of this dependence is constant and provides information about the radius of the defect. The same slope for N\({}^{+}\) and He\({}^{+}\) implanted ions indicates that the carrier scattering centres created by ion implantation have the same radius \(R_{D}\) for both ions. However, the logarithmic dependence of slope on radius of defect given in [23; 24; 25] assures that different defects contribute in a similar way. Equation (1) given in [23; 24; 25] for dependence of carrier mobility in graphene on scattering on neutral centres allows to estimate the radius of generated defects:  
\[1/\mu=(\tau\mathrm{h}N_{D})/(2e\ln^{2}[(\tau n)^{1/2}\;R_{D}]) \tag{1}\]  
where \(\mu\) is the mobility of holes, \(N_{D}\) is the ion induced defect density established from the Raman measurements, \(n\) is the hole concentration determined from the electrical measurements, \(R_{D}\) is a radius of defect which acts as a scattering centre. First of all, a very good agreement with theoretical model suggests that the main scattering centre induced by ion implantation are indeed neutral centres. Defect radius \(R_{D}=0.75\) nm: obtained from Hall measurements was found to be smaller than the one estimated on the basis of Raman experiments and will be discussed later on. Figure 5: Hole concentration \(n_{p}\) versus defect density obtained from Hall (diamonds) and from Raman measurements (squares) after nitrogen (solid points) and helium (open points) ion implantation. The carrier mobility versus defect distance established from defect density is shown in Figure 7. It can be seen that for well separated defects (above 50 nm) the ion implantation has a small effect on mobility value. The value of carrier mobility stays close to the initial 3000 cm\({}^{2}\)/Vs. For defect separation bellow 50 nm a strong decrease of mobility with increase of fluence of implanted He\({}^{+}\) and N\({}^{+}\) is observed. The mobility decreases by almost two orders of magnitude, which indicates that the main scattering mechanism is related to defects generated by ion implantation. It should be noted that there is no difference between N\({}^{+}\) and He\({}^{+}\) implantation which indicates that defects generated by N\({}^{+}\) and He\({}^{+}\) have the same nature. Moreover, a very good compliance between the effects of both applied ions suggests a correct estimation of the ion defect efficiencies for both nitrogen and helium ions determined from Raman measurements. The region of mobility for high implanted fluences and thus for a small distance between defects shows that for \(L_{D}\) close to 2 nm the mobility drops to zero. This is a clear indication that for distance between defects of about 2 nm a transition to hopping regime takes place.