# Study of Implantation Defects in CVD Graphene by Optical and Electrical Methods
## 3 Results  
### Raman Measurements  
The epi-ready surface of the 6H-SiC (0001) is composed of flat terraces of about several microns separated by narrow step edges. Thickness of graphene covering the 6H-SiC (0001) surface may be determined by Raman spectroscopy. The Raman spectra of pristine graphene consist of two distinctive modes. The first one is the G mode which is a one-phonon mode of wavenumber close to 1580 cm\({}^{-1}\) originating from the center of the Brillouin zone. The other mode is the 2D one, which is a two phonon mode of wavenumber 2700 cm\({}^{-2}\) originating from the K point of the Brillouin zone. The Full Width at Half Maximum (FWHM) of the 2D line may be used as a measure of graphene thickness [17]. The FWHM of the order of 20-30 cm\({}^{-1}\) indicate a graphene monolayer. The increase of the FWHM to 40-70 cm\({}^{-1}\) indicates a bilayer or even three layer graphene. Mapping of the FWHM of the 2D line is shown in Figure 1. It is seen that terraces of the 6H-SiC (0001) surface are covered by graphene monolayer. These terraces are separated by step edges which are covered by bilayer graphene. All our Raman measurements for ion implanted samples have been collected from terraces regions which are covered predominantly by monolayers. Two other lines, the D at wavenumber 1350 cm\({}^{-1}\) and D\({}^{\prime}\) at 1620 cm\({}^{-1}\) show up after implantation. They are so called defect induced Raman modes. Example of the Raman spectrum after ion implantation is shown in Figure 2 and all four D, G, D\({}^{\prime}\) and 2D lines are shown. The intensity ratio of the D and G modes \(I(D)/I(G)\) is a powerful tool for determination of the density of defects generated by ion implantation [18]. Phenomenological model proposed by [PERSON] [18] predicts that the \(I(D)/I(G)\) ratio upon increase of defect density increases, reach maximum and next decreases down to some value. This model may be fitted to the experimental \(I(D)/I(G)\) ratio versus ion fluence. This fitting requires three parameters: the number of defects generated by one incident ion \(N_{D}\), the mean radius of ion induced defect \(r_{S}\), and the mean radius \(r_{A}\) of the graphene surrounding the defect in which D mode of the Raman mode is generated. The circular area of width \(r_{A}-r_{S}\) surrounding the defect consists of graphene neighboring the defect boundary region and thus, is responsible for creation of the D Raman mode. The distance \(r_{A}-r_{S}=2\) nm was taken following [18] for both He\({}^{+}\) and N\({}^{+}\). The best fitting to the semi-empirical relation \(I(D)/I(G)\) versus ion fluence proposed in [18] with experimental data was obtained for the following fitting parameters: \(N_{D}=0.045\) and \(N_{D}=0.0025\) and \(r_{S}=1.34\) nm and \(r_{S}=1.5\) nm for N\({}^{+}\) and He\({}^{+}\) respectively. Figure 1: The spatial map of FWHM (Full Width at Half Maximum) of the 2D Raman mode. The FWHM within 20–30 cm\({}^{-1}\) shown by black color indicates single graphene layer. Figure 2: Example of the Raman spectrum of graphene after He\({}^{+}\) ions implantation with ion fluence 1015 cm\({}^{-2}\). The fitted curves with experimental points are shown in Figure 3. It should be noted that the mean distance between generated defects \(L_{D}\) can be obtained directly from the defect density according to formula \(N_{D}=1/L_{D}{}^{2}\). In addition to the information provided by the intensity of the D line, there are other conclusions which can be drawn from the positions of the G and 2D line. The relation between the 2D and the G line allows to evaluate the carrier concentration and strain in the graphene [19]. Such diagram of the 2D versus G line position for helium ion implantation at three different fluences is shown in Figure 4. Experimental points are arranged along parallel lines (shown in Figure 4 as broken lines) for each implantation fluence. Scatter of points along each line represents the spread of uniaxial strain existing in the graphene layer [20].