## 2 Results
### Production of VO Defect Versus C Concentration  
Figure 9 shows the production of the VO defect as a function of the C\({}_{8}\) concentration of the samples (data from Table 4). It was observed that VO production increased as the C concentration of the samples increased. Three groups of samples irradiated with 2 MeV electrons, at three different fluencies, were used. The first group contained four samples of Si1 (i = 1-4) irradiated at 5 \(\times\) 10\({}^{17}\) cm\({}^{-2}\), the second group contained three samples of S2i (i = 1-3) irradiated at 1 \(\times\) 10\({}^{18}\) cm\({}^{-2}\), and the third group contained two samples of S3i (i = 1-2) irradiated at 2 \(\times\) 10\({}^{18}\) cm\({}^{-2}\). In the presence of C, there are three main reactions that take place in the Si lattice in the course of irradiation: V + Si\({}_{\rm I}\)\(\rightarrow\)\(\O\) (annihilation), V + O \(\rightarrow\) VO, and C\({}_{8}\) + Si\({}_{\rm I}\)\(\rightarrow\) C\({}_{\rm i}\). The tendency of C to trap Si\({}_{\rm I}\)'s leads to a decrease in the rate of annihilation of V, which enhances [44] the number of available V to be captured by O atoms. In other words, the formation of VO defects is enhanced. This was observed in the three groups of samples irradiated with three different fluencies as illustrated in the three curves of Figure 9.  
Figure 8: Formation temperature of VO\({}_{2}\) defects as a function of Ge dopant concentration. Reproduced with permission from [128]. American Institute of Physics, 2010. Figure 7: Annealing temperature of VO defects as a function of Ge dopant concentration. Reproduced with permission from [128]. American Institute of Physics, 2010.  
channels control the fate of VO pairs, a subject which needs further investigation. Further, we shall consider V\({}_{\rm n}\)O defects, mainly with the V\({}_{2}\)O and V\({}_{3}\)O members of this family. Figure 11 displays the Lorentzian profiles of the IR spectra in the frequency range of the VO defect in the case of C\({}_{\rm L}\)(a), Ge(b), Sn(c) and Pb(d) samples, respectively, (information about the samples from Table 2), for two characteristic temperatures of 151 and 323 \({}^{\circ}\)C. As seen from Figure 11, in addition to the 830 cm\({}^{-1}\) band of VO pair, bands at \(\sim\)826 and \(\sim\)839 cm\({}^{-1}\) which were attributed [143; 150] to the V\({}_{2}\)O and V\({}_{3}\)O centers, respectively, could be separated in the profiles. The band at \(\sim\)835 cm\({}^{-1}\), also noted in the Lorentzian profiles, is probably related with the V\({}_{\rm m}\)O\({}_{\rm n}\) structure, but its exact identity is not known. Notably, V\({}_{2}\)O and V\({}_{3}\)O defects at 10 K have [151; 152] IR bands at 833 and 842 cm\({}^{-1}\), respectively. Figure 12 shows the amplitudes of the V\({}_{2}\)O and the V\({}_{3}\)O defects, respectively, as a function of the covalent radius of the isovalent dopants for the samples spectra shown in Figure 11. Regarding the V\({}_{2}\)O defect, taking the C\({}_{\rm L}\) material as a basis, which can practically be considered as a simple Cz-Si sample without a C dopant, we observed that for the Ge, Sn and Pb-doped samples, the larger the covalent radius, the smaller the production of the V\({}_{2}\)O defect. The main reactions for the formation of the V\({}_{2}\)O defect are VO + V \(\rightarrow\) V\({}_{2}\)O and V\({}_{2}\) + O \(\rightarrow\)V\({}_{2}\)O. The observed behavior may be attributed [143] to the ability of isovalent dopants to compete with O in capturing vacancies in the course of irradiation. In the case of Ge, the formation of transient GeV pairs which dissociate at room temperature increase the availability of vacancies, thus facilitating the production of more VO pairs, which finally lead to more V\({}_{2}\)O defects, mainly through the reaction VO + V \(\rightarrow\) V\({}_{2}\)O. This mechanism did not occur for the Sn and Pb doped samples. Indeed, the availability of V was decreased in the latter samples due to the formation of SnV and PbV pairs which are stable at room temperature.