## 2 Results
### Production of VO Defect Versus C Concentration
Thus, the production of V\({}_{2}\)O defects was suppressed in the Sn and Pb-doped samples. Apparently, the contribution of the reaction V\({}_{2}\) + O \(\rightarrow\) V\({}_{2}\)O did not seem to alter the balance between the two reactions among the above three dopants, to change the order of V\({}_{2}\)O defect production versus the isovalent dopant radius, as depicted in Figure 12a. It should be stressed, that in the case of the C\({}_{\rm H}\) sample, the tendency of C to react readily with self-interstitials, in contrast with the other three dopants, led to the suppression of the V\({}_{2}\)O defect in comparison with the C\({}_{\rm L}\) sample, as seen in Figure 12a. Regarding the V\({}_{3}\)O defect, the main reactions for its formation are V\({}_{2}\)O + V \(\rightarrow\) V\({}_{3}\)O and V\({}_{2}\) + VO \(\rightarrow\) V\({}_{3}\)O.  
Figure 10: The conversion of the VO to VO\({}_{2}\) defect as a function of the C concentration in the Si samples. Reproduced with permission from [44]. Unfortunately, the relative results provided in Figure 11 were not enough to reach firm conclusions. For instance, the V\({}_{3}\)O band at 839 cm\({}^{-1}\) only appeared in a few temperatures around 300 \({}^{\circ}\)C in the Lorenzian profiles of the Sn-doped sample, and its evolution could not be depicted properly, as seen in Figure 7 of [143]. Nevertheless, some points can be formed. Namely, in the case of Ge-doped Si samples, the production of V\({}_{3}\)O was larger in comparison with the C and Pb-doped samples. The enhancement production of V\({}_{3}\)O has been attributed to the enhancement of the reaction V\({}_{2}\)O + V \(\rightarrow\) V\({}_{3}\)O due to the increased availability [151] of VO and V\({}_{2}\) defects in Ge-doped Si. Additionally, due to the recombination of V\({}_{2}\) by the self-interstitials (V\({}_{2}\) + Si\({}_{i}\)'s \(\rightarrow\) V) the liberated vacancies promote [151] the reaction V\({}_{2}\)O + V \(\rightarrow\) V\({}_{3}\)O which leads to a further increase in V\({}_{3}\)O defects. In the case of C-doped samples, the reaction V\({}_{2}\) + Si\({}_{i}\)'s \(\rightarrow\) V is substantially suppressed due to the tendency of C to trap Si\({}_{i}\)'s (C\({}_{\mathrm{s}}\) + Si\({}_{i}\)'s \(\rightarrow\) C\({}_{\mathrm{ij}}\)) which suppresses availability of V, as in the case of Ge-doped Si. This leads to a lower production of V\({}_{3}\)O defects. In the case of Pb-doped Si, on one hand the production of VO and V\({}_{2}\)O is small, but on the other hand, any liberation of V is limited, resulting in a suppression of the two formation reactions of the V\({}_{3}\)O defects mentioned above. This leads, therefore, to their even smaller production. Notably, our Pb-doped Si also contained carbon in high concentration, which limited the number of available V which may have participated in reactions which favored the formation of V\({}_{3}\)O defects. In our previous work, DFT calculations were employed to calculate the relative energetics of the A-center and its interaction with isovalent dopants. Figure 13a illustrates the VO that is essentially formed from the binding of an O\({}_{\mathrm{i}}\) atom next to V in Si (binding energy \(-1.32\) to \(1.57\) eV, [148] and references therein). In the vicinity of an isovalent dopant, VO pairs preferentially bind at nearest neighbor positions (Figure 13b,d) as compared with next nearest neighbor positions (Figure 13c,e). The binding energy gain of the isovalent atom in nearest neighbor position to the vacancy (in the VO) is considerably higher due to the strong binding (mainly relaxation) of the dopant atoms (particularly due to the relaxation of oversized atoms such Sn and Pb) to the vacant site [148]. The DFT results show that the incorporation of isovalent dopants in Si led to the formation of DVO or DOV clusters. These formed as they reduced the repulsive NN interactions of the isovalent atoms with the oxygen interstitials [148]. Apart from energetics, DFT calculations can provide detailed information on the structure of the defects.