The VO₃ Defect

  VO₃ forms at 450$^\circ$C when VO₂ traps an additional O_i. This defect (shown in Figure 5.4) has an additional O atom, say O_c, next to VO₂. The bonds of the O_c atom are 1.632 Å to the Si atom bordering the vacancy and 1.686 Å to the further Si. These are much shorter bonds and naturally lead to higher O-related local modes. O_c is bonded to a Si atom which is also bonded to another O-atom, say O_a, with length 1.643 Å. O_a is also 1.696 Å away from the other Si atom bordering the vacancy. The third O atom, O_b, also lies within the vacancy and possesses two bonds of length 1.696 Å. Thus the presence of the additional O atom has only slightly perturbed the O atoms within the vacancy. Their separation is 2.646 Å.

The LVMs are given in the table. The 998 and 902 cm^-1 modes are localised on O_c and O_a. The 813 cm^-1 is localised on O_b. The 665 cm^-1 and other modes are extended over all the O atoms. Thus the effect of an additional O is to displace upwards the mode due to VO₂ by about 100 cm^-1 and introduce an additional mode $\sim$1000 cm^-1. This top mode is in good agreement with a mode found at 1005 cm^-1, although the other modes are about 70-100 cm^-1 too low. A similar error was found for VO₂, and this error lies within the uncertainties of the method, and again, the upward mode shift from VO₂ $\rightarrow$ VO₃ is correctly predicted. The prediction and observation of three O-related modes supports the assignment of the modes at 1005, 976, 910 cm^-1 to VO₃ and therefore indirectly the 889 cm^-1 mode to VO₂.

  

Figure 5.4: The O₃V centre in Si. The box indicates the [100] directions.

Just as we had trouble finding the lowest energy structure for VO₂, we also found a low energy structure for VO₃ consisting of an OV centre with two O_i atoms in the dilated bonds neighbouring the Si-O-Si of the OV. This is similar to the alternative VO₂ model described above but with an additional O_s sitting in the vacancy. This proved to be lower energy than the VO₃ model described above, and also had good agreement with experimental LVMs. However since the energies of VO₂ have to be corrected in order to find the actual lowest energy structure we have assumed this also applies to VO₃, and so exclude this model. Experimental stress induced alignment experiments should be able to differentiate between these two centres, since the VO₃ presented above has C_1h symmetry, whereas this low energy VO₃ has C_2v symmetry. Work is currently underway on the higher order VO_n complexes by Lindström and Hallberg, and hopefully they should be able to check this.