The symmetric dimer

  The symmetric dimer structure is a local minimum on the potential surface. It seems to cover quite a large region of phase space, so that the relaxed structure is very dependant on the choice of starting structure, and most starting structures we chose produced a symmetric dimer structure. This was originally published as the dimer structure using AIMPRO [156]. However according to our calculations this is 0.259 eV less stable than the puckered dimer structure. The defect is shown in Figure 6.7. This structure is also electrically neutral with no states in the gap. The vibrational modes are shown in Table 6.4, and as can be seen, they are very different from the experimentally observed dimer modes. Thus these results exclude the symmetric dimer as a model for the 1012 cm^-1 LVM defect.

However, there is an additional mode seen at 1105 cm^-1 in the presence of the dimer modes [151], and it was speculated that this may be two O_i atoms seperated by a single Si-Si bond along $\langle$110$\rangle$ . An alternative explanation is that this is due to the symmetric dimer. Although the calculated symmetric dimer does not have a mode exactly at this value, there is some evidence in favour of this model for the 1105 cm^-1 mode. The defect appears to have an experimental binding energy of 0.2 eV as compared to 0.3 eV for the dimer [151], so an energy difference of 0.1 eV between the two structures is quite close to our calculated value of 0.26 eV. The mode is only observed at 10K, and disappears by 300K. This would be consistent with symmetric dimers getting `frozen in' at lower temperatures with a finite reorientation barrier. At 300K they are able to overcome this and no symmetric dimers are observed. In addition the 1105 cm^-1 mode drops by 50/52 cm^-1 when ¹⁶O is switched to ¹⁸O, very close to our calculated value of 52.6 cm^-1. To fully check this model it would be necessary to calculate the energy barrier between the symmetric and assymmetric structures, as well as locate further experimental modes to improve the assignment.

  

Figure 6.7: The symmetric dimer in silicon (lengths in Å). This is 0.259 eV higher in energy than the assymetric dimer. Black dots mark the ideal lattice sites.