1D thermal donors

The first model is the linear tail model described above, the currently accepted `standard model'. In this case, O_i atoms aggregate in the same $\langle$110$\rangle$ plane as the defect core, in neighbouring BC sites. To form TD16 we require 14 new thermal donors after TD3. If each of these grows through a dimer adding to the previous defect that implies 13$\times$2+4=30 oxygen atoms in TD16. If the scheme is slightly modified and the TDs grow through O_i addition then this number can be reduced to 17. Thus there is a chain of either 7 or 13 O_i atoms on each side of the defect core.

This model seems very unphysical. O_i strains its surrounding lattice, causing 30% Si-Si bond dilation. When paired to form O_2i, there is once again a large strain field produced both above (001) and in front (110) of the defect. Two dimer structures together, the structure of the di-y-lid, seem sufficiently strained to force the core oxygen atoms into tri-valent positions. A model where O_i atoms collect along $\langle$110$\rangle$ next to the defect core is reasonable for the first few O_i atoms, since TD3 is highly tensile along this direction. But it would be unable to equalise the strain field of 7 to 13 O_i atoms on each side. Although the strain field in such a chain might be high enough to force more of these chain O_i atoms into y-lid sites, these would be electrically active, and the Coulombic repulsion with the TD core would be too high.

One way in which a chain model can achieve these 13 different structures is if the chains on either side of the core can be of different lengths, and thus isomers are allowed. In this case, structures such as O_i-TD3-O_3i would be allowed. Table 9.8 shows that a minimum of 6 total `tail' O_i atoms are required for this to explain all the TDs, i.e. a maximum tail length of 5O_i on each side.

The higher order annealing studies do not allow differentiation between an isomer and a serial development model. TDs 12 to 16 were seen simultaneously in a sample annealed for 3 hours at 470$^\circ$C [241], and so there is no information on their relative development; they are named in sequence of decreasing ground state binding energy.

Finally, extremely long tail models may not be consistent with reorientation data[236]. For TD3 $\sim$5 O_i hops are required for reorientation; this would be possible with the di-y-lid model. For higher order TDs there is a small increase in the reorientation time prefactor, corresponding to more hops. However for a long tail thermal donor to reorient through each atom hopping individually, the number of reorientation steps would rapidly increase, as the line has to sweep out a circle to realign itself. One possibly way around this is if the atoms hop towards the core, through the core, and back out along the new defect line; in this case the number of hops required would equal the number of O_i atoms in each `arm' of the defect plus some constant for the core to reorient (presumably, from the TD3 result, five hops for the core).

 

Number of Number of Cumulative

`tail' O_i TD isomers number of TDs

1 1 1

2 2 3

3 2 5

4 3 8

5 3 11

6 4 15