2/3D thermal donors

An alternative model for higher order thermal donors is a more general aggregation of oxygen to a common TD core. In this case dimers are attracted to the core but bond into a variety of bond centred sites around the core including, but not limited to, those along the $\langle$110$\rangle$ defect plane. Although the defect core causes compression along $\langle$100$\rangle$ , there are Si-Si bond sites at angles to this which are dilated due to at least one of the Si atoms being pushed off-site by the strain field of the TD core, and these sites would provide locations for dimer attack. When discussing the mechanism in this general way it is impossible to predict whether the process would be serial, or whether several sites would have equivilent energies, leading to isomeric thermal donors. In a similar way to the calculations shown in Table 9.8, if the TD has six sites surrounding it, four of which lie off the C_2v mirror planes and are symmetrically equivilent, and the other two lie on a mirror plane and are a symmetric pair, there are 18 different permutations obtainable by filling between 0 and 4 of these sites. Hence only four dimers are required to aggregate to the TD core to produce the complete set of observed TDs, if TD isomers are allowed.

However, it appears that any perturbations of the thermal donor core are only extremely small, and directly bonding dimers to the sides of the core might be expected to perturb it to a larger degree. In addition, ENDOR results suggest all oxygen lies along the $\langle$110$\rangle$  plane, and O_i aggregates bonded to the defect core would be expected to provide an ENDOR signal.

An alternative model, and one which seems consistent with experimental data, is one whereby such sites exist much further from the defect core. In this case they are regions of the lattice arranged around the core which exhibit some Si-Si bond dilation, and hence provide weak binding sites for dimers. These adopt these sites, forming a `cloud' of dimers around the core like flies. Thus they would only be expected to weakly perturb the core structure and states. Such sites can be seen in our cluster results; although the bonds directly along $\langle$001$\rangle$ are compressed, those to one side of these show some dilation as the Si atoms directly above the defect core are pushed upwards and away from their neighbours further off this plane.

The thermal donors would be expected to show extremely similar behaviour under this picture with only slight variations from one another. For example, in the reorientation experiments discussed above the core would still rotate as before, with the dimers just shifting position to the new slightly tensile sites. This would be consistent with the ENDOR result since the O atoms would only be weakly bound and not very close to the core, and hence would not show up as part of the core structure. Hence although the total defect could display low symmetry, ENDOR and EPR would only measure the C_2v symmetry of the defect core. Oxygen atoms in neighbouring dilated sites may be responsible for the broad 1060 cm^-1 peak observed after anneals, the broadness of the peak explained by the slight variety in local environment of each of the atoms.

If trimers can occupy these sites it provides an additional variable when determining the number of dimers/trimers needed to give the required number of structural permutations to explain all of the observed TDs, i.e. less dimer sites would be required to explain all of the TDs. For an average of 10 O atoms per thermal donor, this requires (with a core of 4 atoms) an average of either two trimers or three dimers per thermal donor, which is a very modest figure.

In this picture then, there is a dynamic equilibrium concentration of dimers, and eventually trimers, adopting sites around the TDs. The position of the donor level in the gap should gradually increase as the surrounding lattice strain goes up with dimer addition. There is essentially no perturbation of the core and instead an increasing strain of the surrounding lattice, which compresses the $\langle$001$\rangle$  conduction band valleys used to construct the EMT-like donor state, making it increasingly shallow. If this was not the case we would expect a spectrum of vibrational absorption peaks from TDs with slightly perturbed cores, whereas in long time anneals there are only four peaks in the 999-1020 cm^-1 range associated with electrical activity [239]: the 999-TD3 band, the 1006 and 1012 cm^-1 electrically active bands, and a later 1015 cm^-1 band, with the latter three thought to be associated with shallow thermal donors.

A further key piece of evidence for such a picture is that the figure of on average 10 atoms lost from solution per TD appears to be independant of annealing temperature or time [274]. This suggests that TDs form rapidly, and then higher order TDs become either more unstable or unable to trap further atoms. This would be consistent with a result where around 10-14 O_i atoms could bind to the TD with cumulative loss of energy, but thereafter there was an energy increase[274]. This is consistent with this `cloud' picture, where further dimers have to attach further from the defect core and are increasingly weakly bound, until the higher order TDs are in a thermal equilibrium with dimers sticking and releasing at regular intervals.

Such a picture would also be consistent with a revised dimer model where O_i atoms sat on opposite sides of the hexagonal ring site.