Discussion of the di-y-lid model

  The di-y-lid model is consistent with a wide range of experimental thermal donor observations, many of which have been discussed above.

Firstly it contains four oxygen atoms in agreement with early oxygen loss experiments [179]. It consists of a pair of dimers, consistent with dimer formation being the low temperature rate limiting step[143]. It has the correct C_2v symmetry with all O atoms in the same $\langle$110$\rangle$ plane, and none of them on the C₂ axis. In addition it contains only one Si atom on the C₂ core which is displaced significantly from its ideal lattice site [231,232]. The donor activity arises from O instead of a single Si atom in agreement with ENDOR[10]. The defect has two shells of O nuclei [232] corresponding to the trivalent and then divalent O atoms. It exhibits the correct compressive and tensile properties along the various $\langle$001$\rangle$ , $\langle$110$\rangle$ and $\langle$110$\rangle$ directions[236].

The defect gives rise to the correct number of vibrational modes, with both absolute values and isotope shifts extremely close to those experimentally observed[239]. Since it consists of a pair of dimers, its entire formation path can consist of dimer migration and addition, hence the formation barrier is always 1.7 eV and never needs to involve isolated O_i.

It should have an associated inactive form where the two trivalent O atoms become divalent once again; this could either relax back into two dimers separated by a pair of Si-Si bonds, or else into a central dimer flanked by two O_i atoms separated by a single empty Si-Si bond (with further structural rearrangement it is possible to imagine other inactive forms). A final alternative is if the two trivalent O atoms form next-neighbour bonds along $\langle$110$\rangle$ , while the top two Si atoms form a stronger bond which when H passivated could be inactive (see below). The modes of this inactive form might be expected to be slightly higher than isolated dimers given their proximity; experimentally whereas the dimer absorbs at 1012 cm^-1 the inactive TD form absorbs at 1020 cm^-1 [239], consistent with this interpretation.

In agreement with stress induced alignment[236] the defect should be able to reorient within about five `standard' O<sub>i</sub> hops, if some of the motion is coupled and slightly faster. For example, the two core O atoms initially perform a `coupled hop' downwards into the Si-Si bonds lying along $\langle$110$\rangle$. Next the outer two O_i atoms perform standard `hops' to replace the original core atoms. The two O atoms now lying along $\langle$110$\rangle$ next hop outwards, and finally the two atoms remaining on $\langle$110$\rangle$ perform a `coupled hop' downwards to adopt the new core sites along $\langle$110$\rangle$. If these `coupled hops' in total take the same time as a standard O_i hop this would match experiment.

Earlier experiments showed that TD concentration decreased near the sample surface, with rates consistent with oxygen diffusion that was enhanced by around four orders of magnitude[139]. From this it is expected that the out-diffusion should increase with [O_i], but it was found that the depth of depleted material decreases with increasing O concentration[260,261]. This is consistent with increasing oxygen concentration leading to more dimers, which have thus a higher chance of being trapped by a second dimer to form a thermal donor before out-gassing. Thus this result supports a thermal donor model consisting of the binding of two or more oxygen dimers.

The reconstructed Si-Si bond is interesting. Since it is quite dilated it could potentially absorb a lot of the surrounding lattice strain. In this case oxygen dimers might sit in bond sites near to the top of the defect so that their lattice strain is absorbed in this way. This is discussed further below with relation to higher order TDs. Such dimers would be able to rapidly respond to applied stress if the defect core reoriented.

Results of Hallberg showed an initial 1.2 eV formation rate for the TDs that rapidly reverted to the standard 1.7 eV[239]. If the 1006 cm^-1 mode does correspond to the trimer, then as-grown material contains an initial pool of trimers, and this 1.2 eV could correspond to the migration barrier for the trimer to travel to O_i in order to form the di-y-lid thermal donor. Once this pool is exhausted, the dimer migration barrier then becomes the rate limiting step. This is discussed further below.

Carbon passivation of thermal donors may occur by C substitution into the core of this instead of the central Si atom, forming C_sO₄ which would be inactive. This would either form by C_s trapping dimers initially, or else through C_i migrating to a TD and kicking out the core Si atom to replace it. This could go on to kick out a further C_s atom elsewhere and so the process is catalysed and only requires a small number of Si_i atoms to start it off.

Note that this discussion does not address the question of whether this structure represents TD2 or TD3, which is discussed further below.