Di-y-lid is TD3 - a parallel process

A second possibility is that the di-y-lid is actually TD3, and both TD1 and TD2 are pre-cursors to the di-y-lid. Therefore, being bistable isomers, TD1 and TD2 have to be different forms of electrically active trimer.

In this case, the initial 1.2 eV formation energy of TD1 could be explained as a barrier to internal restructure of the trimer. If the dimer is able to migrate to O_i and form a weakly bound trimer, in the initial material there is already a small pool of trimers (there are also some early thermal donors present). These trimers can restructure with a barrier of 1.2 eV. Once these are exhausted, the limiting barrier becomes the trimer formation barrier, i.e. the dimer migration barrier of 1.7 eV. In addition both TD1 and TD2 have an electrically inactive form, with LVMs different to those of the trimer. Thus there has to be a third form for the trimer, although this form may be much higher in energy than the others and therefore only frozen in at lower temperatures.

In such a scheme, presumably TD1 and TD2 could remain in dynamic equilibrium with the inactive trimer form. There are two ways of forming the 4O_i di-y-lid. Either the trimers could migrate, or else they could be only weakly stable and so break into dimers and O_i, so that dimers would eventually meet each other and bind into the di-y-lid. Markevich found his concentration models for the dimer and trimer fitted experiment much better if he assumed a mobile trimer, and such a mechanism would lead to faster di-y-lid formation given the relatively high concentration of O_i compared to O_2i.

This also helps to account for the relative TD concentrations. TD3 is the primary TD. If both TD1 and TD2 are mobile, they can form through dimer addition to O_i. TD3 can then form by trimer addition to O_i. However, if TD3 is immobile, it cannot migrate to O_i. O_i is only moving very slowly on the timescales considered, and thus in order to form higher order TDs, TD3 has to rely on dimers migrating to it; therefore the formation process will slow considerably. Hence there will tend to be a build up of TD3 species.

Against this argument is the necessity that there has to be dimers present in the material to bond with the higher order TDs. However if dimers are reacting with O_i to form trimers, that should rapidly take most dimers out of circulation. This could still be consistent with the above model if the trimer binding energy is so small that the dimers only bond briefly, and most trimers dissociate before forming any of the thermal donors.

The crux of this model then seems to be that TD1 and TD2 form in parallel with the main formation scheme, which is dimers to trimers, and on to the di-y-lid as TD3. However in this form it is not consistent with annealing studies (see Figure 6.11). In the 450$^\circ$C plot, it can be seen that the TD3 absorption exactly maps that of the trimer. This is consistent with a scheme where the trimer migrates to O_i to form a di-y-lid TD3. However, the TD2 signal rises rapidly in line with the dimer concentration to begin with, and then tails off after two hours, until it has almost disappeared after 10 hours or so. If TD1/2 were isomers of the trimer, we might expect the change in their absorption to roughly match that of the trimer, which is not the case.

However this might be understood if the conditions in the material change to make the switch from trimer to TD1/2 less favourable. As the anneal progresses increasing numbers of TDs are produced, which should lead to a shift in the Fermi level. This could shift the relative stability of the trimer and TD1/2, making TD1/2 less favourable. In the first 3 hours of annealing at 450$^\circ$C the trimer peak appears to remain roughly constant, whereas the TD2 peak roughly traces that of the dimer. Thereafter the trimer peak starts to increase while TD2 drops away (see Figure 6.11). We would expect the combined signal from the trimer, TD1 and TD2 to roughly correlate with the dimer; in Figure 6.11b, this appears qualitatively to be the case.

This idea is supported by results from samples subjected to dispersal treatment [271], where during subsequent annealing the decrease in the 1012 cm^-1 band correlates with the growth of the 1006 and 975 cm^-1 bands. From these results it appears that TD1 forms simultaneously with the trimers, but as soon as the donor concentration starts to creep up, the TD1 transform into TD2. From this we might tentatively suggest that TD1 is closer in structure to the trimer, and is slightly less stable than TD2.