Theoretical Results

This section covers our work to date, however further work is required before we can make any definitive statements on the nature of the trimer.

There are many possible configurations for three oxygen atoms. Electrically active configurations will be examined in Chapter 9 so we restrict ourselves to neutral complexes here. In this case there are two primary possible structures, a linear chain (an extension of the dimer along $\langle$ 110 $\rangle$ , see Figure 6.14), or placing all three O_i atoms around the same core Si as shown in Figure 6.13 (in this structure the oxygens all bow `clockwise' around the defects C₃ axis, earning it the name the `Manx' defect!). We relaxed both of these structures in a 134 atom cluster, $\rm Si_{71}H_{60}O_3$ , and found the Manx structure to be 0.248 eV more stable. There is in addition a third possible structure consisting of a dimer with an appended oxygen atom that sits in a perpendicular $\langle$ 110 $\rangle$ plane, thus oxygen atoms sit in three of the six bonds around a hexagonal ring site. This may be more stable as the stress will be spread over two planes. Nothing is currently known experimentally concerning the symmetry of the trimer.

The vibrational modes of the linear and Manx structures are given in Table 6.7.1. The linear structure gives modes which are close to those of the dimer, although these calculations would suggest slightly higher. The Manx structure has modes that are very different. This suggests that the trimer may be the linear O_3i structure, since experimentally its vibrational mode at 1006 cm^-1 is only 6 cm^-1 away from the primary dimer vibration at 1012 cm^-1. Although these calculations predict a slight increase in this mode as opposed to a drop, that could be a cluster size effect, as the end of the trimer chain is quite close to the cluster edge. Alternatively, the `half hexagon' structure described above might be expected to have perturbed dimer-like modes.

**Figure 6.13:** The `manx' oxygen trimer in silicon. The top diagram shows the view along the $\langle$ 111 $\rangle$ , C₃ symmetry axis.
$\begin{figure} \begin{center} \ \psfig {figure=oxygen/dimer/diags/o3/manx.eps,width=7cm} \end{center}\end{figure}$

**Figure 6.14:** The linear chain trimer in silicon; dots mark ideal Si lattice sites.
$\begin{figure} \begin{center} \ \psfig {figure=oxygen/dimer/diags/o3/linear.eps,width=11cm} \end{center}\end{figure}$

**Table 6.6:** LVMs and isotope shifts (cm^-1) for the trimer in the $\langle$ 110 $\rangle$ linear chain structure, and shared central Si `Manx' structure. The `Manx' structure is 0.248 eV more stable.

3c`Linear Chain' structure	3c`Manx' structure
¹⁶O	¹⁷O	¹⁸O	¹⁶O	¹⁷O	¹⁸O

1080.5	24.4	46.5	1176.8	23.6	44.7
948.9	21.6	41.1	1154.3	23.6	44.9
849.9	20.3	38.7	978.2	27.0	51.6
733.3	11.3	21.2	737.9	12.5	23.6
655.7	13.2	24.8	713.5	10.4	19.8
630.1	5.4	10.5	598.4	8.0	14.5
570.5	8.3	15.4	555.1	7.5	14.7
552.2	1.9	4.2	511.4	6.1	11.8
525.3	4.4	8.2