The oxygen dimer

In the absence of impurities, especially those with tensile strain fields which promote oxygen aggregation, the first oxygen complex to be formed is likely to be a dimer. In this section we explore its stability and kinetics of motion.

  

Figure 6.4: The stable assymmetric dimer in silicon (lengths in Å).

An oxygen dimer consisting of two neighbouring BC sited O_i was placed at the centre of the cluster and subsequently relaxed. The lowest energy structure was a `puckered dimer' structure, where both oxygen atoms sit bond centred in a kinked Si-O-Si bond, with the kinks pointing in the same direction along $\langle$110$\rangle$ . Rather than having equal Si-O bond lengths as O<sub>i</sub>, each atom has one short and one long bond, the short bond being formed with the shared central Si atom (see Figure 6.4). This strong bonding is due to the quadropole interaction between the two oxygen atoms; both draw charge from their Si neighbours making them $\delta+$, and thus their shared Si becomes extremely positively polarised. The stability of the dimer is thus attributed to the creation of a [011] chain of aligned polar bonds as in Si$^{\delta+}$-O$^{\delta-}$-Si$^{\delta+}$-O$^{\delta-}$-Si$^{\delta+}$.The defect is electrically neutral with no gap levels. It is notable from the shift in position of the Si atoms compared to the ideal lattice that the defect has a strong strain field in the $\langle$001$\rangle$  direction. However along $\langle$110$\rangle$ its strain field is directional; `behind' the dimer the Si atoms show very little displacement from their ideal sites, but there is a large displacement in front of it. This suggests that as the dimer moves through the lattice it produces in front of it a large `bow wave' of lattice compression.

During our investigation we also found a stable symmetric dimer structure, shown in Figure 6.7. However this is 0.259 eV higher in energy than the assymetric case (and has vibrational modes that disagree with experiment). This is discussed further below with reference to the 1105 cm^-1 mode defect. It exhibits the same strong binding to the shared Si atom. The influence of cluster size on the energy of the dimer was investigated by displacing it so that it is centred on a nearby Si atom, i.e. it is displaced by a/4 (0 1 1). This energy changed by less than 0.08 eV, showing the cluster surface has negligible effect.

This puckered structure is consistent with work by Needels et al [115], but in contrast to Greens Function calculations by Kelly [114] as well as previous AIMPRO calculations on the dimer [156], who both found a symmetric C_2v structure. This is discussed further in Section 6.4.1 below. Seperating the dimer by one Si-Si bond along $\langle$110$\rangle$ raised the cluster energy by 1.7 eV, which is a crude first estimate at a binding energy. However such energy differences are very dependant on the number of bond centred fitting functions used, and the error on such a value may be large. This compares to a dimer binding energy of 2.25 eV for earlier AIMPRO calculations [156] (the energy difference between the dimer and a Si-O-Si-Si-O-Si structure) and 1.0 eV by Needels et al [115] (see Section 6.1.2).

The vibrational modes of the asymmetric dimer are given in Table 6.4. The associated eigenvectors are shown in Figure 6.5. As can be seen, the top two modes roughly correspond to assymetric stretch modes for the inner and outer O atoms respectively. The modes are in good agreement with the experimental values for the 1012 cm^-1 defect, including the shifts with ¹⁶O$\rightarrow ^{18}$O. There are some calculated modes which are not observed, however these have a lower (dipole moment)² and thus absorption intensity. Thus these modes serve to confirm that the 1012 cm^-1 defect is indeed the puckered oxygen dimer.

There is a problem however with the mixed dimer modes; experimental FTIR on mixed ¹⁶O / ¹⁸O samples show no mixed mode absorption. This suggests the atoms are decoupled in some way, e.g. through greater seperation than that of the puckered dimer. Current models of the O-H defect suggest that O and H sit in bonds on opposite sides of a hexagonal interstitial ring site [157]. A possible alternative dimer model would be two O atoms in these positions, which is shown schematically in Figure 6.6. Their strain fields could couple in this way, and if the one buckled into the hexagonal site through Coulombic interaction with the Si neighbours of the other O atom, this would push the other atom to buckle outwards. Thus the two would be inequivilent, leading to the observed experimental mode splitting. In this case rapid migration could still occur with the puckered dimer structure, which would split to give this hexagonal ring as the stable structure. We are currently investigating such a model.

 

¹⁶O ¹⁷O ¹⁸O ¹⁶O¹⁸O ¹⁸O¹⁶O Intensity 4lExperimental [151]

1 1059.6 48.1 0.9

2 1012.5 43 1.0

3 685 10 0.08

4 552 0.5 0.15 4lAssymetric Dimer

1 1069.3 24.8 47.2 8.9 33.2 1.16

2 921.3 21.8 41.6 30.9 15.7 1.00

746.4 10.3 19.3 13.5 5.3 0.26

3 649.6 5.4 10.2 4.1 6.7 0.33

4 592.6 1.6 2.8 0.1 2.7 0.50

551.0 3.9 7.5 1.0 6.5 0.07 4lSymmetric Dimer

1169.6 27.4 52.3 18.6 20.0 1.00

1077.9 27.6 52.6 33.8 32.5 0.76

643.9 0.8 1.5 0.8 0.6 0.42

637.7 3.0 5.3 2.7 2.9

581.3 5.3 9.9 4.7 4.7

536.0 7.5 14.2 7.0 6.8 4lSplit Dimer

1201.5 26.7 50.9 23.1 8.2

1152.0 26.0 49.4 28.7 40.3

647.4 6.5 11.7 7.0 4.5

632.1 5.7 10.5 8.1 1.5

622.2 3.2 6.9 2.2 5.2

569.6 2.2 4.1 2.7 1.7

539.7 4.4 8.3 4.1 4.5

  

Figure 6.5: Atomic motion associated with each vibrational mode for the assymetric dimer (modes in cm^-1). The top two modes roughly correspond to the assymetric stretch for the inner and outer O atoms respectively, the lower modes are wag modes. The 593 cm^-1 mode is largely localised on the core Si atoms and hence shows little shift with oxygen isotope, in agreement with experiment.

  

Figure 6.6: Schematic diagram of a possible alternative dimer model that should show no mixed isotope vibrational mode coupling. The atoms sit bond centred, on opposite sides of the hexagonal interstitial site.