The VO₂ Defect

  

Figure 5.2: The O₂V centre in Si. The box indicates the [100] directions.

This structure (Fig.  1b) has D_2d symmetry with four Si-O bonds of length 1.710 Å. These are shorter than those in VO and lead to higher frequency vibrations. They are, however, longer than those of O_i (1.596 Å [94]), and the defect is still tensile. The Si-O-Si angles are 147$^\circ$ and the O-O separation is 2.61 Å. There are six LVMs (see Table 5.1). The highest at 807 cm^-1 are E modes and represent independent motion of the two O atoms. There are no additional modes in the mixed O-isotope case. The mode at 656 cm^-1 represents stretch of the O-O bond and is IR inactive. The E mode at 574 cm^-1 does display coupled motion of the O atoms. This mode then gives additional O-O bands in the mixed isotopic case. There are no gap levels associated with the defect. The LVM at 807 cm^-1 is about 90 cm^-1 below that possibly assigned to the defect, but no other modes have been reported. It has good agreement with the experimental isotope shifts, and shows the correct upwards shift from VO $\rightarrow$ VO₂.

Since performing this work, new symmetry investigations by Lisby and Bech Nielsen [83] have determined the symmetry of the defect giving rise to the 889 cm^-1 defect as being D_2d. Initial uniaxial stress experiments determined that it was either C_2v or D_2d, but the resolution of the fits was not able to distinguish between the two. They have since performed stress induced reorientation experiments, where stress is applied at 200$^\circ$C, maintained while the sample cools, and then released [83].

If a defect is either tensile or compressive it will tend to reorient itself at the higher temperature with respect to the applied stress field. If, for example, this stress field is applied along $\langle$100$\rangle$ , and the defect has inequivalent $\langle$100$\rangle$ directions, this means the defects will preferentially align. If the defect is tensile along $\langle$100$\rangle$ it will line up with the stress field, and if compressive along $\langle$100$\rangle$ it will line up along one of the two remaining unstressed $\langle$100$\rangle$ directions. If the defect symmetry means it has no preferential $\langle$100$\rangle$ direction, they will remain randomly distributed with respect to the stress direction.

The sample is then cooled to quench this orientation in, and the stress removed. If the sample is now probed using FTIR along different $\langle$100$\rangle$ directions, if the defects are preferentially aligned along one of these the signal will exhibit dichroism, i.e. the signal will appear stronger in one of the $\langle$100$\rangle$  directions than the others. In practise, as the chosen $\langle$100$\rangle$  direction of stress is known, applying FTIR along one of the other $\langle$100$\rangle$ directions and comparing to the sample before stress is sufficient to show such dichroism. If the defect possesses no preferential $\langle$100$\rangle$ direction, there will be no alignment effect and the signal before and after stress will be the same.

Stress applied in this way for VO₂ along $\langle$100$\rangle$ and $\langle$110$\rangle$  produced dichroism whereas $\langle$111$\rangle$ stress did not. This is consistent with D_2d symmetry but not C_2v (which has inequivalent $\langle$111$\rangle$ directions). This result is sufficient to exclude both the V₂O model and the C_2v structure described below, and coupled with our theoretical investigation show that the defect responsible for the 889 cm^-1 line is indeed VO₂.

While investigating this structure we examined various other possible configurations of V + O₂, including a C_2v structure where the oxygen atoms were inserted in O_i positions in bonds neighbouring the vacancy, one either side along the same $\langle$110$\rangle$orientation. Unfortunately we found that this was a lower energy structure than the VO₂ model presented here. We investigated varying the structure to see if we were inadvertently trapped in some local minimum, and also tried varying the basis set, however in every case it remained lower in energy. We also varied the cluster surface treatment, holding the surface H atoms fixed, allowing them to move freely, and constraining them to move in a quadratic spring potential, but again none of these reversed the energies.

This model cannot be the correct one for several reasons; it does not have the correct (D_2d) symmetry and the vibrational modes are wrong. In addition there is coupling between the oxygen atoms, so multiple modes are observed in the mixed isotope case in contradiction with experiment. We are unable at present to explain why we obtained the energies incorrectly, but note that J. Chadi also found that addition of O_i to a VO centre was an endothermic process [95]. One possibility is that there is some charge redistribution to the cluster surface which helps to stabilise pure V-based structures, however this alone is insufficient to explain the difference. Alternatively our charge density modelling may be inaccurate for vacancy-based structures, and the addition of gradient corrections to the exchange-correlation energy or the use of a plane wave basis set may overcome this problem. Recent tests with a new supercell version of AIMPRO that avoids intermediate fits to the charge density correctly gives the D_2d structure as 1.918 eV more stable than the C_2v structure; further investigation is required to determine whether this is an effect of the basis or the supercell.