11 unit cells 0.384 0 .018 12 unit cells 0.387 0 .017 13 unit cells 0.390 0 .016 14 unit cells 0.409 0 .015 15 unit cells 0.585 0 .020
Table 7.2.5 : Energy of defects for step defects using the 1x16 model.
4
4~ (
4
Figure 7.2.10 : Relaxed structure of clustered defect with five vacant dimers. The upper graphic shows a side view with the vacancy situated in the centre.
Perturbations of the regular surface structure of layers two and three can be seen around the vacant sites. The lower graphic shows the top view and shows the sideways relaxations of the upper zinc ions.
Chapter 7 ; ZnO surface studies
4
Figure 7.2.11 : Relaxed structure of clustered defect with three vacant dimers. The upper graphic shows a side view with the vacancy situated in the centre. Perturbations of the regular surface structure of layers one, two and three can be seen around the vacant sites with strong relaxation of a pair of layer one dimers, bringing them close together. The lower graphic shows the top view and shows the sideways relaxations of the upper zinc ions on one side of the vacancy with the more coordinated dimers on the other side.
7.2.4.4 C om b in atio ns o f defects
The defect energies reported here show that several defective structures have defect energies which could be considered low enough to introduce measurable amounts of
C h apter 7 : ZnO surface studies
the defect onto a surface. O f course, the low est energy defect to be identified was the double layer step in the [001] direction, w hich is know n to exist. Further to that we m ay expect to see various other defect structures such as the groove and the pyramidal and triangular pits in various com binations. U nfortunately a m odel big enough to investigate m ultiple defects w ould require m uch m ore com puting power. However, it can be seen that even com binations of the individual defects investigated here w ould yield occupancy factors w hich w ere still consistent w ith the experim ental findings.
7.2.5 Rationalisation of surface structures
Considering the w hole (10Î0 ) surface, our calculations suggest that a fully occupied surface is energetically m ore favourable than a defective one, although steps in the [001] direction w ould be a com m on feature of the surface due to their extrem ely low defect energies. The relaxation o f the fully occupied surface agrees with recent electronic calculations in layer one, but predicts a m ore significant upw ard displacem ent o f the layer two zinc ions. As the layer one zinc ions are m oving down from the surface and the layer tw o zinc ions are m oving up tow ards the surface, the distance narrow s between the tw o layers o f zinc ions. This narrow ing effect may have som e bearing on the experim ental findings o f only small dow nwards relaxations o f the upperm ost zinc ion s[52]. O ur perfect surface m odel shows a net small dow nw ards relaxation o f the upperm ost zinc atom s does occur in relation to the underlying zinc ions, although when the relaxation is considered as a displacem ent from the analogous bulk positions, it appears to be m uch larger. It is not clear if this m oderating effect is included in the experim ental results, but may well play a part in full picture o f the relaxation of the [10 Î0 ] surface.
W hat the author feels is m ore likely to be the source o f discrepancy between the sm aller relaxations reported by experim ent and the larger relaxations reported m ainly by com putational studies is that quantum m echanical studies have always utilised perfect surfaces w hilst the experim ental studies intrinsically include defective
C h apter 7 ; ZnO surface studies
counterparts. W hilst this defect is calculated to be m ore energetically costly than others, it is possible that it could be stabilised w ithin a cluster o f defects in the m anner sim ilar to the stabilisation of defects discussed in section 7.2.4.3. This would allow for a concentration of zinc ions to rem ain close to their analogous bulk positions giving rise to the experim ental findings w hich have been reported, whilst such features have been com pletely absent from calculated w orks w hich have drawn quite different conclusions.
Further defects in the plateau regions o f the surface are predicted to be energetically inexpensive in some cases, although always less favourable than a fully occupied terrace. D ouble layered defects such as grooves and pits are predicted to be am ongst the defects which are energetically least expensive. Concentrations o f defects in the plateau regions o f the surface have been shown to be consistent w ith experim ental findings, although generally, the vacancy concentration predicted to be least expensive per vacancy is 5-10% low er than the m easured value.
At present, what has been observed from and calculated for the [10 Î0] surface is not a com plete or coherent account of the true nature o f a com plex surface. M olecular m odelling using interatom ic potentials can go som e way to bridging the gap between experim ental techniques which tend to average out fine detail and quantum m echanical techniques which, at present, can include only lim ited detail due to the com putational effort required to describe the system. The findings we report here go a long w ay to bridge the gap between w hat have been tw o opposing conclusions by showing the large differences between perfect and defective surfaces and by showing som e o f the possible surface defect structures in detail.