The surface science of titanium dioxide - Niser

74 U. Diebold / Surface Science Reports 48 (2003) 53±229
The directions of the calculated relaxations agree in (almost) all the theoretical papers with the
experimentallydetermined coordinates. The quantitative agreement is not as good as one could expect
from state-of-the art ab initio calculations, however. As Harrison et al. [64] pointed out, the extensive
experience of calculations on bulk oxides which has been built up in recent years leads one to expect
that DFT and HF calculations will reproduce experimental bond lengths to somewhat better than 0.1 AÊ .
For example, the bulk structural parameters of TiO 2 rutile agree better than 0.06 AÊ using soft-core ab
initio pseudopotentials constructed within the LDA, and a plane-wave basis [104].
In particular, all the calculations ®nd a much smaller relaxation for the position of the bridging
oxygen atom. A possible reason for this disagreement was given by Harrison et al. [64]. All the
theoretical results listed in Table 3 are strictlyvalid onlyat zero temperature. It is conceivable that
strong anharmonic thermal vibrations at the TiO 2 (1 1 0) surface cause the discrepancybetween
experimental and theoretical results. However, molecular dynamics simulations using the Carr±
Parinello approach [105] found that the average position in dynamic calculations is only relaxed by
0.05 AÊ rather than by0.27 AÊ , discarding this explanation. Instead, it was suggested that the O atom
might relax laterallyso that it is displaced into an asymmetric position.
Based on these theoretical results, the ®nite temperature has to be taken into account for a proper
evaluating diffraction results. Hopefully, future experiments will show whether a better agreement with
theoreticallypredicted relaxations can be achieved. When considering surface reactions, one also needs
to depart from a static picture of this and other oxide surfaces, and has to keep in mind the substantial
distortions and bond length changes that take place during such large-amplitude vibrations.
It is now well-known that adsorbates often have a signi®cant in¯uence on `re-relaxing' the surface.
Computational studies, e.g. the one given in [106] for the adsorption of Cl, clearlyshow strong effects
upon adsorption. Onlya few experimental exist so far. For example, Cu overlayers on TiO 2 (1 1 0) cause
the Ti atoms at the Cu/TiO 2 (1 1 0) interface relax back to the original, bulk-like positions. The O atoms
relax even stronger, which was attributed to Cu±O bonding [107].
2.2.1.3. Appearance in STM and AFM. Naturally, scanning probe techniques are extremely useful tools
for studying atomic-scale structures at TiO 2 and other metal oxide surfaces, where local changes in
stoichiometryor structure can severelyaffect surface reactivity. On TiO 2 (1 1 0), STM and, more recently,
non-contact AFM, have been used bymanydifferent groups. These techniques have provided valuable
and verydetailed insight into local surface structure. However, the interpretation of STM images of
oxides is somewhat challenging because of strong variations in the local electronic structure, and because
tips can easily`snatch' a surface oxygen atom, which can cause a change in tip states and result in
`artifacts' in STM images. There is now consensus among different groups on what is `really' observed
with STM, at least under `normal' operating conditions.
The dominant tunneling site on TiO 2 (1 1 0) surfaces has been subject to some debate in the past. In
principle, there is uncertaintyas to whether the image contrast is governed bygeometric or electronicstructure
effects. For TiO 2 , atomic-resolution STM is often onlysuccessful when imaging unoccupied
states (positive sample bias) on reduced (n-type) samples. In reduced TiO 2 crystals, the Fermi level is
close to the conduction-band minimum (CBM) in the 3 eV gap, and electronic conduction occurs
predominantlythrough high-lying donor states [78]. Under a typical bias of ‡2 V, electrons can thus
tunnel from the tip into states within 2 eV above the CBM, and be conducted awayfrom the surface.
On the one hand, these CBM states have primarilycation 3d character (the valence band having
primarilyO 2p character, see Section 3) so that one might expect to image the metal atoms as the