As we have already discussed above, most metal surfaces do not
reconstruct. The only change in the geometry upon the creation of the
surface are relaxations of the layer distances. In most cases, the
first to second layer distance contracts like in the simple Finnis and
Heine model
. The charge-smoothing effect which leads to this
relaxation should be more important for more ``open'' surfaces (like
fcc(110)) and less for ``closed'' surfaces (like fcc(111)). This is
indeed the case. Fig.
shows the change in the first layer
distance as a function of the bulk value of this distance (both
normalized to the nearest neighbour distance in the bulk). The bulk
value of the layer distance is a measure for the openness of the
surface. Closed packed surfaces are to the right side of the plot,
open surfaces to the left. The plot does not only show the
experimental values for the distances (which were obtained using
quantitative LEED) but also the result from modern first-principles
calculations. The agreement between experiment and theory is rather
good. We further note that all the points lie more or less on one
line, the ``universal curve'' for the interlayer distance of simple
metals. The only remaining problem is that the qualitative
Finnis-Heine model gets into trouble for the closed packed surfaces.
They relax into the other direction! The first layer distance at the
surface is even bigger than that in the bulk.
Figure: Distance between first and second layer of simple metal
surfaces as a function of bulk interlayer distance (both
normalized by the nearest neighbour distance in the bulk). After
Ref.
[30].
Very many ordered adsorbate systems have been solved using LEED. Actually, it is quite fortunate that so many adsorbates form ordered structures such that they can be studied by this technique! We give just two examples here.
Alkali atoms have always been of great
interest as particularly simple adsorbate systems. We have already
looked at alkalis in the lecture about adsorption. Basically, the
picture is very simple: the alkali s level broadens when the atom
gets close to the surface and gets more or less emptied upon adsorption.
The result is a fairly ionic bond. If the substrate for alkali
adsorption is a stable, closed packed surface of a simple metal one
would expecting simple adsorption sites for the alkali atoms
without a severe perturbation of the substrate, let alone a
reconstruction. A recent LEED investigation of K adsorbed on Al(111)
has shown that this simple picture is not necessarily correct.
[31].
K forms
a
for adsorption at low
temperature and at room temperature. At low temperature the K atoms
are adsorbed in on-top sites on the substrate. However, when adsorbed
at (or heated to)
room temperature they lead to a severe reconstruction of the
surface and are found in substitutional sites (see Fig. ).
Figure: Adsorption geometry for K on Al(111) at 100 K (top) and
300 K (bottom). Both structures give rise to a
LEED pattern. After Ref.
[31].
Another example for an adsorbate-induced reconstruction is the (2x1)
oxygen structure found on Cu(110) at half a monolayer coverage. This
structure is shown if Fig.
. It consists of oxygen-copper
chains in the [001] direction. Evidently, half a monolayer of the top
copper atoms has to be removed or added to form such a structure but
LEED can not give information about the actual mechanism.
Figure: Adsorption geometry for (2x1)-O on Cu(110). Left: top
view of the clean surface, Right: top view of the reconstruction.
After Ref. [33].
As mentioned above, semiconductor surfaces tend to reconstruct, sometimes in rather complicated ways. These reconstructions are very closely related to bonding in semiconductors and thus to the electronic structure. We will come back to this in a later lecture. The reconstructions present a major problem to the LEED analysis because of the complicated structure and the large unit cell. Apart from the reconstructions there is the general feeling that the present LEED theory does not work as good for semiconductors as it does for metals. Why this is so is a tricky questions and definitely beyond the scope of these lectures. Anyway, the LEED structure determination of semiconductor surfaces is an important present research area.
We just want to show two examples of semiconductor reconstructions in
order to illustrate how complicated they can be. The first is the
famous (7x7) reconstruction of Si(111)
. When Si is cleaved in the
(111) plane several reconstructions can be obtained depending on the
temperature at which the cleaving is performed: (1x1), (2x1) and
(7x7). Annealing the cleaved surface to high temperature always
results in the formation of the (7x7) structure which remains also
when cooling the crystal down again. Therefore, it is thought that this
reconstruction is the one with the lowest total energy. Several
structural models have been proposed for the (7x7) reconstruction. The
model which is thought to be the right one is shown in Fig.
.
It has to be pointed out, though, that this structure has not been
found by LEED.
Figure: Left: ideal Si(111) surface. Right:
the Takayanagi model for the Si(111) (7x7)
reconstruction. After Ref.
[34].
Another example is the (2x1) reconstruction of the technologically
important Si(100)
surface. This surface has been studied with a
variety of techniques including quantitative LEED. The model favoured
at present is that of a dimer reconstruction of the surface as shown
in Fig
. There is, however, still a considerable dispute
about the details of the reconstruction, in particular on the
question if the dimer is symmetric or not.
Figure: The unreconstructed Si(100) surface and the asymmetric dimer model.
Studying insulator surfaces with electron spectroscopy immediately brings up the problem that the surface charges up when it is bombarded with electrons or when it emits electrons. No meaningful experiment can be done. If we want to look at insulators with LEED we have to overcome this problem somehow. There are two main strategies to do this. The first is to have a sufficient number of defects in the insulator which provide carriers such that a small conductivity results. In the case of insulating oxides this is mostly done by heating the sample in vacuum which results in oxygen vacancies. The disadvantage is that one studies a modified version of the oxide. The other possibility is to prepare a thin film of the oxide on a metallic substrate. This also gives enough conductivity to do electron spectroscopy but one has to worry about the fact that one may not really study the surface properties of the real bulk material.
Oxides surfaces where used a lot in the early days of surface science because
some are so inert that they can be studied for several days even under
rather poor vacuum conditions. An example for an early LEED
investigation of an insulator is the (001) surface of NiO
. NiO has a
rock-salt structure shown in Fig.
. It is a
prototype material for a highly correlated electron system. The
electronic configuration of the Ni 
ions is 
and this
partially filled band would correspond to a metallic ground state in
a band structure picture. Yet, the strong on-site d-d electron
repulsion causes the material to be an insulator with a band gap of
more than 4 eV! The LEED pattern from NiO(001) was found to be (1x1).
For this surface there are two possibilities of structural changes
consistent with such a LEED pattern: an interlayer relaxation as we
know from metal surfaces and a buckling in the surface layer (i.e. a
structural change where the Ni ions and the oxygen ions are not in the
same plane any more). The latter geometry change is not possible with
only one atom per unit cell.
The LEED result is that the surface shows a small inward relaxation
but no buckling.
Figure: Structure and surface unit cell of NiO (top view).
Top-layer Ni ions are red, second layer Ni ions are pink, oxygen
ions are black.