Chemistry Reference
In-Depth Information
Fig. 4.13
Interlayer spacings
d
12
and
d
23
of Pb(111) films on Ge(111) substrate relative to
bulk spacing. Reproduced from [
9
]
relative to the bulk value of the lattice constant while the second interlayer spacing
d
23
is expanded by about 1.5%. These results are in good agreement with the LEED
measurements [
47
]. Note that the crossover positions of
d
23
are not the
same as that of surface energy. Interestingly, the location of the even odd crossovers
has shifted by a half beating period as compared to the even-odd crossovers in the
corresponding surface energy
E
s
(
d
12
and
L
)
, suggesting that the lattice relaxation depends
on the thickness according to d
E
s
(
L
)/
d
L
. This property is not yet fully understood.
4.6.2 Work Function
The work function (WF) is defined as the minimum energy required to remove an
electron from the surface (see Fig.
4.14
). The theoretical and experimental studies
on the work function exhibit changes due to the alkali metal adsorption [
48
], crystal-
lographic orientation [
49
], and the surface steps [
50
] and reveal that WF is related to
the local density of states near the Fermi level. As we have discussed, the presence
of QWS dramatically modulates the density of states at the Fermi level when the
film thickness is varied. Therefore, one would expect to see thickness-dependent
variations in the work function also.
Based on DFT calculations, Wei and Chou showed that, similar to the surface
energy, the WF of freestanding Pb(111) films also reveals bilayer oscillations as
a function of the film thickness [
6
]. Work function calculations for films on a Ge
substrate have also been performed [
9
] and shown in Fig.
4.15
. Bilayer oscillations
are evident and even-odd crossovers exhibit
∼
9ML periodicity similar to surface
energy results. However, the location of the crossover points is phase shifted by half
of a beating wavelength, similar to the behavior of the lattice relaxations.
