Chemistry Reference
In-Depth Information
Fig. 4.22
Frequencies of localized surface phonon modes at
k
=
0 for different slab thicknesses.
Panels (
a
)and(
b
) stand for longitudinal and transverse modes, respectively. In both cases the
highest corresponding bulk mode frequency is indicated. In panel (
a
) the results considering the
cases of both slab's ends free (
bold symbols
) and fixing one while leaving the other one free (
open
symbols
) are shown. Panel (
b
) stands only for the case of one slab's ends fixed. Panel (
c
)showsthe
contraction of the outermost layer
one could deduce the thermal expansion coefficients of the Pb films of different
thicknesses along the film normal direction.
Shown in Fig.
4.20
are the temperature-dependent photoemission spectra of
23ML (Fig.
4.20
a) and 24ML (Fig.
4.20
b) Pb films by Zhang et al. [
58
]. From
the spectra, the film morphology assumes an atomically flat surface over a macro-
scopic scale. Again, the strongest peaks correspond to the highest occupied QWS.
Note that for both films including other films studied, the QWS peaks shift always
toward higher binding energy with increasing substrate temperature. Furthermore, a
dramatic difference between even and odd Pb layers can be clearly detected.
To quantify the results, the temperature dependence of the QWS binding energy
for several Pb films is fitted linearly and shown in Fig.
4.23
a. While the increased
binding energy of the QWS in Ag/V(100) system was explained as that the energy
of the QWS decreases more than the Fermi energy of the substrate, it could be
attributed to a different reason, namely the thermal broadening of the confinement
