Chemistry Reference
In-Depth Information
(a)
(b)
Fig. 4.21 (a)
Lorentzian peak widths of the QWS of the 22ML (
square
) and 23ML (
triangle
)films
plotted as a function of temperature.
(b)
Measured
(
triangles
) and calculated superconductivity
transition temperature (
diamonds
). Reproduced from [
58
]
λ
3 to 14 layers are calculated and the results are shown in Fig.
4.22
.FromFig.
4.22
,
one can see that both longitudinal and transverse surface modes take place at ener-
gies above the corresponding bulk values due to a 6% contraction of the surface
layer (see Fig.
4.13
). A bilayer oscillatory variation of both surface states is found,
being more pronounced for the longitudinal modes than in the transverse ones as
expected due to their different characters. It is expected that, like the surface energy,
there should be one crossover among these layers with a beating period of 9ML.
However, the beating effect is not found in the DFT calculations. More theoretical
studies are needed to reconfirm this.
4.6.4 Thermal Expansion
Temperature dependence of the PES spectra width was used to investigate many-
body effects with regard to electron-phonon coupling. The peak positions, i.e., the
binding energies of the QWS in the temperature-dependent spectra, could be used to
understand the thermal expansion behavior of the thin films. From this dependence,
