Chemistry Reference
In-Depth Information
For Pb films on the Ge(111) substrate, there is a 11% mismatch between the
lattice constants (Ge, 5.76 Å; Pb, 5.04 Å). This large mismatch makes it impossible
to carry out directly first-principles calculations for the Pb(111) and Ge(111) inter-
faces. A technical trick to overcome this obstacle is to rot
a
te th
e
substrate by 30
◦
and
place a 2
(
√
3
×
√
3
R
30
◦
)
surface. Such
a method enables to accommodate the lattice mismatch between Ge and Pb and the
substrate remains semiconducting. Another way adopted is to artificially compress
the substrate to match the lattice constants, such as for Si(111) substrate in [
35
].
But in this approach, the substrate may become metallic and change its conducting
nature, which is not desirable.
The surface energies of Pb films on the Ge(111) substrate and their discrete sec-
ond derivatives are plotted in Fig.
4.9
. Similar to the freestanding films, there are
bilayer oscillations interrupted by crossovers. The separation between the crossovers
is about nine monolayers but the crossovers are located at 5 monolayers, 13 mono-
×
2 Pb unit cell on a bulk truncated Ge(111)-
Fig. 4.9 (a)
Surface energies of Pb(111) films on a Ge(111) substrate.
(b)
The second derivative
of surface energy of Pb(111) films on a Ge(111) substrate
