Chemistry Reference
In-Depth Information
d
E
QW
d
T
=−
2
E
QW
α
Z
(4.13)
The linear thermal expansion coefficients of the Pb films in the confined direction
were calculated by the experimental thermal shift of QWS binding energy in terms
of (
4.11
) and (
4.12
), and the results are shown in Fig.
4.23
b. Several observations
can be made as follows: (1) the thermal expansion coefficients in the film normal
direction are greatly enhanced compared to the bulk Pb; (2) there is a 2ML oscilla-
tion for the Pb films from 21 to 24ML; (3) the overall trend is that a lower expansion
coefficient corresponds to a film with a higher QWS binding energy. Since the thick-
ness of the Pb films is very small, the linear expansion coefficient in the film plane
(
xy
-plane) should be very closed to that of bulk Si, while in
z
-direction, a great
enhancement can be expected because of what called Poisson effects and that the
linear expansion coefficient of Si (2
10
−
6
K
−
1
) is one order of magnitude lower
.
8
×
10
−
5
K
−
1
). To understand the global enhancement of the
linear thermal expansion coefficient along the confined direction, we use
than that of Pb(2
.
89
×
α
P
, and
α
Z
to describe the linear expansion coefficient of the freestanding film, the confined
film in the film plane, and the film normal (
z
) direction, respectively.
α
r
,
α
Z
can be
expressed as
(α
r
−
α
P
)η
1
2
α
Z
=
α
r
+
(4.14)
−
η
where
α
P
by the linear expansion coef-
ficients of bulk Pb and bulk Si, respectively, and taking
η
is the Poisson ratio. Substituting
α
r
and
η
as the Poisson ratio of
bulk Pb(0.44), we obtain
α
r
. That means, in an ideal case, the
thermal expansion in
z
-direction should be enhanced by 2.414 times of the bulk
value, which is adequate to explain the global enhancement of the experimental
data in Pb/Si(111).
α
z
that equals 2
.
414
4.6.5 Superconductivity
Advances in the thin film growth via QSE also prove to be essential to study the
superconductivity in 2D geometry. Because the normal state resistance is a criti-
cal factor in destruction of the superconductivity, excellent film quality is required
to investigate the inherent physics of low-dimensional superconductors [
60
]. For
example, when the normal state resistance reaches the quantum resistance for the
Cooper pairs, the superconductivity disappears [
61
]. While the normal state resis-
tance was the control knob in the earlier studies of the thin film superconductiv-
ity, atomically smooth films achieved in the quantum growth regime render the
film thickness as the well-controlled fundamental parameter [
12
-
14
]. Indeed, it is
already known that the boundary scattering sets the limit of the resistivity at low
temperatures [
62
,
63
].
Various groups have measured the superconducting transition temperature
T
C
of Pb films and Pb islands employing various methods such as contactless mag-
