Chemistry Reference
In-Depth Information
π
2
k
F
−
λ
beat
=
k
BZ
≈
9ML
(4.7)
The salient features of the re-entrant bilayer-by-bilayer mode are attributed to the
quantum nature of the film stability, as confirmed quantitatively in DFT calculations
disscussed above.
4.4.4 Transition from Smooth Film to Island Regime
The island morphologies can never be formulated as a unique, reversible, and path-
independent function of deposition temperature, annealing temperature, and depo-
sition amount, even though 2D flat-top objects do form at low deposition temper-
atures because of size quantization effects. The contact area between the islands
and the substrate changes upon annealing whereas for a continuous film, the con-
tact area remains preserved during the morphological evolution. Reduction of the
surface energy upon creating taller islands should ultimately lead to 3D clusters in
thermodynamic equilibrium [
38
]. Hence, the stability arguments presented for the
case of a closed 2D morphology cannot be used here. At low temperatures, on the
other hand, one can think of a local equilibrium concept where a number of nearby
local energy minima may be accessible within the “attempt range” of the system.
From this perspective, the gradual evolution of taller islands can be thought of as
successive jumps over multiple energy barriers, each time reaching a lower point in
the global energy landscape.
The demarcation between the low temperature quantum growth region and the
high temperature thermodynamic limit is a delicate one. For the quantum regime,
the local stability concept is better suited whereas at high temperature the global
energy landscape must be used [
21
]. It is well known that deposition of Pb(111) at
150-220 K produces flat-top islands with fairly uniform heights [
25
]. The selected
height can be tuned by changing the deposition or post-annealing temperature: the
lower the temperature, the lower the average island height. The first selected height
turns out to be 5ML, then comes the 7 and 9ML islands at elevated temperatures.
Once the 5 (or 7 or 9ML) high islands cover the whole surface, the growth continues
in layer-by-layer or bilayer-by-bilayer fashion depending on the temperature [
8
].
This new growth mode, i.e., the initial formation of flat-top islands followed by 2D
layer growth, has been explained in terms of
quantum phase separation
[
22
].
The roughening of initially flat continuous films (grown at very low tempera-
ture) upon warming is closely connected to this quantum phase separation: films
deposited at 110-150 K exhibit some surface roughness because of the limited sur-
face diffusion at low temperature. As the temperature is raised, the film first becomes
smooth and then upon further annealing it will develop deep holes that go all the
way down to the interfacial wetting layer (see Fig.
4.11
). The ejected material from
these holes accumulates around the holes, thus creating local areas of higher film
thicknesses. Figure
4.11
shows the evolution of an initially 6.5ML thick Pb deposit
(wetting layer
+
.
×
5
5ML) on a Si(111) 7
7 substrate, as seen with STM. Snapshots
