Chemistry Reference
In-Depth Information
Fig. 6.2
Atomic configuration of smooth epitaxial interface at low temperature. Since the adatom
energy does not exceed the energy barriers for direct incorporation inside the substrate, the surface
alloying is entirely blocked, (
6.1
). The interface structure evolves by diffusion of adatoms exclu-
sively on the outermost substrate layer resulting in formation of 2D islands and attachment to the
steps of terraces
6.4.1 Size and Shape Effects in Cluster Diffusion on Smooth
Domains
In the last decade, extensive theoretical and experimental studies revealed that the
diffusion coefficient
D
of clusters scales with the number
N
of atoms in them
as
D
N
−
α
. Being dependent on the dominant mass-transport mechanism, the
∝
exponent
α
takes values
α
=
3
/
2 for periphery diffusion (PD),
α
=
1 for terrace
diffusion (TD), and
2 for evaporation/condensation mechanism [
7
,
26
-
28
].
Unfortunately, the values of the above scaling exponents reflect highly simplified
cases. In fact, cluster migration is a quite complex phenomenon influenced by simul-
taneously acting diffusion mechanisms. The transport process is found to be also
timescale dependent, because of the long-time behavior of edge and step fluctuations
[
6
,
8
]. As a result the terrace diffusion dominates at long times whereas the edge dif-
fusion plays a key role at short times. That is why, the experimentally observed non-
universal scaling exponents reflect the contribution of competing mass-transport
processes. The experimental evidence of exotic oscillatory behavior of the surface
diffusion coefficient of clusters as a function of their size is another challenge
[
29
-
35
]. The effect of “magic clusters” mobility mostly relates to different geo-
metric configurations (compact or non-compact structures) of atomic assemblies. In
some specific cases of heteroepitaxial systems, a soliton or dislocation mechanism
could be essential for island diffusion, too [
32
-
35
]. In the next section, we will
demonstrate that besides the above effects, the commensurability between overlayer
and substrate has to be taken into account of diffusion behavior of 2D islands.
In the present model, the diffusion on smooth epitaxial interface was evaluated by
the trace of the center of mass of
N
-atomic cluster. As seen in Fig.
6.3
, this center
follows Einstein random walk behavior. The computational data are collected for
six-atomic cluster at
T
α
=
1
/
10
6
MC steps.
=
400 K over 1
×
