Chemistry Reference
In-Depth Information
Figure 5.2. Scheme of a parallelepiped-shaped nucleus (n) on a substrate (s) and
attached to a step (
). Molecules coming from the vapour phase (v), represented
by arrows exhibiting different trajectories, interact with the flat substrate, terrace or
nucleus surfaces, diffuse and then desorb or attach to a step or start to nucleate. In
the aggregation regime, the incoming material aggregates into the existing islands
and finally they coalesce. The heterogeneous growth is symbolized by a different
grey scale.
σ
The major physical insight of the BCF model is that growth (the model can also
be applied for sublimation) is strongly mediated by the presence of steps, acting
as active and efficient sites for the attachment and detachment of molecules onto
the terraces. During growth the concentration of the molecules exists in dynamic
equilibrium with the step-edges by a balance between the rate of attachment and
detachment from the step-edges, their rate of diffusion on the terraces governed by
diffusion coefficient
D
s
, by desorption processes and deposition of molecules with
a flux
m
. The diffusion is by far the most important kinetic process in film growth
in the sense that sufficient surface mobility is mandatory in order to obtain smooth
and uniform films. The BCF model assumes that the incorporation of molecules
occurs at a time scale much faster than the motion of steps. In Section 5.5 we shall
see that diffusion of molecules along the steps, the so-called periphery diffusion,
terrace diffusion and attachment-detachment processes induce step fluctuations,
that is the motion of steps.
The expression for
G
is given by (Molas
et al
., 2000):
L
2
h
L
2
G
=−
G
V
+
G
S
=−
µ
+
γ
+
Lh
γ
⊥
,
(5.1)
where
G
V
and
G
S
(
G
V
>
0,
G
S
>
0) represent the bulk and interface contributions
to
G
and
µ
stands for the chemical potential per unit volume.
µ
=
µ
v
−
µ
n
,
