Chemistry Reference
In-Depth Information
From Eq. (5.2a) it becomes clear that the stronger (weaker) the adhesion of the
nucleus on the substrate, the smaller (larger)
G
c
. The role of inhomogeneities
in the substrate, such as defects, impurities, etc., is not taken into account in the
model but they may become relevant because they would reduce
G
c
. In Section 5.4
we shall deal with the case of a cylinder-shaped nucleus growing onto a substrate
following the arguments described here. In this case
L
c
will be replaced by the
critical 2D radius
R
c
. Note that
h
µ
−
γ
must be non-zero in order to avoid
mathematical singularities and that
G
c
2.
All interface tensions are defined as positive and we consider
=
h
γ
⊥
L
c
/
>γ
nv
in
order to intentionally account for anisotropy. This favours 2D growth but does not
prioritize the Frank-van der Merwe mechanism over the others. In fact growth is
always
2D, as indicated by the BCF model, but depends on the lateral size of the
terraces. Small terraces necessarily imply 3D growth.
The chemical potential and interface tension terms can be defined in a consistent
way if the dimensions of the nuclei are sufficiently large. The nuclei considered here
should be large enough, well beyond the discrete nature of such nuclei, to be able to
apply thermodynamic parameters. Estimates of the size of such nuclei range from
a few molecules to relatively large
R
c
values. In the case of (BEDT-TTF)
2
I
3
, layers
grown on HOPG surfaces, where single-layer deep pits have been created by thermal
etching, reveal that nucleation is completely suppressed in pits with
R
c
<
γ
⊥
nv
50 nm
(Hooks
et al
., 1998) while for thin
p
-NPNN films
R
c
<
25 nm, as derived from
the minimum distance between spiral centres of coupled spirals (Fraxedas
et al
.,
1998), a point that will be discussed later in Section 5.5. On the other hand, critical
nucleus sizes
i
, obtained from the scaling of the nucleation density
N
as a function
of the
D
s
/
m
ratio, give
i
=
4 for pentacene grown on chemically oxidized Si(100)
=
(Ruiz
et al
., 2003) and
i
5 for Alq
3
on H-terminated Si(100) (Brinkmann
(
D
s
/
m
)
−
χ
,
et al
., 2002b).
N
,
D
s
and
m
are related through the expression
N
∝
where
2). Here
i
represents the number of monomers, and for cluster
sizes larger (smaller) than
i
the nuclei tend to grow (dissociate). The estimates are
clearly compatible but the difference in range perhaps lies in the crystallinity of the
nuclei.
In the absence of steps
χ
=
i
/
(
i
+
γ
⊥
σ
v
=
0 and
γ
⊥
n
σ
=
γ
⊥
nv
, giving rise to
γ
⊥
=
4
γ
⊥
nv
and Eqs. (5.2a) and (5.2b) transform into:
2
⊥
γ
4
h
2
nv
G
c
=
µ
−
γ
,
(5.3a)
h
γ
⊥
nv
h
µ
−
γ
.
L
c
=
2
h
(5.3b)
