Chemistry Reference
In-Depth Information
edge will not remain so abrupt and the moving edge speed will not be constant.
This deviation from experimental observation will become more apparent for larger
coverage deficits (
). Although it should be accessible in the coverage range
that has been examined experimentally, no such change of profile shape evolution
or non-constancy of speed was observed for coverages as low as 0.09ML below
θ
c
−
θ
θ
c
.
A similar criticism for this model applies if instead of
the temperature is changed.
Depending on the activation energies of
D
c
above and below
θ
D
2
in
the model will change with temperature. This implies that the shape of the profile
will be different at different temperatures and it will not remain dispersionless. This
has not been observed experimentally. Only if the activation energies above and
below
θ
c
the ratio
D
1
/
θ
c
are the same will the non-classical features be preserved with changes of
temperature. Temperature-dependent measurements below
θ
c
are in progress.
3.4.2 Adatom Vacancy Model
Another model that has been considered [
3
] and possibly can account for these
unusual observations is based on an adatom-vacancy diffusion mechanism that at
the minimum can provide a phenomenological explanation, but at the cost of intro-
ducing a number of assumptions and energy barriers. Vacancy generation can be
energetically possible since the wetting layer is dense and considerable strain can
develop, even for the amorphous layer on the (7
7) surface. If we define the local
variables,
c
a
(
r
,
t
) the adatom concentration,
c
v
(
r
,
t
) the vacancy concentration, and
θ
×
(
r
,
t
) the coverage that remains in the wetting layer, then we can write rate equa-
tions describing how these local concentrations change with
t
:
∂
c
a
(
r
,
t
)
2
=
D
a
∇
r
c
a
(
r
,
t
)
+
[
R
G
θ(
r
,
t
)
−
R
R
c
a
(
r
,
t
)
c
v
(
r
,
t
)
]
(3.9a)
∂
t
∂θ(
r
,
t
)
=−
∂
c
v
(
r
,
t
)
=−
[
R
G
θ(
r
,
t
)
−
R
R
c
a
(
r
,
t
)
c
v
(
r
,
t
)
]
(3.9b)
∂
t
∂
t
where
R
G
,
R
R
are temperature-dependent rates that describe how adatoms and
vacancies are thermally generated and
D
a
is the adatom diffusion coefficient on top
of the wetting layer. This set of equations assumes that only adatoms diffuse and
that vacancies are immobile. The first equation states that a change in
c
a
(
is due
to either adatom diffusion, adatom generation from the wetting layer, or elimination
of adatoms by recombination with static vacancies. The second equation states that
vacancies are generated simultaneously with the thermally excited adatoms from the
wetting layer or are lost by recombination. Since a vacancy cannot move, by mass
conservation if a vacancy is generated at (
r
,
t
) then the coverage at this location
must decrease correspondingly.
As initial condition, one assumes the experimental situation where a circular hole
has lower coverage
r
,
t
)
(
c
v
(
r
<
r
0
,
t
=
0
)>
0
)
compared to the coverage outside the
hole. In [
3
],
c
v
=
0
.
5 was assumed. The adatom concentration
c
a
(
r
,
t
)
is determined
