Chemistry Reference
In-Depth Information
with the substrate. During the time that atoms from the upper layers hop across
the profile edge into the lowest layer, mass at the edge is replenished quickly by
fast diffusion on top of this layer. The advancing profile shape does not change
because diffusion in the upper layers is fast compared to diffusion within the lower
layer. The coverage profile shows two unperturbed edges: the receding edge in the
upper layer serves as the source of atoms that are incorporated at the unperturbed
edge of the layer in contact with the substrate. The speed of the lower advancing
edge decreases as its distance from the upper source edge increases with time. This
clearly shows a film that does not behave as Pb/Si of Figs.
3.5
and
3.6
where the
motion of a single edge with constant speed demonstrates that the whole layer moves
collectively.
The BM method was used for the analysis in [
6
] with
r
/
√
t
the scaled vari-
able so the profile speed was decreasing with
t
. Since diffusion of the second layer
was higher than diffusion in the first layer, the derived coverage dependence
D
c
(θ)
showed a gradual jump starting from 0.5ML in the first layer to a value five orders of
magnitude larger in the second layer; but the coverage width of the transition region
between these two values, 0.3ML, is much larger than essentially discontinuous
jump (that was assumed in the modeling of profile evolution in Pb/Si (Sect.
3.4.1
).
Finally, for Li/Mo(112) there is no critical region and critical coverage
θ
c
where the
diffusion coefficient decreases with an exponential or power law dependence on the
coverage difference (
θ<θ
c
.
Concentration profiles that do not disperse with
t
have been also observed with
LEEM in a more complicated system, Au/Si(111) [
51
], but at much higher temper-
ature 910 K and with smaller spreading speeds 7
θ
c
−
θ
)for
10
−
2
nm/s than that observed in
Pb/Si(111). The Au/Si(111) is complex because from the dense 1 ML high coverage
phase on one side to zero coverage (i.e., the clean Si(111) (7
×
×
7)) on the other side
of the profile edge, two superstructures form, the Au(
√
3
×
√
3) and Au(5
1). The
system is not homogeneous as in the current work. In the experiment of [
51
], addi-
tional edges were identified separating the 1ML from the
√
3 phase, the
√
3from
the (5
×
1) phase had
two distinct phases with coverages differing by 0.1ML). Only the edge separating
the (5
×
1) phase, and the (5
×
1) from the (7
×
7) phase (even the (5
×
7) phase was moving at a constant speed. In this system the
time measured for the edge to diffuse to a given location is the time to arrive at the
location and the time to convert from the random atom position to the ordering of the
local phase. The data were accounted quantitatively if diffusion on top of the (5
×
1) from the (7
×
1)
was the fastest process and the measured diffusion time was determined by the time
for these atoms to move from the top of the (5
×
×
1) to the layer below and expand
the (5
1) domain area, analogous to the carpet unrolling mechanism. Besides these
inhomogeneities, the higher temperature, and the lower advancing speed, no critical
coverage
×
θ
c
was identified in [
51
].
No such inhomogeneities exist in the Pb/Si(111) system and if the same local
coverage
within the hole is realized, the same phase forms irrespective of whether
it was added by deposition as in Fig.
3.8
or by diffusion from the edge. There is
only one boundary observed and the speed across the moving layer is the same.
θ
