Chemistry Reference
In-Depth Information
On the reconstructed (1
1) surfaces the adatoms migrate preferentially
along the dimmer rows, giving rise to an anisotropy in the surface diffusion. This
anisotropy is essential for the step dynamics only when the surface diffusion is slow
and the step kinetics is relatively fast, i.e.
D
s
is small and
K
is large. In this case the
characteristic length
d
s
=
×
2) and (2
×
D
s
K
is small (
d
s
l
) and the expression for the surface
flux
j
can be further simplified to
FD
s
kT
n
s
=
v
drif
t
n
s
j
=
(12.2)
Since
D
s
is the coefficient of surface diffusion in a direction perpendicular to the
steps the flux
j
has essentially different values on neighbouring terraces because
they have 90
◦
difference in the dimmer orientation. On terraces having dimmer rows
perpendicular to the steps the diffusion is easy and the surface flux from one step to
the neighbouring one is large. In contrast, on terraces having dimmer rows parallel
to the steps diffusion of adatoms from one step to the neighbouring one is slow, the
surface flux is small and has negligible contribution to the motion of the steps. So
that one can account only for the surface flux on the terraces of the first type and
write the expression
d
l
d
t
=−
FD
s
kT
n
s
2
j
=−
2
(12.3)
for the rate of increase of the width of such a terrace. Here
D
s
is the coefficient
of easy diffusion, i.e. diffusion along the dimmer rows. The sign minus appears
in the right-hand side of the above expression because
F
0 is assumed for
a step-up direction of the electromigration force (see Fig.
12.1
). That is why the
electromigration pushes the atoms detached from the descending step toward the
ascending step where they attach to kink sites. As a result the terrace shrinks. The
terraces of the other type increase their width. The process could be reversed by
reversing the electric current direction. Then the wide terraces decrease in width
whereas the narrow terraces expand.
>
Fig. 12.1
Schematic view of a vicinal surface with straight steps. The adatoms have a drift velocity
induced by an electric force
F
. The width of the
i
th terrace is
l
i
=
x
i
+
1
−
x
i
and the concentration
of adatoms on it is
n
i
