Chemistry Reference
In-Depth Information
400 nm
2
) of a silver island simultaneously decaying in
Fig. 5.5
Time-lapse STM images (400
×
10
9
A/m
2
with the current direction upward in the
images as shown and thus a wind force direction downward [
79
]
size and moving under a current density
∼
6
.
7
×
motion will be in the same direction as the electromigration force [
55
]. The results
in Fig.
5.5
clearly show the island displacement occurring in the opposite direction
to the current and thus in the same direction as the electromigration wind force.
Thus the electromigration-induced motion for Ag islands on Ag(111) is the result
of biased diffusion along the step edges (Fig.
5.5
).
The theoretical prediction for the velocity of the island motion due to biased step
edge diffusion is [
55
]
aD
L
F
k
B
TR
0
V
=
(5.5)
where
a
the lattice constant,
D
L
the macroscopic step diffusion constant,
F
the wind
force, and
R
0
the island radius can now be used to determine the magnitude of the
force biasing edge diffusion. The decay of the islands as they are moving provides a
natural mechanism to determine the velocity as a function of island radius. By quan-
tifying the island center of mass positions, the velocity can be determined as shown
in Fig.
5.6
(top panel) with values of 0.02-0.12 nm/s for island radii from 55 nm
down to 15 nm. The decay rate is independent of island size, at
5nm
2
/s, and
combining this information yields the velocity vs. radius plot of the bottom panel of
Fig.
5.6
, which yields an excellent fit (solid line) to the inverse radius prediction of
(
5.5
).
To determine the electromigration force from (
5.5
), it is necessary to evaluate
the edge diffusion constant, which is related to the step stiffness and step mobility
defined in (
5.2
). Because the island exposes all step orientations, it is necessary to
consider how these quantities vary with orientation. For straight step edges,
−
5
.
θ
=
0,
β
is (equation 23 in [
47
])
(
−
)
k
B
T
β(
3
y
1
a
//
=
2
y
y
2
(5.6)
0
)
−
2
y
−
3
1
+
3
z
z
e
−
2
ε
k
/
k
B
T
. The kink energy
with
y
=
and
z
=
ε
is 0.117 eV, so the resulting
(
1
−
z
)
β(
0
)
=
4
.
52 eV/nm at 318 K. For rough step edges (
θ
=
0), we can calculate an
β
average value of
using (equation 18 in [
47
])
