Chemistry Reference
In-Depth Information
exp
E
DB
i
kT
D
i
∝
−
(6.7)
in which
k
is the Boltzmann constant, the spreading of alloyed stripe depends on
a series of increasing diffusion barriers
E
D
i
for entering in the first, second, third,
i
th atomic rows. The evaluation of
E
D
i
is a complex problem that should account
for simultaneously acting physical effects such as elastic strain, non-symmetric ter-
race relaxation, step anisotropy, adlayer-substrate atomic interactions. The atomic
relaxation is favorable exclusively in the direction out of the step, whereas inside
the terrace the elastic strain increases and resists the penetration of foreign atoms.
Therefore, the finite width of the stripe is a result of non-symmetric elastic strain
field (physical boundaries) of alloyed domains at step edges.
6.5.2 Step Anisotropy Contribution to Step Diffusion Barriers
An important detail of step diffusion barriers relates to the crystallographic
anisotropy of terraces. A very telling example of low-indexed
orientations
of epitaxial interface is presented in Fig.
6.11
. The symmetry and the resulting
atomic arrangement on fcc(111) surface generate atomic terraces with two kinds
of steps, A and B, Fig.
6.11
(inset down right), each of them having different step
free energy and relaxation ability [
7
,
41
].
Simple analysis of the geometrical atomic configuration presented on the inset
down right in Fig.
6.11
shows that the atomic shift toward the nearest-neighbor
threefold symmetry hollow site for Cu atom of the B-step (left step direction)
costs less energy compared to that for identical peripheral Cu atom of the A-step
(right step direction) on the terrace. The elastic strain generated by foreign atoms
diffused into the terrace matrix is reduced preferably in the B-step direction. The
favored terrace relaxation in direction B is consistent with the larger stripe width
L
S
at the terrace step B, compared to the stripe width
L
S
at the terrace step A,
Fig.
6.8
. Simulation snapshot analysis for equilibrium atomic configurations at con-
stant
T
<
111
>
4
L
S
. Therefore, the stripe width is affected by
the step anisotropy resulting in different relaxation of the elastic strain in the system
generated by “larger” foreign Pb atoms in the terrace [
4
,
42
].
The presented diffusion scenario is rather promising for manipulation of high-
indexed epitaxial interface. If the initial atomic configuration of the system is con-
sisted of equidistant terraces on vicinal surface then the formation of alloyed stripes
is restricted exclusively to the single step of the terrace, Fig.
6.12
.
The interface forms staircase-up or staircase-down configuration of 2D regular
stripes. In the energy gap
T
L
≤
300 K reveals
L
S
=
≈
1
.
≤
T
H
the stripe width depends on
T
through the
relaxation ability of the vicinal terrace. The critical terrace width was found to be
three times the spreading width of stripe. Below this value the terrace is completely
alloyed. Therefore, even at
T
L
T
≤
T
≤
T
H
, the vicinal epitaxial interface having
