Chemistry Reference
In-Depth Information
12.4.2 Sublimation with Slow Atom Attachment-Detachment
Kinetics
This regime was studied in detail by Krug et al. [
32
]. Substituting expression (
12.17
)
into (
12.28
) one obtains again a continuity equation (similar to (
12.30
)) with
6
g
Kn
s
2
kT
x
z
x
z
xx
+
z
x
∂
1
1
z
x
Fh
0
J
=
(12.40)
∂
Here again the steady-state shape of the bunch is defined by
J
=
J
st
=
Kn
s
2
kT
Flh
0
[
13
]. The “mechanical analog” in this case requires a “potential
energy”
2
3
Flh
0
y
3
/
2
Fh
0
y
U
(
y
)
=−
+
(12.41)
Krug et al. [
32
] found out that this “potential” admits two types of periodic tra-
jectories depending on the “total energy”
E
(see (
12.34
)) being negative or positive.
In other words, there are two bunch shapes with different scaling properties. When
the maximum slope
z
x
h
0
l
H
1
/
2
[
32
]. These shapes are not of
physical interest since the slope of the vicinal surface is
h
0
/
l
and a bunch with a
maximum slope, which is just 1.5 times larger, is difficult to distinguish in the real
experiments, where
h
0
/
3
2
≤
one has
L
∼
01. The observable bunch shapes correspond to the
limit where the “potential energy” is dominated by the first term, i.e.
l
≈
0
.
2
3
Flh
0
y
3
/
2
U
(
y
)
=−
(12.42)
and one should solve an equation similar to (
12.35
). Thus one obtains
986
H
1
/
3
g
1
/
3
Flh
0
L
=
2
.
(12.43)
12.5 Important Experiments
The scaling relations for the shape of bunches (
12.38
), (
12.39
), and (
12.43
)arethe
basic quantitative results of the theoretical work on step bunching, induced by direct
electric current heating of Si crystals. These results opened a pathway for a number
of interesting experiments. Fujita et al. [
15
] used scanning tunnelling microscope to
study the bunch shape and its scaling properties. The initial surface with uniform
step train was created by passing a direct current in the step-up direction for 15 s
at 1300
◦
C. Step bunches were produced with currents in the step-down direction
at 1250
◦
C, and in the step-up direction at 1145
◦
C. The cooling time from 1250 to
600
◦
C and 1145 to 600
◦
C was less than 3 and 4 s, respectively. The change of the
