12.2 Heteroepitaxy
357
Table 12.1 Epitaxial relationship for various film/substrate combinations, ZnO (or GaN) on c-, a- and r -sapphire and
Si(111)
ZnO
Al 2 O 3
ZnO
Al 2 O 3
ZnO
Al 2 O 3
ZnO / GaN
Si
[00.1]
[11.0]
[ ¯
10.2]
[111]
[00.1]
[00.1]
[00.1]
[11.0]
[11.0]
[ ¯
10.2]
[00.1]
[111]
[11.0]
[01.0]
[11.0]
[00.1]
[00.1]
[0 ¯
1.1]
— / [2 ¯
1.0]
[ ¯
110]
Fig. 12.8 X-ray
diffraction intensity from
the asymmetric ZnO (10.4)
(upper panel) and the
sapphire (10.10) (lower
panel) reflections as a
function of the azimuthal
sample orientation
(rotation angle φ around
the [00.1] axis). The peaks
appear at different tilt
angles ω due to an overall
tilt of the mounted sample
(dashed sinusoidal lines).
The ZnO [00.1] axis is not
tilted with respect to the
sapphire [00.1] direction
=30°
-180
180
Al O
(1 0.10)
2
3
90
Tilt (deg)
0.4
0.2
0
-0.2
-0.4
0.4
0.2
0
-0.2
-0.4
(deg)
Tilt (deg)
0
-90
ZnO
(1 0.4)
If substrate and epilayer have different space groups, the formation of domains can occur [1139].
The two-dimensional symmetries of various substrates are listed in Table 11.1. The group theoretical
minimum number of domains N RD in dependence of the two-dimensional symmetries of substrate and
epilayer with rotational symmetries C n and C m , respectively, is given by [1140]
N RD =
lcm(n, m)
m
,
(12.2)
where lcm denotes the least common multiple. The values are listed in Table 12.2 and visualized in
Fig. 12.10.
If the main symmetry axes of substrate and epilayer are not aligned, mirror domains appear. An
example is the growth of GaN(00.1) on Ge(111), for which it has been reported that the major symmetry
directions do not align exactly. There is a 4
◦ in-plane rotation of the lattices with respect to the usual
[11.0] ] [1 ¯
10] in-plane relationship [1141] (cmp. the exact alignment for GaN/Si(111) in Table 12.1).
Due to 3 m mirror symmetry of the substrate, the misaligment is equivalent for clockwise and counterclockwise rotation. Therefore two domains with an angle of 8
◦ occur (Fig. 12.11).
Another well-known domain effect in heteroepitaxy is the occurence of antiphase domains of
zincblende semiconductors (e.g., GaAs, GaP, InP, . . .) grown on Si(001) with monoatomic steps;
357
Table 12.1 Epitaxial relationship for various film/substrate combinations, ZnO (or GaN) on c-, a- and r -sapphire and
Si(111)
ZnO
Al 2 O 3
ZnO
Al 2 O 3
ZnO
Al 2 O 3
ZnO / GaN
Si
[00.1]
[11.0]
[ ¯
10.2]
[111]
[00.1]
[00.1]
[00.1]
[11.0]
[11.0]
[ ¯
10.2]
[00.1]
[111]
[11.0]
[01.0]
[11.0]
[00.1]
[00.1]
[0 ¯
1.1]
— / [2 ¯
1.0]
[ ¯
110]
Fig. 12.8 X-ray
diffraction intensity from
the asymmetric ZnO (10.4)
(upper panel) and the
sapphire (10.10) (lower
panel) reflections as a
function of the azimuthal
sample orientation
(rotation angle φ around
the [00.1] axis). The peaks
appear at different tilt
angles ω due to an overall
tilt of the mounted sample
(dashed sinusoidal lines).
The ZnO [00.1] axis is not
tilted with respect to the
sapphire [00.1] direction
=30°
-180
180
Al O
(1 0.10)
2
3
90
Tilt (deg)
0.4
0.2
0
-0.2
-0.4
0.4
0.2
0
-0.2
-0.4
(deg)
Tilt (deg)
0
-90
ZnO
(1 0.4)
If substrate and epilayer have different space groups, the formation of domains can occur [1139].
The two-dimensional symmetries of various substrates are listed in Table 11.1. The group theoretical
minimum number of domains N RD in dependence of the two-dimensional symmetries of substrate and
epilayer with rotational symmetries C n and C m , respectively, is given by [1140]
N RD =
lcm(n, m)
m
,
(12.2)
where lcm denotes the least common multiple. The values are listed in Table 12.2 and visualized in
Fig. 12.10.
If the main symmetry axes of substrate and epilayer are not aligned, mirror domains appear. An
example is the growth of GaN(00.1) on Ge(111), for which it has been reported that the major symmetry
directions do not align exactly. There is a 4
◦ in-plane rotation of the lattices with respect to the usual
[11.0] ] [1 ¯
10] in-plane relationship [1141] (cmp. the exact alignment for GaN/Si(111) in Table 12.1).
Due to 3 m mirror symmetry of the substrate, the misaligment is equivalent for clockwise and counterclockwise rotation. Therefore two domains with an angle of 8
◦ occur (Fig. 12.11).
Another well-known domain effect in heteroepitaxy is the occurence of antiphase domains of
zincblende semiconductors (e.g., GaAs, GaP, InP, . . .) grown on Si(001) with monoatomic steps;