4.3 Dislocations
85
Fig. 4.19 Dislocation line orientation angle α (versus the projected c-axis direction) for the a-plane prismatic slip
system for m-azimuth and vice versa (solid line) and the m-plane prismatic slip system for m-azimuth (and a/a) (dashed
line) as a function of interface inclination angle θ. Experimental data from epitaxy on semipolar planes are shown for
(Al,Ga) 2 O 3 /Al 2 O 3 (square), (Al,Ga)N/GaN (diamond, cmp. Fig. 4.18b), (In,Ga)N/GaN (circles), GaN/Si (hexagon) and
(Mg,Zn)O/ZnO (star). Adapted from [325, 326]
dislocation can be dissociated into two partials. This is energetically favorable. As an example we
consider the reaction (Fig. 4.20a)
1
2
¯
101
→
1
6
¯
1 ¯
12
+
1
6
¯
211
.
(4.22)
The length of the full dislocation is a 0 /
√
2. The length of the Shockley partial is a 0 /
√
6. Thus the
energy E = G b
2 of the full dislocation is E 1 = Ga
2
0 /2 and the sum of the energies of the partials
is smaller, E 2 = 2Ga
2
0 /6 = Ga
2
0 /3. In Fig. 4.20b a TEM image of a Ge/Si interface with a Shockley
partial is shown.
4.3.2 Visualization of Dislocations by Etching
Defects can be made visible using etching techniques. This is particularly popular for finding dislocations. Many etches are anisotropic, i.e. the etch velocity varies for different crystal directions. As an
example the result of etching a silicon sphere in molten KOH and a germanium sphere in a HNO 3 /HF
solution are shown in Fig. 4.21. The remaining bodies exhibit those planes with low etching velocity.
The etch velocity of various etch solutions has been investigated in detail in particular for silicon
(Fig. 4.22).
In a planar geometry, etch pits indicate the presence of dislocations, as shown in Fig. 4.23 for Ge
of different orientation. The anisotropic etch prepares {111} planes. The dislocation core is at the
intersection of the planes. In Fig. 4.24 hexagonal etch pits stretched along [1 ¯
10] are developed by
molten KOH [330, 331]. The sides of the base are along [110], 130 and 310. The depth and width
of the pits increases with increasing etching time. On the (00 ¯
1) surface, the orientation of the pits is
rotated by 90
◦ because of the polar [111]-axis of the zincblende structure [330]. Such etch pit develops
85
Fig. 4.19 Dislocation line orientation angle α (versus the projected c-axis direction) for the a-plane prismatic slip
system for m-azimuth and vice versa (solid line) and the m-plane prismatic slip system for m-azimuth (and a/a) (dashed
line) as a function of interface inclination angle θ. Experimental data from epitaxy on semipolar planes are shown for
(Al,Ga) 2 O 3 /Al 2 O 3 (square), (Al,Ga)N/GaN (diamond, cmp. Fig. 4.18b), (In,Ga)N/GaN (circles), GaN/Si (hexagon) and
(Mg,Zn)O/ZnO (star). Adapted from [325, 326]
dislocation can be dissociated into two partials. This is energetically favorable. As an example we
consider the reaction (Fig. 4.20a)
1
2
¯
101
→
1
6
¯
1 ¯
12
+
1
6
¯
211
.
(4.22)
The length of the full dislocation is a 0 /
√
2. The length of the Shockley partial is a 0 /
√
6. Thus the
energy E = G b
2 of the full dislocation is E 1 = Ga
2
0 /2 and the sum of the energies of the partials
is smaller, E 2 = 2Ga
2
0 /6 = Ga
2
0 /3. In Fig. 4.20b a TEM image of a Ge/Si interface with a Shockley
partial is shown.
4.3.2 Visualization of Dislocations by Etching
Defects can be made visible using etching techniques. This is particularly popular for finding dislocations. Many etches are anisotropic, i.e. the etch velocity varies for different crystal directions. As an
example the result of etching a silicon sphere in molten KOH and a germanium sphere in a HNO 3 /HF
solution are shown in Fig. 4.21. The remaining bodies exhibit those planes with low etching velocity.
The etch velocity of various etch solutions has been investigated in detail in particular for silicon
(Fig. 4.22).
In a planar geometry, etch pits indicate the presence of dislocations, as shown in Fig. 4.23 for Ge
of different orientation. The anisotropic etch prepares {111} planes. The dislocation core is at the
intersection of the planes. In Fig. 4.24 hexagonal etch pits stretched along [1 ¯
10] are developed by
molten KOH [330, 331]. The sides of the base are along [110], 130 and 310. The depth and width
of the pits increases with increasing etching time. On the (00 ¯
1) surface, the orientation of the pits is
rotated by 90
◦ because of the polar [111]-axis of the zincblende structure [330]. Such etch pit develops