362
12 Heterostructures
Fig. 12.16 SEM
cross-sectional image of
MOVPE GaN grown on
patterned r-sapphire
exposing a (11.2) growth
front. Based on SEM
image courtesy of F.
Tendille
r-Al O
2
3
GaN
A [11.0]
C [00.1]
R [11.2]
M [11.0]
C [00.1]
[11.2]
[11.3]
1 µm
Fig. 12.17 Optical image
of the surface of a
supercritical, plastically
relaxed In x Ga 1−x As film
on GaAs. Image width is
about 1 mm. The
cross-hatch pattern is due
to misfit dislocations along
[110] and [1 ¯
10]. A
pseudomorphic layer
would exhibit no contrast
under the given conditions
12.2.6 Pseudomorphic Structures
Heterostructures can generally be made from any sequence of materials. However a mismatch in lattice
constant (or a different crystal structure) leads to strains and stresses that are of the order of 10
3 atmos
for strains of 1% (σ ∼ C, C ≈ 5 × 10
10 Pa) as discussed in Sect. 5.3.3. The total strain energy is
∝ C
2 . Above a critical thickness h c ∝
−1 (cf. Sect. 5.4.1) defects, e.g., misfit dislocations (relaxing
strain with their edge components), are generated (Sect. 12.2.7). There are a number of semiconductor
combinations that are lattice matched and thus can be grown with arbitrary thickness. Al x Ga 1−x As is
closely lattice matched to GaAs for all Al concentrations. See Fig. 6.25 for lattice-matched pairs, e.g.,
In 0.53 Ga 0.47 As/InP. Often, thin layers of lattice-mismatched materials with thickness smaller than the
critical thickness are used.
For many device applications the ability to grow pseudomorphic layers thicker than the critical
layer thickness would be beneficial. The use of compliant substrates was proposed in [1154] to meet
this demand. A recent review on compliant substrate technologies can be found in [445]. Schemes
12 Heterostructures
Fig. 12.16 SEM
cross-sectional image of
MOVPE GaN grown on
patterned r-sapphire
exposing a (11.2) growth
front. Based on SEM
image courtesy of F.
Tendille
r-Al O
2
3
GaN
A [11.0]
C [00.1]
R [11.2]
M [11.0]
C [00.1]
[11.2]
[11.3]
1 µm
Fig. 12.17 Optical image
of the surface of a
supercritical, plastically
relaxed In x Ga 1−x As film
on GaAs. Image width is
about 1 mm. The
cross-hatch pattern is due
to misfit dislocations along
[110] and [1 ¯
10]. A
pseudomorphic layer
would exhibit no contrast
under the given conditions
12.2.6 Pseudomorphic Structures
Heterostructures can generally be made from any sequence of materials. However a mismatch in lattice
constant (or a different crystal structure) leads to strains and stresses that are of the order of 10
3 atmos
for strains of 1% (σ ∼ C, C ≈ 5 × 10
10 Pa) as discussed in Sect. 5.3.3. The total strain energy is
∝ C
2 . Above a critical thickness h c ∝
−1 (cf. Sect. 5.4.1) defects, e.g., misfit dislocations (relaxing
strain with their edge components), are generated (Sect. 12.2.7). There are a number of semiconductor
combinations that are lattice matched and thus can be grown with arbitrary thickness. Al x Ga 1−x As is
closely lattice matched to GaAs for all Al concentrations. See Fig. 6.25 for lattice-matched pairs, e.g.,
In 0.53 Ga 0.47 As/InP. Often, thin layers of lattice-mismatched materials with thickness smaller than the
critical thickness are used.
For many device applications the ability to grow pseudomorphic layers thicker than the critical
layer thickness would be beneficial. The use of compliant substrates was proposed in [1154] to meet
this demand. A recent review on compliant substrate technologies can be found in [445]. Schemes