Biomedical Engineering Reference
In-Depth Information
6.4
InGaN QDs and Material Parameters
The basic considerations of the previous section allowed us to establish the overall
behavior of the electrostatic built-in field in isolated nitride-based QDs and how
this affects the electronic and optical properties in general. This analysis also gave
insight into the changes in the built-in potential when both the QD geometry and
the aspect ratio are changed. However, to perform realistic electronic structure
calculations, more details about the QD geometry, such as the size and the
composition are required. Here input from growth simulations and/or experimental
data is required.
For InGaN/GaN QDs the shape is often approximated by truncated pyramids
with a hexagonal base, or by using ellipsoidal or lens-shaped dot geometries [
11
,
15
,
47
,
64
,
66
,
71
], as indicated by experimental studies [
68
-
70
,
72
]. Looking at
the geometrical features in more detail, experiments also reveal that the average
diameter of InGaN QDs scatters around 15-25 nm while the average height is
approximately 2-6 nm [
22
,
70
,
72
]. When looking at the indium compositions of
InGaN QD systems, structures with 15-35% indium have been reported in the
literature [
72
,
73
]. There has been no detailed measurement on the variation of the
indium content in stacked InGaN QDs. However, the analysis of coupled InGaAs
QDs shows that, due to strain relaxation in the structure, the indium composition of
the upper QD is typically higher than in the lower one [
74
].
When looking at the strain fields, the electrostatic built-in fields and the electronic
structure of stacked InGaN/GaN QDs, the relative orientation of the different QDs
with respect to each other is also important. Based on the experimental data in
[
75
] and the discussions in [
22
], we assume a vertical stacking of the QDs in
our analysis. This assumption is also consistent with the experimental findings on
stacked InGaAs/GaAs QDs [
74
].
Having outlined the experimental observations on the shape, size, and indium
content of InGaN/GaN QDs and QDMs, the theoretical description of these systems
also needs as input the values of material parameters such as elastic constants,
valence band and conduction band offsets, piezoelectric coefficients, etc. Detailed
studies of the influence of different parameter sets on the electrostatic built-in
fields and the electronic structure of QWs and QDs can be found, for example,
in [
13
,
76
]. Here, we focus our attention on one quantity, namely the shear strain-
related piezoelectric coefficient
e
15
which turns out to affect the electrostatic built-in
potential and consequently the electronic structure of stacked InGaN/GaN QDs
significantly. When looking at the values of the piezoelectric coefficients
e
31
and
e
33
given in the literature, these values scatter mainly in magnitude but not in sign.
Turning to the shear strain component, there is not only uncertainty in the magnitude
of
e
15
, but there is also conflicting evidence as to its sign [
24
]. The initial and
often used values of Bernardini et al. [
77
] and Vurgaftman et al. [
44
] are positive,
while more recent results recommend a negative value of
e
15
[
78
-
81
]. For example,
bias-dependent photoluminescence measurements on semi-polar InGaN QWs have
recently been used to determine the sign of
e
15
, concluding that
e
15
<
0[
80
].
