Biomedical Engineering Reference
In-Depth Information
From this analysis one might expect an even further reduction of the oscillator
strength in a QDM compared to an isolated QD, since the wave functions are
localized is localized on different QDs, leading to a large spatial separation of the
electron and hole wave functions. However, this need not be the case if we assume
that electrons and holes can become trapped in both dots. In addition, we have made
the simplifying assumption above of two identical QDs. As discussed before, during
the growth of a stack of QDs, the geometrical properties of the dots are likely
to change from layer to layer. Furthermore, the indium content is probably also
different in the different QDs, leading therefore to different confinement energies as
well as strain fields. This will then also modify the built-in potential. Consequently,
further studies are required to analyze in detail how the change in composition and
in geometry affects the built-in field in QDMs and how this impacts the electronic
and optical properties of such systems. This will be the topic of the next section.
6.6.2
Non-identical QDs
Having discussed the built-in potential and the electronic structure of InGaN/GaN
QDMs made up of two identical dots in the previous section, we turn now and
present a detailed analysis of the electronic structure of an InGaN/GaN QDM
made up of two
non-identical
dots. Following the analysis of the previous section,
we study the electronic structure of the InGaN/GaN QDM as a function of the
barrier thickness
D
.Weusevaluesof
D
3nm, which are
based on the experimental data in [
22
]. Here, we consider QDs identical in size
and shape but different in their composition. The difference in indium composition
mimics therefore already the effects (changes in confinement energy, strain and
built-in fields) which can also arise from a change in the QD geometry. Since
the average diameter of InGaN QDs scatters around 15-25 nm while the average
height is approximately 2-6 nm [
22
,
70
,
72
], we assume a diameter
d
≈
1
,
2
,
4
.
1
,
6
.
2, and 8
.
≈
19
.
2nm
and a height
h
1 nm for both QDs. As discussed before in Sect.
6.4
, there is 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 higher than in the lower
one [
74
]. We assume an indium content of 20% in the lower dot and 25% in the
upper dot. Based on the experimental data in [
75
] and the discussions in [
22
], we
assume a vertical stacking of the two QDs. Again, we use
e
15
<
≈
3
.
0 for this study,
according to our recommendation in Sect.
6.4
.
In a first step we consider the single-particle electron (
e
h
ψ
1
) and hole (
ψ
1
) ground
e
h
state wave functions. Figure
6.11
shows the charge densities for
1
as a
function of
D
. The blue and red isosurfaces correspond to 10% and 50% of the
maximum values, respectively. When looking at the results in detail, we find again a
ground state switching for the holes, but this time not for the electrons. For
D
ψ
1
and
ψ
≈
1nm
h
e
ψ
1
is localized in the lower QD (In
0
.
2
Ga
0
.
8
N QD) while
ψ
1
is localized in the upper
