Biomedical Engineering Reference
In-Depth Information
2.4
2
2.3
2.2
1
2.1
2
10
0
0
2
4
6
8
D
(nm)
Fig. 6.13
Single-particle energy gap for the InGaN QDM (
dashed line
) and an isolated
In
0
.
25
Ga
0
.
75
NQD(
dashed-dotted line
) as function of the barrier thickness
D
.
Solid line
:Nor-
malized dipole matrix element squared
d
11
2
.[From[
92
]]
|
|
h
1
and
ψ
are localized on different QDs [cf. Fig.
6.11
], we find that for
D
≈
2nmand
d
11
|
2
D
φ
tot
and increase in the
radiative recombination rate for carriers in the upper dot. For example, for
D
≈
4
.
1nm,
|
>
1, indicating an effective reduction of
≈
2nm,
d
QDM
11
d
QD
2
2
, reflecting the
|
|
is increased by a factor of order two compared to
|
11
|
change in the slope of
φ
tot
in the upper dot of the QDM compared to an isolated
QD [cf. Fig.
6.12
b]. Note that
φ
tot
in an isolated QD is already significantly reduced
compared to a QW structure of the same composition and height, as discussed in
detail in Sect.
6.3.2
and in [
16
]. Therefore, the increase of
d
11
|
2
for small
D
further
emphasizes the benefit of using QDs instead of QWs in optoelectronic devices. It
should be noted that
|
d
11
|
2
|
>
1 for the ground state transition is again a consequence
of
e
15
<
0. With
e
15
>
0,
φ
tot
in a QDM would be similar to the
D
≈
1 nm case
d
11
|
2
[Fig.
6.12
a], and as discussed in Sect.
6.5
in detail. Since
1 is in qualitative
agreement with the experiment [
21
,
22
], this further supports our earlier conclusion
of
e
15
<
|
>
d
11
|
2
0[
24
,
86
]. For larger values of
D
(
D
>
5nm),
|
drops below unity.
Looking at
D
φ
tot
inside the upper dot is almost identical
to the slope inside a single QD [cf. Fig.
6.12
d]. However, the magnitude of
≈
6
.
2 nm, the slope of
φ
tot
at
the bottom (top) of the upper dot is slightly increased (decreased) compared to an
isolated QD. This change in
φ
tot
leads is accompanied by an increased (decreased)
d
11
|
h
1
e
2
lateral confinement for
ψ
(
ψ
1
), resulting in
|
<
1for
D
>
5nm.
6.7
Conclusions
In summary, we have presented a detailed analysis showing that the built-in electric
field in an isolated QD is significantly reduced compared to that in a QW of the same
height and the same indium content, with a further reduction in field achievable
