Biomedical Engineering Reference
In-Depth Information
To shed more light on the sign of
e
15
, we have used two different approaches in
two different systems to gain further insight into the sign of
e
15
. In the following
two subsections we briefly outline these approaches and summarize their outcomes,
which further support
e
15
<
0. Section
6.4.3
then analyzes the impact of the sign of
e
15
on the total built-in potential in an isolated lens-shaped InGaN/GaN QD with
realistic dimensions and indium content.
6.4.1
Sign of e
15
from Analysis of the Built-In Field in
Non-polar Nitride-Based QDs
As discussed above the strong electrostatic built-in fields in
c
-plane InGaN/GaN
heterostructures limit their applicability for optoelectronic devices. To circumvent
the problems arising from growth along the polar
c
-axis (
-direction), there
has been a rapid increase in studies of non-polar growth of III-nitride structures,
where the
[
0001
]
-direction lies within the growth plane [
10
,
82
-
84
]. Growth of QWs
along a non-polar direction can eliminate polarization-induced fields, and hence give
improved radiative recombination rates [
9
], since there is no discontinuity in the
polarization vector along the [0001]-direction.
In contrast to a non-polar QW, QDs grown along a non-polar direction still
have
[
0001
]
-oriented side facets. These interfaces give rise to a discontinuity in
the polarization vector, Eq. (
6.2
), leading then to a net polarization potential across
the QD. However, optical measurements suggest that the polarization potential is
strongly reduced in non-polar (In)GaN QDs compared to their
c
-plane counter-
parts [
10
,
83
,
85
].
Recently, we have presented a detailed analysis of the different contributions
to the electrostatic potential of non-polar wurtzite GaN/AlN and InGaN/GaN
QDs [
24
,
41
,
71
]. Special attention was paid to the sign of the piezoelectric constant
e
15
. Since the contribution from the spontaneous polarization in InN/GaN QDs is
negligible compared to the strain-induced component, a significant electrostatic
built-in field might be expected even in non-polar
pure InN
systems, independent
of the sign of
e
15
. However, our results for non-polar InGaN/GaN QDs with a more
realistic indium content (15%) [
71
] reveal that the built-in fields are negligible in
these systems. This finding has recently been confirmed experimentally [
85
].
While the total potential for InN/GaN QDs is almost entirely due to the piezo-
electric contribution, spontaneous and piezoelectric potentials contribute almost
equally in GaN/AlN QDs [
24
,
38
]. Our investigations [
24
] reveal that only a
negative value of
e
15
leads to a strong reduction of the built-in field in non-polar
GaN/AlN QDs compared to their polar counterparts, as observed experimentally.
Furthermore, we have recently shown [
11
] that when using
e
15
<
[
0001
]
0 and assuming
realistic QD geometries for these non-polar structures an increased spatial overlap
of the electron and hole ground state wave functions is observed, in agreement with
optical measurements discussed in the literature [
10
,
83
]. Therefore, we conclude
that
e
15
is most likely to be negative in wurtzite nitrides, a conclusion further
supported by the results presented in the next section.
