Biomedical Engineering Reference
In-Depth Information
in a QDM made up of closely spaced stacked dots. This reduction provides a
potential route to circumvent the “green gap problem” present in current nitride-
based optoelectronic devices.
In contrast to a wurtzite
c
-plane QW, where the built-in field depends on two
piezoelectric coefficients,
e
33
and
e
31
, the potential drop across a QD structure
depends also on the shear coefficient,
e
15
. Considerably less attention has been paid
to this third coefficient, with disagreement in the literature even as to the sign of
e
15
. We have investigated in detail the impact of
e
15
, showing that the behavior of
the potential both inside and outside an isolated QD strongly depends on its sign.
In the case of
e
15
<
0, the potential outside the dot returns to zero and can even
change sign. This behavior has to be contrasted with the result using
e
15
>
0, where
the potential does not change sign outside the dot, and where there is also a larger
potential drop between the top and bottom of the dot. The sign of
e
15
then strongly
affects the built-in potential both in an isolated dot and also in a stack of QDs.
An accurate analysis of InGaN QDs therefore requires knowledge of the sign
of
e
15
. We have undertaken a number of studies to this end. Firstly we have
analyzed the built-in fields in non-polar GaN/AlN QDs. Secondly the first-order
piezoelectric tensor in (111)-oriented zinc blende systems has been compared to
the first-order piezoelectric tensor in
c
-plane wurtzite. Both investigations support
e
15
<
0. These findings are in agreement both with recent experimental studies and
with the outcome of recent ab initio calculations of the piezoelectric coefficients in
InN, GaN and AlN. We therefore recommend
e
15
<
0 for studies of wurtzite nitride-
based heterostructures.
Following this detailed discussion of the built-in potential in InGaN QDs and the
sign of the piezoelectric coefficient
e
15
we have investigated the impact of strain
and the built-in fields on the electronic structure of InGaN/GaN QDMs. These
studies revealed that the molecular-like description of bonding and anti-bonding
states breaks down for both electrons and holes, even when assuming that the QDM
is made up of two identical QDs. Due to the high effective hole mass and the lack
of inversion symmetry along the growth direction, the strain field on its own is
already sufficient to prevent the formation of bonding and anti-bonding hole states.
In addition to this effect, the electron and hole levels are significantly modified
by the presence of the built-in field. When taking the built-in field into account,
we find a ground state switching for electrons and holes. For very small spacer
layer thicknesses (
D
2 nm) the electron ground state is localized at the top of the
upper QD while the hole ground state is localized near the bottom of the lower QD.
However, when going to larger barrier thicknesses (
D
≤
2 nm), the electron ground
state wave function is localized near the top of the lower QD while the hole ground
state wave function is localized near the bottom of the upper QD. This ground state
switching follows from the behavior of the built-in field in an isolated QD, where
the sign of the potential along the growth direction changes a few nanometers away
from the QD, directly as a consequence that
e
15
<
>
0.
Following this analysis of the impact of strain and built-in fields on the electronic
structure of an idealized InGaN/GaN QDM system made up of two identical QDs,
we then turned to consider the more realistic case of a
c
-plane InGaN QDM made
