Biomedical Engineering Reference
In-Depth Information
0.8
e
15
>
0
e
15
<
0
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−10
−5
0
5
10
15
z
(nm)
Fig. 6.5
Total built-in potential
φ
tot
for a lens-shaped In
0
.
25
Ga
0
.
75
N/GaN
c
-plane QD (height
h
=
3
2 nm) for a line-scan through the center of the dot along the
c
-direction (
z
-
axis). The results are shown for positive and negative values of the shear strain-related piezoelectric
coefficient
e
15
.
1 nm, diameter
d
=
19
.
drop between the top and the bottom surface is reduced compared to the result with
e
15
>
0. Secondly, the sign of
e
15
affects the potential profile outside the dot. With
e
15
<
φ
tot
returns towards zero and changes sign a few nanometers away from
the QD. This is to be contrasted with the result obtained for
e
15
>
0,
0, where the
potential does not change sign outside the QD. The behavior of
φ
tot
outside a single
QD will also affect
φ
tot
in a stacked QD system. Therefore, we turn our attention in
the following section to
φ
tot
of a system of two InGaN/GaN QDs stacked along the
c
-axis.
6.5
Built-In Fields in InGaN QDMs
In this section we discuss the electrostatic built-in fields in stacked InGaN/GaN
QDs first before turning to the analysis of the electronic structure of InGaN/GaN
QDMs in Sect.
6.6
. To keep the analysis simple and transparent, we study here the
built-in potential
φ
tot
for two identical lens-shaped In
0
.
25
Ga
0
.
75
N/GaN QDs which
are stacked along the
c
-axis. Later, in Sect.
6.6.2
, we deal with the realistic situation
of non-identical QDs. The QDs considered in this section have a base diameter
of
d
1 nm following the discussions in Sect.
6.4
.
Based on our findings in the previous section, we use the piezoelectric coefficients
from Shimada [
78
], which predict
e
15
<
=
19
.
2 nm and a height of
h
=
3
.
0 for GaN and InN, respectively. Here, we
study the total built-in potential for two different spacer layer thicknesses
D
, namely
D
≈
1 and 4.1 nm. In Sect.
6.6
, we will extend this discuss to even larger spacer