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
 
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