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a
2.83
2.82
2.81
E e
E e
2.8
2
4
6
8
D (nm)
b
E 1 h
E 2 h
0.141
0.1405
2
4
6
8
D (nm)
Fig. 6.7 TB single-particle energies of the first two bound ( a ) electron and ( b ) hole states in the
absence in the absence of strain and built-in fields as a function of the spacer layer thickness D .
The reference energy for our results is set to the unstrained valence band maximum of GaN. [From
[ 91 ]]
structure on its own. In a third step, Sect. 6.6.1.3 , we then add the electrostatic built-
in potential, so that the separate impact of each component to the electronic structure
can then be clearly seen.
6.6.1.1
Electronic Structure Without Strain and Built-In Field
In this section we analyze the electronic structure of InGaN/GaN QDMs when
we artificially switch off strain and built-in fields. The energies E e , h
1
2 of the first
,
2 ) single-particle states are shown
in Fig. 6.7 a and b, respectively. Here, electron and hole levels form bonding
and anti-bonding molecular orbitals. Therefore, the single-particle energies split
symmetrically around the electron and hole ground state energy of the isolated
In 0 . 25 Ga 0 . 75 N/GaN QD. This behavior is similar to a real diatomic molecule (e.g.,
H 2 ). However, one can infer from Fig. 6.7 that electronic coupling between the dots
is only possible for small D values ( D
1 ,
2 ) and hole (
1 ,
two bound electron (
ψ
ψ
ψ
ψ
2 nm for holes).
This weak coupling arises for two main reasons. Firstly, due to the high effective
hole masses in the nitride system,
<
4 nm for electrons and D
<
2 are strongly confined in the QD.
Therefore very small spacer layer thicknesses D are required to achieve coupling
between these valence states. Secondly, even though the electron effective mass is
much lower, the large conduction band offset prevents an effective inter-dot coupling
between the electron ground state wave functions until small spacer layer values.
1 and
ψ
ψ
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