Biomedical Engineering Reference
In-Depth Information
Electron Ground State e | 2
D 1nm
D 2nm
D 4.1nm
D 6.2nm
D 8.3nm
Hole Ground State 1 h | 2
D 1nm
D 2nm
D 4.1nm
D 6.2nm
D 8.3nm
h
1 ,
respectively, for different spacer layer thicknesses D . The QD geometry is shown in light gray
and the blue and red probability density isosurfaces correspond to 10% and 50% of the maximum
value. [From [ 91 ]]
e
1 and
Fig. 6.10
Probability densities of the electron and hole single-particle wave functions
ψ
ψ
the ground state energies for electrons and holes approach the ground state energies
of an isolated QD in a continuous way from above or below the respective energy.
However, as we discussed in Sect. 6.5 , the profile of the built-in potential outside an
isolated InGaN/GaN QD can lead to ground state switching for electrons and holes.
We saw in Sect. 6.5 that for small D , the ground state electron wave function could
be expected to be localized at the top of the upper QD while the hole ground state
wave function is expected to be localized at the bottom of the lower QD. For larger
D , the change in sign in
φ tot in an isolated QD becomes important, and in this case
the electron ground state wave function is expected to be localized at the top of the
lower QD while the hole ground state wave function is expected to be localized at
the bottom of the upper QD.
To confirm this behavior, Fig. 6.10 shows isosurfaces of the probability densities
of the electron (
1 ) ground states as a function of D . The blue and
red isosurfaces correspond to 10% and 50% of the maximum value, respectively.
As expected from the single-particle energies,
1 ) and hole (
ψ
ψ
φ tot breaks the symmetry between
the two QDs, and bonding and anti-bonding states are not formed. Furthermore,
Fig. 6.10 shows that the built-potential indeed leads to ground state switching for
both electrons and holes. For small spacer layer thicknesses,
1 is localized at the
ψ
1 is localized at the bottom of the lower QD. This
behavior is therefore similar to the behavior one would expect in two coupled
QWs. The situation changes for D
top of the upper dot, while
ψ
1 is localized at the
>
2 nm. In this case
ψ
1 is localized at the bottom of the upper dot. This
ground state switching explains therefore the kink in the energy spectrum shown in
Fig. 6.9 . Again, the reason for this ground state switching is the profile of the total
built-in potential
top of the lower QD while
ψ
φ tot above and below an isolated InGaN/GaN QD and is a direct
consequence of e 15 <
0.
 
Search WWH ::




Custom Search