Biomedical Engineering Reference
In-Depth Information
Fig. 9.5
(
a
) The tunnel
coupling parameter as a
function of the inter-dot
separation. At
t
a
b
2
100
1.5
0the
bonding-antibonding
transition of the ground state
takes place. (
b
) The total
maximum relaxation rate
(
blue dashed line
)andthe
contribution from the PE
coupling (
red solid line
). (
c
)
Contribution to the total
relaxation rate from the DP
coupling. (
d
) Relaxation rate
for hole states at
T
=
0K(
red
solid line
), 20 K (
blue dashed
line
), and 40 K (
green dotted
line
)for
D
=
7nm
=
1
50
0.5
0
0
5
10
15
20
5
10
15
20
D
(nm)
D
(nm)
c
d
5
D
= 7 nm
4
4
3
2
2
1
0
0
5
10
15
20
-0.2
-0.1
0
D
(nm)
ε
(mV/A)
to the electron case. In contrast to the electron case, this dependence for holes is
non-exponential. The sign of
t
is related to the character of the ground state: the
positive one means that the ground state is bonding, while the negative sign implies
an antibonding ground state. The vanishing of tunnel coupling which takes place
about
D
23 nm in our system is caused by the transition from a bonding to
antibonding ground state [
86
-
88
].
We calculated the maximum magnitude of the relaxation rate as a function of the
distance between the dots. The resulting total magnitude as well as its contributions
from the DP coupling and the PE coupling is shown in Fig.
9.5
b,c. For small
distances (
D
=
10
.
0), both relaxation rates vanish. Similarly like for electrons, the
reason is that for small
D
, the energy splitting is large and there is a low density of
phonon states at very high frequencies. In the case of
D
→
the relaxation rates also
drop down because of vanishing overlap between the wave functions. On the other
hand, for distances near
D
→
∞
0) the maximum magnitude of
the relaxation rate drops down by two orders of magnitude compared to the highest
value. The reason is an extremely narrow energy splitting. However, near the critical
distance the phonon-assisted relaxation remains very slow not only at the resonance
but also for any electric field. The phonon-assisted relaxation rate at
D
=
10
.
23 nm (where
t
=
=
7nmasa
function of electric field at three temperatures (
T
0K,20Kand40K)isshown
in Fig.
9.5
d. In this case, the results are qualitatively similar to the electron case.
=
9.3.2
Phonon-Assisted Excitation Transfer
In this section we discuss the evolution of the exciton state in a DQD system
coupled to its phonon reservoir. We assume here that the only coupling between
