Biomedical Engineering Reference
In-Depth Information
Fig. 9.23 The phonon
spectral density for a few
values of the distance
between the dots [ 52 ]
0.06
D
= 4 nm
= 6 nm
= 8 nm
0.05
0.04
0.03
0.02
0.01
0
0
2
4
6
8
10
12
14
hw
(meV)
Fig. 9.24 The decay of
exciton occupation with
phonons ( left :
2
1
1
|+〉
| Y +
| Y
|+〉
| Y +
| Y
E =
1
.
77 meV; right :
2
55 meV) for the same
initial conditions as in
Fig. 9.22 [ 52 ]
E =
3
.
0
0
0
1
2
0
1
2
time [ns]
time [ns]
1
T = 0 K
= 40 K
= 120 K
T = 0 K
= 40 K
= 120 K
0
0
1
2
0
1
2
time [ns]
time [ns]
Fig. 9.25
The decay of exciton occupation for the initial state
( | + )
for the distance D
=
6nmata
few temperatures, dominated by relaxation
( θ = π /
3
)
. Left : with strong carrier-phonon coupling
(2
E =
1
.
77 meV); right : with a weaker coupling (2
E =
7
.
1meV)[ 52 ]
thermal quasi-equilibrium and the resulting decay becomes slower. This effect of
the resulting redistribution of occupations can be observed also for higher values of
2
close to the second minimum of the spectral density (see Fig. 9.25 , right panel),
but the effect is weaker and appears at higher temperatures.
The effect of thermal extension of the exciton lifetime can be directly reflected
in the dynamics of photoluminescence (PL), which may be observed in a time-
resolved experiment. In such an experiment, the sample is excited with a light pulse
and the decay of PL can be measured as a function of time. We calculate the PL
signal by multiplying the occupations of the eigenstates
E
| Ψ +
and
| Ψ
,bythe
corresponding decay rates
Γ 0 is the spontaneous decay
rate for a single dot. The PL depends on the occupations of the states (dark and
Γ ± = Γ 0 (
1
±
sin
θ )
,where
 
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