Appl. Phys. Lett. 92, 063116 (2008); https://doi.org/10.1063/1.2844886 92, 063116
© 2008 American Institute of Physics.
Decay dynamics of neutral and charged
excitonic complexes in single
quantum dots
Cite as: Appl. Phys. Lett. 92, 063116 (2008); https://doi.org/10.1063/1.2844886
Submitted: 14 January 2008 • Accepted: 22 January 2008 • Published Online: 14 February 2008
M. Feucker, R. Seguin, S. Rodt, et al.
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Decay dynamics of neutral and charged excitonic complexes in single
InAs/GaAs quantum dots
M. Feucker, R. Seguin, S. Rodt,a兲A. Hoffmann, and D. Bimberg
Institut für Festkörperphysik, Technische Universität Berlin, D-10623 Berlin, Germany
共Received 14 January 2008; accepted 22 January 2008; published online 14 February 2008兲
Systematic time-resolved measurements on neutral and charged excitonic complexes 共X,XX,X+,
and XX+兲of 26 different single InAs/GaAs quantum dots are reported. The ratios of the decay times
are discussed in terms of the number of transition channels determined by the excitonic fine
structure and a specific transition time for each channel. The measured ratio for the neutral
complexes is 1.7 deviating from the theoretically predicted value of 2. A ratio of 1.5 for the
positively charged exciton and biexciton decay time is predicted and exactly matched by the
measured ratio indicating identical specific transition times for the transition channels involved. ©
2008 American Institute of Physics.关DOI: 10.1063/1.2844886兴
Single quantum dots 共QDs兲provide the key for quantum
computing1,2and quantum cryptography.3For real devices,
the dynamics of the recombination is of utmost importance
because it limits the maximum modulation frequency of the
device and the coherence time of the emitted light. The elec-
tron and hole wave functions and, therefore, the oscillator
strength varies from dot to dot because of structural
variations.4Therefore, a spread of decay times is expected
for different QDs. Additionally, different excitonic com-
plexes in the same QD show different decay times for two
main reasons. First, the number of possible recombination
channels varies due to differences of the electronic fine struc-
ture of the various complexes. Second, the oscillator strength
of a specific transition depends on the single-particle wave
functions and their overlap being influenced by the number
of charge carriers constituting the complex. For equal spe-
cific transition times 共STTs兲, the exciton 共X兲decay time is
expected to be twice as long as the biexciton 共XX兲decay
time since the XX has two possible decay channels and the X
has only one. Previous studies of the decay of Xand XX in
InAs QDs were limited to a few QDs and reported factors
vary from 7.5 共Ref. 5兲via 2.3 共Ref. 6兲to 1.1.7Theoretical
predictions range between 4 and 1.5.8,9
In this letter, we present a study of 26 different single
InAs/GaAs QDs yielding an average factor of 1.7⫾0.4 for
the decay time ratio of X/XX. Furthermore, we expand the
study to positively charged excitons 共X+兲and biexcitons
共XX+兲. We predict a ratio of 1.5 and observe experimental
values yielding 1.5⫾0.2. This close agreement shows that
the STTs for X+ and XX+ are very similar in contrast to the
STTs of Xand XX.
The InAs QDs were grown by metal-organic chemical
vapor deposition epitaxy in a GaAs matrix on a GaAs共001兲
substrate. During QD growth, the rotation of the wafer was
interrupted and nominally 1.6 monolayers of InAs were de-
posited at 500 °C. The interruption leads to a lateral gradient
of the QD density. In certain regions of the wafer, the QD
density is extremely low 共⬇107cm−2兲giving spectroscopic
access to single QDs.
The QDs were investigated using a JEOL JSM 840 scan-
ning electron microscope equipped with a cathodolumines-
cence setup.10 The sample was mounted onto the tip of a
helium flow cryostat providing temperatures as low as 6 K.
All measurements throughout this letter were performed at
this temperature. The luminescence was dispersed by a 0.3 m
monochromator equipped with a 1200 lines/mm grating.
Single QDs were identified by luminescence mapping of the
sample. The various QD emission lines were assigned to
different excitonic complexes following Ref. 11.
For time-integrated measurements, a liquid-nitrogen
cooled Si charge-coupled-device camera was used. The time-
resolved measurements were performed with a Si avalanche
photo diode and a beam-blanking unit for pulsed excitation.
The beam-on time was 5 ns with a repetition rate of
25 MHz. This pulse configuration allowed luminescence de-
cay from a steady-state situation, thus, excluding the influ-
ence of the capture process. Performing transient line shape
analysis, the decay times could be evaluated with an accu-
racy of 0.1 ns. The dynamic range of these experiments cov-
ered up to three orders of magnitude enabling the observa-
tion of weak slow components.
Typical transients of the decay of four different excitonic
complexes 共X,XX,X+, and XX+兲in one QD are shown in
Fig. 1.12 All transients are dominated by a fast initial decay
typically followed by a second slower component. The decay
from different QDs shows a systematic pattern: The XX+
a兲Electronic mail: [email protected].
FIG. 1. 共Color online兲Typical transients of the different excitonic com-
plexes 共X,X+, XX, and XX+兲of one QD. The transients were fitted by a
biexponential function. The fast component constitutes the radiative decay
time. The second component stems from a refilling process from neighbor-
ing defect states or other QDs. The inset shows a typical time-integrated
spectrum of a single QD.
APPLIED PHYSICS LETTERS 92, 063116 共2008兲
0003-6951/2008/92共6兲/063116/3/$23.00 © 2008 American Institute of Physics92, 063116-1
decays the fastest followed by the XX,bytheX+, and finally
by the X.
The amplitude of the slower component of the transients
is very small. For Xand X+, its relative amplitude compared
to the fast decay ranges between 0 and 0.1 and for XX and
XX+, it ranges between 0 and 0.01. The time constants of the
slower components vary between 4 and 9 ns. This compo-
nent originates from processes feeding the initial state of the
decay after the external excitation has been switched off. X
and X+ having longer initial decay times exhibit a more pro-
nounced second component than XX and XX+, suggesting a
feeding process from an external charge carrier reservoir
rather than an intrinsic feeding. Such slow components were
previously controversially attributed to reemission and lat-
eral transfer of charge carriers13,14 or to conversion of dark
excitons to bright excitons via spin-flip processes.15 For the
X+, XX, and XX+ decays, the spin flip can be ruled out as
these complexes possess no such dark states. Instead, the
source of the feeding process is suggested to be outside of
the QDs, e.g., neighboring shallow defect states or reemis-
sion from other QDs. In the following, we will focus on the
dominant fast component.
Figure 2shows the dominant decay times of X,X+, XX,
and XX+ as a function of the X+ recombination energy. A
clear sequence of decay times for the excitonic complexes is
obvious. Xexhibits the longest decay time followed by X+,
XX, and finally, XX+, analogous to Fig. 1and in agreement
with previous reports on InAs/GaAs QDs.5,6
No clear trend for a dependence of the decay times on
the X+ energy is identified. Apparently, the structural param-
eters, which lead to differences in the transition energies, do
not control the decay times in the same way. Interestingly,
the scatter of the Xdecay times is much larger than that
of the other excitonic complexes. The mean decay times
are
共X兲=1.22⫾0.25 ns,
共X+兲=0.97⫾0.15 ns,
共XX兲
=0.76⫾0.12 ns, and
共XX+兲=0.66⫾0.14 ns. The standard
deviation of
共X兲is almost twice as large as for the other
complexes. The Xwave function seems to be more sensitive
to the structural properties of the QD than the wave functions
of complexes containing more holes.
The decay times of the neutral and charged complexes
will now be compared with respect to the number of allowed
transitions of each excitonic complex.
The radiative decay time
共EC兲of an excitonic complex
共EC兲is composed of the specific transition time
if of all
recombination channels involved16
1
共EC兲=兺
i,f
ni
1
i,f
,共1兲
with the mean population ni共兺ni=1兲of the initial state. It is
assumed that the STTs for different transition channels 共兩i典
→兩f典and 兩i⬘典→兩f⬘典兲 of one complex are identical 共
i,f
=
i⬘,f⬘=
EC兲since the oscillator strength is independent of
the actual spin configuration as long as the spin selection
rules are obeyed. Under this precondition, the expected
excitonic decay times
共X兲,
共X+兲,
共XX兲, and
共XX+兲are
determined by the number of allowed recombination chan-
nels and their STTs, respectively.
Figure 3shows the energy schemes of the four excitonic
complexes to illustrate the different transition channels. The
initial and final states are labeled with their respective total
spin configurations.
The initial configuration of the optically active Xcon-
sists of the two bright states with the spin configuration
兩−1典⫾兩1典.17,18 The dark states 兩−2典⫾兩2典are optically forbid-
den and do not contribute to the recombination process. The
exciton fine structure splitting of the QDs probed here was
determined to be less than 20
eV. Hence, the mean initial
population n⫾1of the two bright states is 1
2. Each state pos-
sesses one recombination channel to the ground state 兩0典. The
decay time then amounts to
共X兲=
X.
In contrast to X,XX consists of a single initial state 兩0典
with n0=1 and possesses two recombination channels to the
two final states: the bright states of the X共兩−1典⫾兩1典兲. Hence,
the decay time amounts to
共XX兲=1
2
XX.
To compare the decay times of Xand XX, identical STTs
for both complexes are assumed. Narvaez et al.16 calculated
almost identical STTs 共
X=
XX兲for the Xand XX in lens
shaped InAs/GaAs QDs of various sizes. Under this assump-
tion, a decay time ratio of
共X兲/
共XX兲=2 follows.
The initial and final states of X+ consist of two degen-
erate states 兩⫾1
2典and 兩⫾3
2典, respectively. For each initial
state, only one final state is allowed due to the spin selection
rules. Since the initial states are equally populated
共
n⫾1/2
=1
2
兲
, the decay time of X+ following Eq. 共1兲yields
1
共X+兲=1
2
1
+1/2,+3/2
+1
2
1
−1/2,−3/2
⬇1
X+
.共2兲
The initial configuration of XX+ consists of the two de-
generate states 兩⫾3
2典. The final state of the XX+ is a triplet,
each component consisting of three doublets.19,20 The transi-
tion to the 兩⫾7/2典state is forbidden, while the transition to
the 兩⫾5/2典state is allowed. The transition probability into
the 兩⫾1/2典state is reduced to 1
2since it is composed of a
FIG. 2. 共Color online兲The dominant decay times of the different excitonic
complexes are shown as a function of the X+ recombination energy. No
clear dependence on energy can be seen.
FIG. 3. 共Color online兲Energy scheme for the recombination channels of the
different excitonic complexes. The spin configurations of the different initial
and final states are shown. Thick lines correspond to twofold degenerate
states.
063116-2 Feucker et al. Appl. Phys. Lett. 92, 063116 共2008兲
superposition of an allowed and a forbidden state.21 Thus, the
decay time of the XX+ accounts to
1
共XX +兲=1
2
冉
1
2
1
+3/2,+1/2
+1
2
1
−3/2,−1/2
冊
+1
2
1
+3/2,+5/2
+1
2
1
−3/2,−5/2
⬇3
2
1
XX+
.共3兲
Just like for the neutral complexes, equal STTs 共
X+
=
XX+兲for the charged complexes are assumed. Since the
probed QDs are of small size and, therefore, in the strong
confinement regime, adding a neutral pair of charge carriers
should alter the wave functions only slightly. The expected
ratio of decay times
共X+兲/
共XX+兲then amounts to 1.5.
In Fig. 4, the measured ratios of the Xand XX decay
times 共black squares兲and of the X+ and XX+ decay times
共red circles兲are plotted as a function of X+ recombination
energy. Again, no apparent trend can be seen. The mean
value of
共X兲/
共XX兲is 1.7 with a standard deviation of 0.4.
For
共X+兲/
共XX+兲, the mean value results to 1.5 with a
standard deviation of 0.2.
The mean
共X兲/
共XX兲value is clearly below the pre-
dicted value of 2 with a large scatter of the individual values.
Qualitatively, the argument based on the number of involved
transition channels holds. The exact value, however, cru-
cially depends on the specific QD since the STTs differ a lot
from case to case and are not always comparable as in Ref.
16. Wimmer et al. calculated a size dependent ratio between
1.5 and 2.8The change in the ratio is governed mainly by
共X兲, thus, supporting our measurements.
The measured mean value of
共X+兲/
共XX+兲matches
exactly the expected value of 1.5. The scatter is considerably
smaller than for
共X兲/
共XX兲with a standard deviation of 0.2
indicating a stronger similarity of the STTs of X+ and XX+
from dot to dot than for the neutral complexes. Here, the
number of allowed transitions is the key parameter determin-
ing the ratio of decay times of both complexes.
The comparison of the measured
共X兲and
共X+兲shows
that the STTs
Xand
X+differ strongly. Adding a single
charge carrier to an excitonic complex influences the wave
functions and, therefore, their overlap is much stronger than
adding a neutral pair of charge carriers.
In summary, we presented a systematic study of the de-
cay dynamics of excitonic complexes in 26 different single
InAs/GaAs QDs. The influence of the specific transition
times and electronic fine structure on the dynamics was ana-
lyzed. Surprisingly, the scatter of the neutral exciton’s decay
time from dot to dot is larger than the scatter of the other
complexes’ decay times indicating a greater sensitivity of the
exciton wave function to details of the structural properties
of the QD. No dependence on the transition energy was ob-
served in the 1.26–1.35 eV range. The mean value of
共X兲/
共XX兲was 1.7⫾0.4, thus, below the value of 2 as
given by the different number of decay channels alone. This
implies shorter STTs for Xthan for XX. For
共X+兲/
共XX+兲, a value of 1.5 was predicted. The mean measured
ratio is 1.5⫾0.2, thus, matching the expected theoretical
value. This indicates similar STTs for the transition channels
of X+ and XX+. The additional positive charge carrier seems
to stabilize the wave function overlap when an additional
exciton is added to the complex.
This work was supported by the Deutsche Forschungs-
gemeinschaft in the framework of SfB 787 and the SANDiE
Network of Excellence of the European Commission, Con-
tract No. NMP4-CT-2004-500101. We are indebted to K.
Pötschke for the growth of the sample.
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FIG. 4. 共Color online兲Ratio of the decay times of the neutral and charged
complexes as a function of X+ recombination energy. The dashed lines
indicate the mean values. The means of the ratios are 1.7⫾0.4 and 1.5⫾0.2,
respectively. The greater scatter of the
共X兲/
共XX兲ratio stems from the
greater scatter of the Xlifetime.
063116-3 Feucker et al. Appl. Phys. Lett. 92, 063116 共2008兲
