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Thermal stability of emission
from single InGaAs/GaAs quantum
dots at the telecom O‑band
Paweł Holewa1,4, Marek Burakowski1,4, Anna Musiał1*, Nicole Srocka2, David Quandt2,
André Strittmatter2,3, Sven Rodt2, Stephan Reitzenstein2 & Grzegorz Sęk1
Single‑photon sources are key building blocks in most of the emerging secure telecommunication and
quantum information processing schemes. Semiconductor quantum dots (QD) have been proven to be
the most prospective candidates. However, their practical use in fiber‑based quantum communication
depends heavily on the possibility of operation in the telecom bands and at temperatures not
requiring extensive cryogenic systems. In this paper we present a temperature‑dependent study
on single QD emission and single‑photon emission from metalorganic vapour‑phase epitaxy‑grown
InGaAs/GaAs QDs emitting in the telecom O‑band at 1.3 μm. Micro‑photoluminescence studies reveal
that trapped holes in the vicinity of a QD act as reservoir of carriers that can be exploited to enhance
photoluminescence from trion states observed at elevated temperatures up to at least 80 K. The
luminescence quenching is mainly related to the promotion of holes to higher states in the valence
band and this aspect must be primarily addressed in order to further increase the thermal stability
of emission. Photon autocorrelation measurements yield single‑photon emission with a purity of
g
(
2
)
50K
(0)=
0.13
up to 50 K. Our results imply that these nanostructures are very promising candidates
for single‑photon sources at elevated (e.g., Stirling cryocooler compatible) temperatures in the
telecom O‑band and highlight means for improvements in their performance.
The field of quantum information science would greatly benefit from development of robust, efficient and on-
demand single-photon sources (SPSs)1,2. In the past two decades, semiconductor quantum dots (QDs) have been
investigated in that context in various material systems and have proven to be excellent single-photon emitters3–5.
Epitaxial single In(Ga)As/GaAs QDs emitting below 1
µm
have enabled the development of SPSs with record sin-
gle-photon purity (i.e. with ultra-low probability of multiphoton emission events)6,7, high indistinguishability8–10,
high photon extraction efficiency11 and single-photon flux12. Most of these properties can also be achieved using
electrical triggering9,13 which brings the QD solution closer to real-world applications. QDs of this kind also
benefit from compatibility with state-of-the-art GaAs-based semiconductor technology which provides mature
and hence highly optimized growth, high structural quality, scalability and well developed methods for the fab-
rication of complex photonic structures (e.g., distributed Bragg reflectors—DBRs or photonic crystal cavities).
An important prerequisite for practical SPSs is compatibility with the existing telecommunication infrastruc-
ture based on standard silica fibres to enable low loss long-haul quantum communication in the relevant spectral
range of 1.3μm (O-band with local absorption minimum and vanishing dispersion) and 1.55μm (C-band
with global absorption minimum). One of the approaches is to utilize frequency conversion of near-infrared
QD emission to shift it to 1.55μm14,15. This is currently considered as the nearly optimal QD source and the
down-conversion process can erase the small spectral difference between the two remote sources making pho-
tons originating from them indistinguishable, but the approach is rather complex and the conversion has still
relatively low efficiency. In addition, it requires alaser of a very specific wavelength to be mixed with the QD
emission inside a nonlinear medium. Therefore, it is appealing to develop sources directly emitting at the target
wavelength. In the case of InAs QDs on GaAs the emission redshift to 1.3μm is typically achieved via strain
engineering and by, e.g., capping with a strain reducing layer (SRL)16–21 or the nucleation on metamorphic buffer
layers22. QDs with SRL have recently been used for the demonstration of a practical, compact, and fibre-integrated
SPS at telecom O-band with working temperature of 40 K23,24. For SPSs emitting at 1.55μm, the primarily
OPEN
1Laboratory for Optical Spectroscopy of Nanostructures, Department of Experimental Physics, Wrocław University
of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland. 2Institute of Solid State Physics,
Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany. 3Present address: Institute of
Experimental Physics, Otto-Von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany. 4These authors
contributed equally: Paweł Holewa and Marek Burakowski. *email: anna.musial@pwr.edu.pl
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considered candidates are single InAs/InP quantum dashes25,26, InAs/InP QDs27–30, and InAs/GaAs QDs based
on the metamorphic layer approach31,32. Other approaches for telecom wavelength SPSs, despite their single-
photon emission at room temperature, have their own drawbacks, e.g., atomic sources suffer from probabilistic
nature of emission events33, random direction of emission and low radiative rates. One has to keep in mind that
widely used process of parametric down-conversion34 is also a probabilistic photon generation scheme, which
is also under development in the telecom.
The second pivotal requirement for practical, solid-state SPS for quantum communication is single-photon
emission at significantly elevated temperatures of the emitter to make such quantum devices more compact,
practical and cheaper. Reaching room temperature operation with QDs emitting at telecom wavelengths encoun-
ters fundamental limits of the quantum localization energy and inter-level spacing with the highest reported
temperatures where the single-photon emission at telecom wavelengths is still observable at 120K35. This is out
of reach for thermoelectrical cooling, but on the contrary, the Stirling cryocooling can be successfully applied to
reach temperatures as low as 27K23,24 and fulfils the requirements for compact, easy and relatively cheap opera-
tion without need for cryogenic liquids.
Studying the influence of temperature on the stability and purity of single-photon emission from QDs enables
the determination of the highest working temperature for a given SPS design and the identification of processes
responsible for quenching of QD emission and deterioration of single-photon purity. For single InGaAs/GaAs
QDs with SRL emitting at 1.3μm so far only Olbrich etal. carried out a temperature-dependent study36. They
reported single-photon emission at liquid nitrogen temperature (77K) with second order correlation function
at zero time delay
g(2)(0)=0.21
using the negative trion radiative recombination36. The structures investigated
in this paper differ fundamentally from those investigated in Ref.36: In our case the emission is dominated by
positively charged complexes due to unintentional carbon p-doping in the metalorganic chemical vapour depo-
sition (MOCVD) process37 in contrast to negative trions exploited in the case of previous study. Additionally,
differences between the two groups of nanostructures in QD morphology resulting from details of the growth
procedure (i.e., exact growth parameters) are reflected in a modified electronic level structure and s–p energy
splitting38. Moreover, in the present work the QDs are embedded in deterministically fabricated mesas which
makes them relevant for high-yield single-photon sources and is crucial in view of their practical applications.
We present a detailed temperature dependent study of micro-photoluminescence (µPL) and single-photon
emission to explore the physics of InGaAs/GaAs QDs grown by MOCVD with SRL and emitting at 1.3µm. We
identify excitonic complexes based on power-dependent and polarization-resolved µPL measurements und study
them further by means of temperature-dependent µPL which allows us to identify the main µPL quenching
mechanism in the investigated nanostructures. Furthermore, we probed single-photon emission with photon
autocorrelation measurements in the temperature range of (5–50) K. The experimental findings allow us to point
out the dominating factors limiting single-photon emission purity atelevated temperatures.
Results
Identification of excitonic complexes. In order to investigate in detail the temperature stability of emis-
sion and the impact of elevated temperatures on the single-photon purity from a single QD, excitonic complexes
were first identified by means of excitation power-dependent and polarization-resolved µPL measurements.
Owing to relatively small mesa size (disk shaped) of 1.3µm and the QD spatial density of afew times
109/cm2
it was possible to spectrally isolate individual emission lines of high intensity and low background signal from a
single QD at 5K (see Fig.1a). Data from the same exemplary QD are presented throughout the manuscript. Dif-
ferent excitonic complexes, namely very prominent positive (X+) trion, exciton (X), and for this particular QD
also negative (X−) trion as well as biexciton (XX) were pre-identified by means of excitation power-dependent
µPL (Fig.1b). The observed line pattern is rather typical for this type of QDs37. We obtained linear scaling factors
of emission intensity for exciton (
IX∼P1.08(5)
), superlinear for trions (
IX
+
∼P1.17(8)
and
IX
−
∼P1.50(14)
) and
quadratic for biexciton (
IXX ∼P1.95(22)
), as expected39,40. Figure1c presents polarization-resolved µPL spectra,
where we observed the fine structure splitting (FSS) of the neutral exciton. We determined FSS of
FSS =67 µeV
for this QD by fitting the polarization dependence of the emission energy with sine function (see Fig.1c—right
panel). The extracted
FSS
value is within the range of FSSs typically observed for these QDs37,41.
The trion complexes were identified based on the absence of FSS in polarization-resolved measurements
supported by their superlinearPL intensity power dependence. Noteworthy, a distinction between positively
and negatively charged excitonic complexes was possible by comparing the emission spectrum with the results
of 8-band k.p calculations of the QD’s electronic structure combined with the configuration interaction method
for excitonic states due to their significantly different binding energies37. Theoretical modelling (not shown here)
reveals that these energies depend on exciton emission energy and for the reported QD, X− and XX should be
confined much stronger (
EX
−
≈EXX ≈4
meV) than X+ (
EX
+
≈1
meV).
Temperature stability. To study the temperature stability of the QDs and to pinpoint the main carriers’
escape channel from these QDs we performed μPL studies in the range of temperatures from 5 to 80K. The cor-
responding µPL spectra of the QD under study are presented in Fig.2a. Although the X+ intensity was slightly
lower than the X intensity at 5K, it turned out to dominate the spectrum in the intermediate temperature range
of 20 to 75K. In fact, a pronounced X+ µPL intensity increase was detected towards 30K and the emission was
still visible even above the liquid nitrogen temperature of 80K. At this temperature the X+ µPL intensity was
reduced by a factor of 7 in comparison to its maximal value at 30K.
A detailed quantitative analysis of the temperature dependence of emission from a studied QD is presented
in Fig.2c. With increasing temperature, a redshift of all lines can be observed (see Fig.2a,b) following the
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renormalisation of the QD material band gap energy (Eg). One can model the temperature dependence of energy
gap taking into account temperature-dependent bosonic distribution of phonons by42:
with
Eg(0)
the energy band gap at 0K, S the electron–phonon coupling constant,
ℏω
the average phonon energy,
kB the Boltzmann constant, and T the temperature. Fitting the experimental data with the formula above allows
to extract mean phonon energy of
ℏω
= (8.0 ± 1.2) meV which corresponds well to the GaAs transversal acous-
tic phonons43 confirming the predominant coupling of QD excitons with bulk phonons of the matrix material.
The data for the temperature dependence of linewidth γ = γ(T) (Fig.2d) were fitted using amodel including
the linear contribution of acoustic phonons and exponential thermal activation of optical phonons with energy
of
ELO
, coupled to the exctionic complex44:
A fit to the temperature-induced linewidth broadening reveals at T = 0K line broadenings of approximately
γ0 = 80 μeV for X+, X−, XX and γ0 = 140 μeV for X. Here the difference in linewidths at low temperatures could be
a result of stronger spectral diffusion (dynamical broadening due to charge fluctuations in the QD environment
including defects in the SRL and charged surface states) caused by more pronounced Stark shift due to higher
polarizability of the Xstate than the other excitonic complexes45,46.
The strong increase of linewidth setting in at about 40K can be explained by the larger contribution of phonon
sidebands to the total emission in this temperature range. Therefore, the determined full width at half maximum
(FWHM) corresponds rather to the width of the phonon sidebands than to broadening of the zero-phonon line
(ZPL)47. We found that the linewidths of the ZPL for all excitonic complexes are dominated by spectral diffusion:
broadenings at the lowest investigated temperature are significantly greater than spectral resolution of our setup
(< 25μeV) and much larger than the lifetime-limited homogenous linewidth (0.7 μeV). We attribute the enhanced
spectral diffusion to charged states at etched mesa surfaces. This interpretation is supported by the fact that even
broader lines of (155 ± 50) µeV were observed in QDs embedded in smaller mesas with diameters of 0.3µm. The
higher optical quality ofQDs in large mesas originates from the fact that in this case the probability that the QD
is far away from the mesa sidewalls is higher and the influence of fluctuating charges trapped due to roughness of
the etched mesa surface are a primary cause of spectral diffusion48. Increasing FWHM of emission is the reason
for spectral lines to spectrally overlap and in consequence for the degradation of single-photon emission purity.
E
g(T)=Eg(0)−S�ℏω�
coth
�ℏω�
2kBT
−1
γ
(T)=γ0+γacT+
γ
LO
exp(ELO/kBT)−1.
Figure1. μPL spectra from the investigated InGaAs/GaAs QD embedded in a mesa of 1.3 μm diameter at 5K.
X—exciton, X+—positive trion, X−—negative trion, XX—biexciton. (a) Spectra for different excitation powers in
the range of (0.05–10)
µW
. (b) Double logarithmic plot of the µPL intensity as a function of excitation power.
Symbols denote the measured data points, the solid lines represent I ∝ Pα dependence with a near quadratic
(1.95) and linear (1.08) behavior for biexciton and exciton, respectively. Positive and negative trions exhibit
superlinear dependence (1.17 and 1.50, respectively). (c)Polarization-resolved µPL spectra for perpendicular
polarization angles for X in the left panel and polarization dependence of emission energy for X and XX in the
right panel, both indicating exciton fine structure splitting of
FSS
=
67 µeV
.
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The changes of emission intensity shown in Fig.2a–c are characteristic for the investigated type of QDs,
similar results were obtained for other QDs in the same structure. To explain the µPL quenching (Fig.2c),
we compare our findings with recently reported results of 8-band k.p calculations for such dots which yielded
the s–p splitting of (60–80) meV38. Here, the lower splitting corresponds to the higher QD emission energy.
Noteworthy, the QDs analyzed here have even higher emission energies than those studied previously in Ref.38.
Additionally, 8-band k.p calculations predict s–p splitting to be shared by approximately (20–30) meV for holes
and (40–50) meV for electrons. Analyzing the µPL temperature dependence we found characteristic activation
energies responsible for quenching of individual emission lines to be in the range of (10–20)meV. This allows
us to conclude that the dominant mechanism for the µPL quenching process is the promotion of holes to excited
valence band states (confined levels) in the QD and subsequently their increasing thermal escape probability. The
temperature-dependent data for X and XX are well explained by Arrhenius dependence with a single activation
energy. In contrast, for charged complexes a modification of the standard fitting formula was needed to account
for the µPL intensity increase (decrease) in the low temperature range for X+ (X−). As discussed in Ref.36, this
charging temperature effect can be related to thermal activation of one type of carriers from areservoir, resulting
in selective amplification (reduction) of X+ (X−) emission at elevated temperatures (see Fig.2c). The temperature
dependence of µPL intensity I(T) can be described by 36:
Figure2. Temperature-driven evolution of μPL spectra from 5 to 80K for
1
2
P
sat
(a) and
Psat
(b). Analysis of
μPL temperature dependence for QD excitonic complexes: (c)µPLintensity (d) µPL linewidth. Symbols denote
measured data, colored lines represent fits to the experimental data.
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where I0, IP are initial and reservoir-gained intensities, E1, E2 are activation energies of processes responsible
for increase, decrease of emission intensity, respectively, and B1, B2 are the amplitudes of thermally-activated
processes with energies E1 and E2. In the case of charged complexes, a distinct temperature interplay of their
relative intensities was observed in the low temperature range: the activation energy E1 ≅ 1.9meV was assigned
to the pronounced μPL intensity increase of X+ at temperatures up to 30K. This energy is characteristic also
for X− µPL intensity reduction indicating thermal activation of positive carrier traps (i.e. holes present due to
unintentional carbon p-doping in MOCVD growth) in the vicinity of the QDs, resulting in higher probability of
X+ formation. We could not observe clear correlations between the obtained activation energies for μPL thermal
quenching (E2) and the associated type of excitonic complex for the investigated QDs. This further indicates that
the thermal intensity behavior is rather related to the s–p splitting and not to the QD size and specific type of
excitonic complex. Then, the promotion of holes to higher QD states is the main path for thermal quenching of
µPL intensity driven by the small interlevel spacing of the valence band confined states.
The temperature-dependent µPL study was carried out for two excitation regimes: at the exciton saturation
power (Psat = 3.0µW) and at a half of the saturation power (0.5 Psat). The corresponding results are shown in
Fig.2a–d. A qualitative difference for both excitation powers can only be observed in the case of the positively
charged trion. Here, the activation energy of E1 ≅ 1.9meV is visible only for the excitation power below satura-
tion, for which the thermally activated carriers can still supply QDs and thus cause the X+ µPL increase, and
simultaneously the X− µPL decrease. At Psat, the trion µPL emission rate is limited by its radiative lifetime and even
excess availability of thermally activated carriers cannot further increase the emission intensity. The observed
relative increase in the intensity of X+ with respect to X can be related to increased probability of the QD being
charged with residual carrier before the optical excitation.
Single‑photon emission. Single-photon emission was probed by measuring the second-order photon
autocorrelation function g(2)(τ) and fitting the normalized histograms of coincidences with49:
where the function value for τ = 0 [g(2)(0)] reflects the multiphoton emission probability, the antibunching time
constant is
t
rise =
1
Ŵ+W
p
, with the electron–hole radiative recombination rate
Ŵ
and the effective pump rate Wp.
Experimental histograms are plotted together with the corresponding
µPL
spectra inFig.3a–c. While
Ŵ
(530MHz for X+, based on the time-resolved µPL experiment) is known to stay approximately constant with
temperature36, the observed decrease of trise reflects the increase of the effective pump rate with temperature: the
laser excitation power was increased with temperature to counteract the thermal quenching of µPL intensity.
Moreover, Wp increases also due to additional carriers, thermally activated from the reservoir (as discussed
above for X+). The values of multiphoton events’ suppression and rise times obtained from fitting to the histo-
grams of coincidences in Fig.3a–c right panels are: (a)g(2)(0) = 0, trise = 1.9ns, (b) g(2)(0) = 0.17, trise = 1.0ns, and
(c)g(2)(0) = 0.13, trise = 0.64ns with standard errors of fitted g(2)(0) values of 0.073, 0.11, 0.21, respectively. Here,
the degradation of multiphoton suppression for elevated temperatures reflects the increasing contribution of
uncorrelated background emission as seen in the associated µPL spectra due to temperature-induced quench-
ing of QD emission. This contribution can be estimated by the ratio
ρ=S/(S+B)
50 with intensity of signal S
and background B, which decreases from
ρ=0.87
at 5K to
ρ=0.57
at 50K. For all measurements the spectral
filtering was kept constant and its bandwidth (0.43nm) was in all cases broader than the FWHM of the X+
emission line yielding 0.26nm, 0.27nm, and 0.40nm for 5K, 25K, and 50K, respectively. Therefore the low
degradation of the g(2)(0) value is not achieved artificially by narrowing the spectral filtering, but is an inherent
property of investigated structures.
Conclusions
In conclusion, we performed a detailed temperature- and power-dependent study of photoluminescence from
single MOCVD-grown InGaAs/GaAs QDs, emitting in the telecom O-band at 1.3μm, and embedded in deter-
ministically fabricated mesas. Our studies provide important information about the temperature stability of
single QD emission and assist atbetter understanding of processes involved in the temperature-induced deg-
radation of single-photon emission purity. These processes include the increase of uncorrelated background
photons and simultaneous decrease of the line intensity. Excitonic complexes in the QD were identified based
on polarization-resolved and excitation-power-dependent µPL. The positive trion was found to be the thermally
most stable excitonic complex, with its emission still visible at the temperature up to at least 80K (liquid nitrogen
accessible), and with single-photon emission purity of g(2)(0) = 0.13 at 50K, what is particularly important in
view of future applications due to applicability of cryogen-free cooling23,24. The positive trion emission intensity
has amaximum around 30K which is actually an ideal temperature when building a practical single-photon
sources exploiting the Stirling cryocooling.
Our analysis indicates that the reason for non-monotonic temperature-dependence of the charged states
is the thermal activation of holes from their traps in the QD vicinity. Moreover, we identified the excitation of
holes to higher QD states in the valence band as the dominating mechanism for the µPL thermal quenching
in the investigated range of temperatures. Both carrier loss and uncorrelated background photons at the same
wavelength as the emitting line deteriorate the purity of single-photon generation from the studied QDs. While
I
(T)=
I0+IP
1−
1−1
1+B1exp(−E1/kBT)
1+B2exp(−E2/kBT),
g
(2)(τ)=
1
−
1
−
g
2(
0
)
×
e
−|τ|
trise
,
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the uncorrelated background photons are adominant process in multiphoton suppression degradation and
could be limited by quasi-resonant51,52 or resonant53 excitation schemes, the reason for carrier loss, namely the
holes’ level separation which is responsible for the µPL quenching, would have to be tailored in the QD epitaxial
growth (e. g., by including Al-containing barriers close to the QD/SRL to reduce thermal escape of carriers), in
order to increase the thermal stability of the emission.
Methods
Fabrication process. The investigated sample was grown by MOCVD on GaAs (001) substrate and consists
ofa300nm GaAs buffer layer, a distributed Bragg reflector composed of 23 pairs of GaAs/Al0.9Ga0.1As layers
and a single layer of self-assembled In0.75Ga0.25As QDs grown inStranski–Krastanow mode. Before the final
634nm GaAs capping layer, a nominally 4nm thick In0.2Ga0.8As SRL was deposited following the growth of
QDs in order to redshift the emission down to 1.3 µm17. Mesas were deterministically fabricated by means of
in-situ 3D electron-beam lithography54,55: first a bright QD was spectrally and spatially identified by means of
low-temperature cathodoluminescence by applying electron dose low enough not to invert the CSAR62 resist
spin-coated on the sample surface beforehand, and directly afterwards acylindrical mesa coinciding in position
with the pre-selected QD was defined in the resist by electron beam lithography. The sample was further dry
etched using plasma reactive ion etching and the designed pattern was transferred from the resist to the GaAs
capping layer. Mesas were fabricated with diameters in the range of 0.25µm to 2.1µm. All results presented in
this manuscript were obtained for a QD in a mesa of 1.3µm diameter.
Experimental setup. During spectroscopic measurements the structure was kept in the continuous-flow
liquid-helium cryostat. Identification of excitonic complexes and temperature-dependent measurements were
performed in a µPL setup equipped with amicroscope objective with NA = 0.4, 1m focal-length single-grating
monochromator and InGaAs multichannel array detector (pixel size: 25μm), providing spatial and spectral
Figure3. Single-photon emission from the X+ at cryogenic and elevated temperatures: spectra registered on
superconducting nanowiresingle-photon detectors—SNSPDs (left panel) and corresponding autocorrelation
histograms (right panel), measured under continuous wave non-resonant excitation at (a) T = 5K, (b) T = 25K,
and (c) T = 50K.
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resolution of 2µm and on the order of 25μeV, respectively. Photon statistics measurements were conducted
using aHanbury Brown and Twiss setup configuration56 with amonochromator of 0.32m focal length acting
as a band-pass filter with 0.43nm bandwidth (kept constant for measurements at all temperatures). The filtered
signal was coupled to a 50:50 fiber beam splitter. Each of its outputs was connected to NbN superconducting
single photon counting detector with
∼10−15%
quantum efficiency and 10dark counts/s at 1.3µm. The photon
correlation statistics was acquired by a multichannel picosecond event timer with time-bin width set to 256ps.
Inboth types of experiments the QD was excited non-resonantly by a continuous wave semiconductor diode
laser with energy of 1.88eV (λ = 660nm) and 1.56eV (λ = 787nm) for the temperature-dependent µPL and
autocorrelation measurements, respectively.
Received: 20 October 2020; Accepted: 25 November 2020
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Acknowledgements
The authors acknowledge financial support via the “Quantum dot-based indistinguishable and entangled photon
sources at telecom wavelengths” project, carried out within the HOMING programme of the Foundation for
Polish Science co-financed by the EU under theERDF. Support from the Polish National Agency for Academic
Exchange is also acknowledged. This work was also supported by the FI-SEQUR project jointly financed by the
European Regional Development Fund of the European Union in the framework of the programme to promote
research, innovation, and technologies (Pro FIT) in Germany, and the National Centre for Research and Develop-
ment in Poland within the 2nd Poland-Berlin Photonics Programme, Grant Number 2/POLBER-2/2016 (project
value 2 089 498 PLN). Support from the German Science Foundation via CRC 787 is also acknowledged.
Author contributions
P.H. and A.M. performed autocorrelation measurements. P.H. and M.B., supervised by A.M., performed micro-
photoluminescence measurements and wrote the first version of the manuscript. D.Q. designed and grew the
sample under supervision of A.S.; N.S. patterned the sample under supervision of S.R. S.R. and G.S. supervised
the work of the Berlin and Wroclaw teams, respectively. All authors took part in the preparation of the final
version of the paper. P.H. and M.B. contributed equally to this work.
Competing interests
The authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to A.M.
Reprints and permissions information is available at www.nature.com/reprints.
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