![Figure 1 | Schematics of the quantum-dot-in-nanowire system. a, The nanowire consists of GaAs. The quantum dot forms close to the outer edge of an AlxGa1−xAs shell. Aluminium segregates at the nanowire edges owing to the lower mobility of aluminium. At the outer edge of the AlxGa1−xAslayer, Al segregates further in the [112] directions, leading to Al depletion and the formation of a nanoscale inclusion, an Al-poor](/figures/figure-1-schematics-of-the-quantum-dot-in-nanowire-system-a-23l56u3v.webp)
ARTICLES
PUBLISHED ONLINE: 3 FEBRUARY 2013 | DOI: 10.1038/NMAT3557
Self-assembled quantum dots in a nanowire
system for quantum photonics
M. Heiss
1†
, Y. Fontana
1†
, A. Gustafsson
2
, G. Wüst
3
, C. Magen
4
, D. D. O’Regan
5
, J. W. Luo
6
,
B. Ketterer
1
, S. Conesa-Boj
1
, A. V. Kuhlmann
3
, J. Houel
3
, E. Russo-Averchi
1
, J. R. Morante
7,8
,
M. Cantoni
9
, N. Marzari
5
, J. Arbiol
10
, A. Zunger
11
, R. J. Warburton
3
and A. Fontcuberta i Morral
1
*
Quantum dots embedded within nanowires represent one of the most promising technologies for applications in quantum
photonics. Whereas the top-down fabrication of such structures remains a technological challenge, their bottom-up fabrication
through self-assembly is a potentially more powerful strategy. However, present approaches often yield quantum dots with
large optical linewidths, making reproducibility of their physical properties difficult. We present a versatile quantum-dot-in-
nanowire system that reproducibly self-assembles in core–shell GaAs/AlGaAs nanowires. The quantum dots form at the apex
of a GaAs/AlGaAs interface, are highly stable, and can be positioned with nanometre precision relative to the nanowire centre.
Unusually, their emission is blue-shifted relative to the lowest energy continuum states of the GaAs core. Large-scale electronic
structure calculations show that the origin of the optical transitions lies in quantum confinement due to Al-rich barriers. By
emitting in the red and self-assembling on silicon substrates, these quantum dots could therefore become building blocks for
solid-state lighting devices and third-generation solar cells.
S
emiconductor quantum dots have been shown to be excellent
building blocks for quantum photonics applications, such as
single-photon sources and nano-sensing. Desirable properties
of a single-photon emitter include high-fidelity anti-bunching
(very small g
2
(t = 0)), narrow emission lines (ideally transform
limited to a few microelectronvolt) and high brightness (>1 MHz
count rate on standard detector). For simplicity, these properties
should be achieved either with electrical injection or non-resonant
optical excitation. Desirable properties of a nano-sensor include
a high sensitivity to local electric and magnetic fields, with
the quantum dot located as close as possible to the target
region. A popular realization involves Stranski–Krastanow InGaAs
quantum dots embedded in a three-dimensional matrix, which
are excellent building blocks for the realization of practical single-
photon sources
1
. However, the photon extraction out of the
bulk semiconductor is highly inefficient on account of the large
mismatch in refractive indices of GaAs and vacuum. An attractive
way forward is to embed the quantum dots in a nanowire
2
. To
solve the extraction problem, the nanowire is designed to operate
as a single-mode waveguide, a so-called photonic nanowire, with a
taper as photon out-coupler
3
. Also, for nano-sensing applications,
a quantum dot in a nanowire can be located much closer to the
active medium. Top-down fabrication of the photonic waveguide
is technologically complex, however. Bottom-up fabrication of
the photonic waveguide is very attractive
4–6
, but it is at present
challenging to self-assemble quantum dots in the nanowires with
1
Laboratoire des Matériaux Semiconducteurs, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland,
2
Solid State Physics, The Nanometer
Consortium, Lund University, Box 118, Lund S-221 00, Sweden,
3
Department of Physics, University of Basel, Klingelbergstrasse 82, CH4056 Basel,
Switzerland,
4
Instituto de Nanociencia de Aragon-ARAID and Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50018
Zaragoza, Spain,
5
Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland,
6
National
Renewable Energy Laboratory, Golden, Colorado 80401, USA,
7
Catalonia Institute for Energy Research, IREC. 08930 Sant Adrià del Besòs, Spain,
8
Department dÉlectrònica, Universitat de Barcelona, 08028 Barcelona, Spain,
9
Interdisciplinary Center for Electron Microscopy, École Polytechnique
Fédérale de Lausanne, 1015 Lausanne, Switzerland,
10
Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Ciència de Materials de
Barcelona, ICMAB-CSIC, E-08193 Bellaterra, CAT, Spain,
11
University of Colorado, Boulder, Colorado 80309, USA.
†
These authors contributed equally to
this work. *e-mail: anna.fontcuberta-morral@epfl.ch.
narrow linewidths and high yields
7,8
. Nano-sensing applications are
at present not highly developed. Other degrees of freedom of the
quantum-dot-in-nanowire system that can be usefully exploited
are the mechanical modes for optomechanics, and doping for p–n
junctions with applications in light harvesting
9,10
.
Here we present a promising new quantum-dot-in-nanowire
system. A schematic of the physical structure is shown in Fig. 1a.
The structure consists of Al-poor Al
x
Ga
1−x
As (x ∼ 10%) quantum
dots in an Al-rich Al
x
Ga
1−x
As (x ∼ 60%) barrier wrapped in an
intermediate Al-content matrix (x ∼ 33%). The quantum dots form
in the ridge of an AlGaAs nanowire. The self-assembly is driven by
the different Ga and Al adatom mobilities on the nanowire surface,
leading to Al segregation. The quantum dots can be positioned
close to the nanowire surface or close to the nanowire core during
the growth simply by choosing the growth mode, lateral or radial,
and the overall diameter of core and shell. We note that the
quantum dot size is independent of the core diameter. Significantly,
the nanowire growth is not complicated by fluctuations in crystal
structure (polytypism). We find that the quantum dots are very
stable, surviving prolonged electron beam bombardment, exposure
to air and so on, and that the quantum-dot-in-nanowire growth
is very reproducible from one run to the next: there is a wide
window of parameters under which they form. The quantum dots
have excellent optical properties even when they are located just
a few nanometres from the surface: individual quantum dots are
very bright (Megahertz count rate) even without engineering the
NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 1
© 2013 Macmillan Publishers Limited. All rights reserved.
ARTICLES
NATURE MATERIALS DOI: 10.1038/NMAT3557
h
QD
¬0.095
e
QD
1.837
E
c
(Γ)
E
v
(Γ)
E
c
(Χ)
E
c
(L)
(112)
(211)
(121)
GaAs
AlGaAs (60% Al)
AlGaAs (30% Al)
AlGaAs QD (10% Al)
a
b
(eV)
0
¬0.3
¬0.05
¬0.15
1.52
22
1.62
1.78
0.00
¬0.25
1.50
2.00
¬0.3
h
0
¬0.028
e
0
1.655
¬
¬¬
Figure 1 | Schematics of the quantum-dot-in-nanowire system.
a, The nanowire consists of GaAs. The quantum dot forms close to the
outer edge of an Al
x
Ga
1−x
As shell. Aluminium segregates at the nanowire
edges owing to the lower mobility of aluminium. At the outer edge of the
Al
x
Ga
1−x
Aslayer, Al segregates further in the [112] directions, leading to Al
depletion and the formation of a nanoscale inclusion, an Al-poor
Al
x
Ga
1−x
As quantum dot. b, The band edge diagram showing from left to
right the Al
x
Ga
1−x
As matrix and barriers, the lowest energy states confined
to the quantum dot and the external GaAs capping taken from atomistic
pseudopotential theory.
photonic modes, the linewidths are small (sub-100 µeV) and the
photons are highly anti-bunched (the upper bound on g
2
(t = 0) is
just 2%) even with intense non-resonant excitation.
An unusual feature is the blue-shift of the quantum dot emission
relative to emission from electrons and holes in the lowest energy
continuum states, in this case emission from the GaAs substrate,
the core. This wavelength ordering of quantum dot and continuum
emission is reversed relative to Stranski–Krastanow quantum dots.
We interpret this unusual result with large-scale calculations using
both the empirical pseudopotential method (modelling explicitly
500,000 atoms in this dot-in-wire structure) and density functional
theory (modelling a wire geometry with up to 12,000 atoms). The
calculations show that whereas the states at the band edge of the
system as a whole are indeed located in the GaAs layers, states
at higher energy exist, confined to the quantum dot. The results
are summarized in an energy level diagram, Fig. 1b, which shows
the band edge valence and conduction states, h
0
and e
0
, and the
quantum dot valence and conduction states, h
QD
and e
QD
. For
Stranski–Krastanow dots, the continuum states are associated with
the wetting layer, a thin 2D layer connecting the quantum dots,
and lie at higher energy than the lowest energy quantum dot states,
e
0
and h
0
. For the quantum-dot-in-nanowire system presented
here, this energy reversal of quantum dot and continuum emission
represents a new Ansatz for a solid-state single-photon emitter.
100 nm
20 nm
(101)
¬
(112)
¬
¬
(211)
¬
¬
(121)
57% Al 48% Al
10 nm
AlGaAs
86420
Distance (nm)
As
Ga
Al
ef
EDX counts (a.u.)
EDX counts (a.u.)
Distance (nm)
10 nm
60
40
20
0
60
40
20
0
86420
ab
cd
28% Al 38% Al
Figure 2 | Structure of quantum-dots-in-a-nanowire.
a, Aberration-corrected high-angle annular dark-field STEM image of the
entire cross-section of a GaAs nanowire coated with multiple
Al
0.33
Ga
0.77
As/GaAs shells. b, Zoom-in of a. c, Detail of the Al-poor
quantum dot located within the fork-like Al-rich stripes. The colouring has
been chosen to enhance the contrast between the different regions.
d, Three-dimensional atomic model of the cross-sectional STEM image
shown in c. The different colours have been introduced for clarity.
e,f, Chemical profiling of a single quantum-dot-in-nanowire using EDX
spectroscopy along two orthogonal directions.
For Stranski–Krastanow dots, the wetting layer creates problems on
non-resonant excitation: it can emit strongly
11
and trap charges over
times comparable to the radiative lifetime
12
, resulting in an increase
in g
2
(t = 0) as the pump power is increased
13
. These problems
are bypassed here. This, along with the high material quality, is
responsible for the very high fidelity photon anti-bunching in the
emission from a single quantum-dot-in-nanowire.
GaAs nanowires were grown by molecular beam epitaxy on a
2 inch Si(111) substrate using the gallium-assisted method
14
. After
stopping the axial growth, the conditions were switched from axial
to lateral to grow Al
x
Ga
1−x
As shells with Al compositions of x = 33%
and x = 51% (refs 15,16). In the lower Al content shell, we also
alternated the Al
x
Ga
1−x
As shells with 20 nm thick GaAs quantum
wells. The nanowires were characterized structurally in cross-
section using high-angle annular dark field scanning transmission
electron microscopy (STEM). Images of a GaAs nanowire covered
with alternating layers of Al
0.33
Ga
0.77
As and GaAs are shown in
Fig. 2a–c. The lighter regions correspond to GaAs and the darker
regions to Al
x
Ga
1−x
As, with the contrast correlating directly with the
Al content (Z-contrast). We observe the formation of dark stripes at
the nanowire corners, indicating Al enrichment. This accumulation
is consistent with the difference in chemical potential and adatom
mobility on (110) and (112)-type facets
17–20
. More intriguing is
the morphology of some stripes at the end of the Al
x
Ga
1−x
As
layer (Fig. 2b,c). The stripes open up, leaving a region of a few
2 NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials
© 2013 Macmillan Publishers Limited. All rights reserved.
NATURE MATERIALS DOI: 10.1038/NMAT3557
ARTICLES
ab c
d
0
1
Cathodoluminescence intensity (a.u.)
1 µm1 µm 200 nm
Figure 3 | Cathodoluminescence of a single nanowire. a, Electron
microscopy image of a GaAs nanowire with a Al
0.75
Ga
0.25
As shell.
b, Cathodoluminescence mapping of a nanowire detecting emission at
677 nm. c,d, Detailed cathodoluminescence map showing spatially
localized cathodoluminescence centres corresponding to quantum dots
less than 200 nm apart on two adjacent edges of the nanowire emitting at
677 nm.
nanometres in extent with low Al content: this region constitutes
the quantum dot. Figure 2c shows how the Al-rich stripe following
the (10
¯
1) plane bifurcates into two Al-rich stripes parallel to the
(1
¯
1
¯
2) and (
¯
2
¯
11) planes, forming a Y-like shape, terminated on a
polar (121) plane. Chemical profiling realized by energy-dispersive
X-ray (EDX) spectroscopy along the two principal directions of
the quantum dot is shown in Fig. 2e,f. In the direction from the
quantum dot base towards the apex, the Ga signal decreases and the
Al signal increases, whereas across the base, the Ga and Al signals
remain constant. This information is consistent with a shape in the
form of a pyramid, as described in the Supplementary Information.
We have probed the optical functionality of these novel quantum
dots with both cathodoluminescence (Fig. 3) and photolumines-
cence (Fig. 4). In both cases, in addition to a broadband emission
around 820 nm (1.51 eV), which we attribute to emission from
the GaAs core, we observe sharp emission lines at higher energy,
in the red part of the spectrum, Fig. 4a. Representative cathodo-
luminescence measurements in the spectral region 630–690 nm
(1.97–1.80 eV) along with the corresponding electron microscopy
image are shown in Fig. 3. Whereas the 820 nm cathodolumines-
cence is spatially continuous (see Supplementary Information), the
677 nm cathodoluminescence is spatially discontinuous along the
nanowire (Fig. 3b–d): there is a chain of bright, nanoscale emitters.
This suggests that the quantum dots identified in the structural
characterization are indeed responsible for the optical emission
in the red. This is reinforced by images at higher magnification
(Fig. 3c,d), which show extremely localized emitters separated
laterally by less than 200 nm, corresponding to quantum dots on
adjacent edges of the nanowire.
Further confirmation that the structures identified in the TEM
analysis are optically active comes from photoluminescence charac-
terization of individual quantum dots. The photoluminescence was
collected in a side-on geometry and its polarization dependence was
measured as a probe of the dielectric environment. The broadband
emission from the core is strongly polarized along the axis of the
nanowire, reflecting the pronounced dielectric anisotropy (Fig. 4b).
However, the sharp photoluminescence lines from individual quan-
tum dots are preferentially polarized in quantum-dot-dependent
directions and, in some cases, the polarization lies in a direction per-
pendicular to the nanowire axis (Fig. 4b). This observation supports
the assignment of the sharp quantum dot photoluminescence lines
to emitters located not on the nanowire axis but close to the surface.
A zoom-in of a typical photoluminescence spectrum of a single
quantum dot is depicted in Fig. 4c. For this particular quantum
dot, the emission is centred at 676 nm (1.83 eV), with a full-width
at half-maximum (FWHM) of 36 µeV. The linewidth varies from
dot to dot. The smallest linewidth observed so far is ∼29 µeV,
with most quantum dots showing sub-100 µeV linewidths. The
single quantum dot photoluminescence is very bright: the count
rate on our single-photon detector is ∼2 MHz at saturation (see
Supplementary Information). A decay curve of the single quantum
dot emission following pulsed excitation is also shown in the
Supplementary Information. The decay is described by a sin-
gle exponential over three decades. Given the brightness of the
quantum dots, the physical mechanism of this decay must be
spontaneous emission, with the associated lifetime, τ = 450±20 ps,
representing the radiative decay time. In other words, once an
electron–hole pair is created in the quantum dot, it decays by
spontaneous emission and not by electron and hole relaxation to
the band edge states, e
0
and h
0
. The value of τ is sub-nanosecond,
consistent with a large electron–hole overlap
21
, that is, inconsis-
tent with a transition involving an electron and hole localized in
different regions of space: both electron and hole are confined
to the quantum dot.
To determine the quantum character of the emission, namely,
the nature of the anti-bunching, we have measured the time-
dependence of the second-order intensity correlation g
2
(t) with
a Hanbury Brown–Twiss interferometer. g
2
(t = 0) characterizes
the fidelity of the anti-bunching. Furthermore, with cw excitation,
the full g
2
(t) function is sensitive to the dynamics, with two-level
and three-level systems behaving very differently. This allows us
to probe if the quantum-dot-in-nanowire behaves like a two-level
atom for which g
2
(t) = 1 − exp(−|t |/τ). An example histogram
with cw excitation is shown in Fig. 4d. There is a very clear dip
at time delay zero (t = 0), demonstrating anti-bunching in the
photon statistics. To probe two-level behaviour, we take τ from
the lifetime measurement, and we measure in situ the temporal
response function of the experimental set-up (see Supplementary
Information) to quantify the jitter (dominated by the detectors).
We then calculate the convolution of the two-level atom result with
the system response. Figure 4d shows that this procedure describes
the experimental results extremely well. We stress that this method
does not involve any fit parameters; in fact, the agreement cannot
be improved by allowing τ to vary in a fit procedure. In this way,
we find that the upper bound on the true value of g
2
(t = 0) is
2%: the fidelity of the photon anti-bunching is extremely high.
This result is corroborated by measurements of g
2
(t = 0) using a
pulsed laser source. However, as a more significant and general
statement, we find that this quantum-dot-in-nanowire mimics a
two-level atom very closely.
The origin of these two-level-atom-like optical properties is,
at first sight, not so obvious based on a comparison with the
well-known Stranski–Krastanow dots. In a conventional Stranski–
Krastanow InGaAs quantum dot embedded in a GaAs matrix, the
GaAs has the highest energy band edges, higher than the InGaAs
quantum dot, and higher too than the wetting layer which forms an
intermediate 2D energy band. Photoexcitation of the wetting layer
NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 3
© 2013 Macmillan Publishers Limited. All rights reserved.
ARTICLES
NATURE MATERIALS DOI: 10.1038/NMAT3557
Wavelength (nm)
QDs Core
5x
kCounts (s
¬1
)
0
1
0
1
0
1
0
1
NW core (820 nm) QD1 (624 nm) QD2 (638 nm) QD3 (634 nm)
ca
b
kCounts (s
¬1
)
Wavelength (nm)
Energy (meV)
675.9 676.1 676.3
d
Counts
g
2
Time delay (ns)
680 700 720 740 760 780 800 820
0
10
20
30
1,833.8 1,833.41,834.2
0
20
40
60
80
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
800
0
200
400
600
¬4 ¬2 0 2 4
Figure 4 | Photoluminescence of a quantum-dot-in-nanowire system. a, Photoluminescence recorded from a nanowire with non-resonant excitation at
488 nm. The broad peak at 820 nm arises from emission from the GaAs core; the sharp peaks at shorter wavelength arise from the quantum dots.
b, Azimuthal polarization analysis of the emission from the nanowire core and from three quantum dots. c shows a photoluminescence spectrum at a
sample temperature 4.2 K with 0.03 µW µm
−2
with an excitation wavelength of 632.8 nm. The points are the measured counts on the
charge-coupled-device camera, the black curve is a Lorentzian fit. The blue curve corresponds to the spectrum after deconvoluting the spectral response of
the detector (Lorentzian with FWHM 46 µeV) and therefore represents the quantum dot alone: the quantum dot photoluminescence spectrum has a
FWHM of 36 µeV for this particular quantum dot. d, A g
2
measurement of a quantum-dot-in-nanowire (different quantum dot to a) using continuous wave
excitation at 632.8 nm. The count rate (right y-axis) was normalized to unity far from the dip at delay zero t = 0 (left y-axis). The radiative lifetime τ of this
quantum dot was measured to be 450 ps by recording the decay curve following pulsed excitation (see Supplementary Information). The black curve
shows the convolution of the ideal two-level atom result, g
2
(t) = 1 − exp(−|t|/τ ), with the response of the detectors (Gaussian with FWHM 0.62 ns) and
describes the data extremely well. The blue curve shows the two-level atom response only.
creates electrons and holes which relax rapidly into the quantum
dot levels. In contrast, in the current quantum-dot-in-nanowire
system, Fig. 1a, GaAs forms the lowest energy band edges, Fig. 1b,
and acts as the ultimate sink for photoexcited carriers. Furthermore,
the 2.5 nm 60% Al shell at first sight poses a rather ineffective barrier
for the quantum dot-confined electrons.
To understand the two-level-like emission features at energies
above the GaAs band gap, we have studied theoretically quantum
confinement in these large scale nanostructures. The two state-of-
the-art approaches used are the empirical pseudopotential method
for a quantum-dot-in-nanowire of more than a half-million atoms,
and density functional theory for a quantum wire of more than ten
thousand atoms. For the empirical pseudopotential calculations,
the computational cell, Fig. 2e, contains the 10% Al quantum dot
with a square base in the (121) plane, of height 9.0 nm, and four
facets (112), (211), (121), and (212) to complete the pyramid;
the 60% Al barrier, parallel to the quantum dot facets, having a
thickness of 2.5 nm; the 30% Al layer; and the GaAs substrate,
parallel to the quantum dot (121) plane containing 14 monolayers
of GaAs. The total number of atoms in the computational cell
is 511,104. We solve the atomistic Schrödinger equation using
as potential the superposition of the atomistic pseudopotentials
of Ga, Al and As at the corresponding lattice sites given by the
structure, in a basis of the linear combination of bulk bands
22
using
the folded spectrum method
23
, allowing the eigensolutions to be
obtained in a physically interesting energy window. Excitonic effects
are calculated from the single-particle states with a configuration
interaction calculation. We find that the highest occupied molecular
orbital and lowest unoccupied molecular orbital of the whole
system reside indeed on the GaAs substrate (correspondingly, in the
nanowire core), as shown in Fig. 5a. This supports our assignment
of the broadband emission at 1.51 eV to the nanowire GaAs core.
The 67 lowest hole levels of the system as a whole (h
0
–h
66
) are
localized in the GaAs. The first hole state confined to the quantum
dot is h
QD
and corresponds to hole state h
67
with energy 95 meV
below the bulk GaAs valence band edge (67 meV below the system
Highest occupied molecular orbital state h
0
), as shown in Fig. 1b.
For the electron states, the lowest 19 electron levels of the entire
system (e
0
–e
18
) are localized on GaAs, and the first state confined
to the quantum dot is e
QD
, corresponding to e
19
with energy
317 meV above the bulk GaAs conduction band edge (182 meV
above the system lowest unoccupied molecular orbital state e
0
),
as shown in Fig. 1b. The wavefunctions of states e
0
, h
0
, e
QD
and
h
QD
are shown in Fig. 5a. The calculated emission energy of the
quantum dot-localized states is 1.902 eV (652 nm), red-shifted from
the single-particle transition energy 1.932 eV by excitonic effects.
Turning next to the density functional theory calculations, we
have studied a quantum wire bound by polar and non-polar
interfaces, thereby taking into account both internal electric fields
and charge reorganization effects. We model the 10% Al quantum
dot by an infinite [1
¯
21]-oriented wire embedded in a 60% Al matrix
with thickness either 1.4 nm (5,000 atom system) or 2.5 nm (12,168
atom system), as shown in Fig. 5b–d. In both cases, the interface
polarity was found to be insufficient to induce charge separation.
We observe clearly defined quantum dot-localized states close to
the valence and conduction band edges (Fig. 5b–d). Using the
experimental bulk GaAs band gap for the core region where the
edge states are dominant, but otherwise retaining our computed
band offsets, we predict transitions between these levels at 1.94 eV
(640 nm), in broad agreement with both the unscreened calculation
4 NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials
© 2013 Macmillan Publishers Limited. All rights reserved.
NATURE MATERIALS DOI: 10.1038/NMAT3557
ARTICLES
a
e
0
= 1.655 eV
AlGaAs QD
(10% Al)
AlGaAs (60% Al)
GaAs
AlGaAs, polar interface
(60% Al)
15.6 nm
12,168 atoms
10 nm
5,000 atoms
bd
c
h
0
= ¬0.028 eV
e
QD
= 1.837 eV
h
QD
= ¬0.095 eV
AlGaAs QD
(10% Al)
AlGaAs (60% Al)
AlGaAs (30% Al)
GaAs
Figure 5 | Atomistic calculations of electronic states in a quantum-dot-
in-nanowire system. a, Pseudopotential eigenstate densities for a 10% Al
content Al
x
Ga
1−x
As quantum dot, 9 nm high, surrounded by a 2.5 nm
thickness 60% AlGaAs barrier embedded in an 30% AlGaAs matrix and
sitting on a pure GaAs substrate (4 nm thickness in computational cell).
Plotted are the lowest energy conduction and valence states (e
0
and h
0
,
respectively) and the lowest energy quantum dot-bound conduction and
valence states (e
19
and h
67
, respectively). b–d, The localized Kohn–Sham
states nearest the band edges, computed using self-consistent
linear-scaling density functional theory, and viewed along the [1
¯
11] axis.
b, Highest localized valence state, 0.07 eV below the band edge, for a
5,000 atom model system (10.0×10.0× 1.3 nm
3
, fully periodic),
simulating the thin (1.4 nm) 60% Al barrier between the 10% Al quantum
dot with a pure GaAs nanowire shell. c, Corresponding conduction state,
located at 0.36 eV above the band edge. d, As c, but for a 12,168 atom
system (15.6× 15.6× 1.3 nm
3
, fully periodic, with a barrier of width
2.5 nm); 0.27 eV above the conduction edge. b–d were produced using
VESTA 3 (ref. 41).
and the experimental observation. We find that the thin 1.4 nm,
60% Al barrier is sufficient to provide quantum confinement
irrespective of the polarity of the facets. Hence, both the atomistic
pseudopotential of the quantum-dot-in-nanowire and density
functional theory (DFT) of a charge-reorganized nanowire with
the same cross-section predict states with both electrons and holes
confined to the quantum dot.
In summary, we report the self-assembly of a high-quality
quantum-dot-in-nanowire system using two basic components,
GaAs and AlAs. Self-assembly is not strain driven. Instead, it
proceeds by the different adatom mobility of Ga and Al on the
host substrate. This mechanism may well be effective with other
semiconductor materials (see Supplementary Information). The
shape and composition of the quantum dots has been determined
by high-resolution, atom-selective electron microscopy. Individual
quantum dots are bright and spectrally pure emitters of highly
anti-bunched light even with non-resonant excitation and even,
furthermore, when they are positioned just a few nanometres
from the nanowire surface. The operating principle is that both
electron and hole states involved in the transition lie above the
respective band edges of the nanowire itself, a point we understand
quantitatively using atomistic calculations of the electronic states.
As well as applications as single-photon sources, an immediate
possibility is the application of these quantum dots as nano-sensors
and in forging a coupling between the optical and mechanical
properties. By adjusting the core and shell diameters of the
nanowires, the quantum dot emission can be efficiently funnelled
into a waveguide mode in the nanowire. Furthermore, there are easy
routes to embedding the quantum dots in a radial p–n junction
24
,
opening up applications involving not just quantum light creation
but also charge control
25
, single-photon detection
26
and spin
27,28
.
Methods
Nanowire growth. The nanowires were grown using a DCA P600 MBE machine.
The nanowire core structures were obtained under rotation at 7 r.p.m. at a
temperature of 640
◦
C under a flux of Ga equivalent to a planar growth rate of
0.03 nm s
−1
and a V/III ratio of 60. The conditions were then switched from axial to
radial growth by increasing the As pressure and reducing the substrate temperature.
A 50 nm Al
x
Ga
1−x
As shell was grown with Al compositions x = 0.33, 0.51 and 0.70
and capped with 5 nm GaAs to prevent oxidation. One sample was grown with
alternating layers of GaAs/AlGaAs at x = 0.33.
Electron microscopy. Cross-sections of the nanowires perpendicular to the
growth axis were prepared by mechanical polishing and ion milling. 3D atomic
models were obtained using the Rhodius software package
29
, which allows
complex atomic models to be created, including nanowire-like heterostructures
30
.
High-angle annular dark-field scanning transmission electron microscopy
analyses were performed in an aberration-corrected probe FEI Titan 60–300 keV
microscope. EDX analysis was performed using a FEI Tecnai OSIRIS microscope
operated at 200 kV using the Super-X (0.9 radian collection angle) detector and
Bruker Esprit software.
Optical spectroscopy. The nanowires were transferred to a fresh silicon substrate
and subsequently probed side-on. Cathodoluminescence was realized in an adapted
scanning electron microscope
31
. Photoluminescence measurements were made
with a confocal optical microscope with sample scanning, exciting with a low-power
HeNe laser at 632.8 nm or Ar
+
Kr
+
laser at 488 and 514 nm. The photoluminescence
was dispersed with a monochromator-array detector system. Photoluminescence
in a bandwidth of 0.5 nm was sent to a Hanbury Brown–Twiss photon coincidence
set-up with two nominally identical silicon avalanche photodiodes. The pulsed
measurements (see Supplementary Information) were performed with a Q-switched
semiconductor laser diode at 635 nm, using time-correlated single-photon counting
to record the decay curve (Supplementary Information).
Pseudopotential calculations. The screened atomic potentials are adjusted by
the empirical pseudopotentials method to correct for the DFT errors in band
gaps, effective masses, inter-valley splittings and band offsets
32
. The single-particle
problem is solved numerically in a plane-wave basis, including spin–orbit (340 meV
for GaAs), using the folded spectrum method
33
, which allows eigensolutions to
be obtained in a physically interesting energy window (about 300 meV from
band edges) rather than at all energies. The calculation is carried out with a fixed
potential without iterating to self-consistency.
Self-consistent DFT calculations. Using linear-scaling DFT (ref. 34), as
implemented in the ONETEP method
35–37
, which captures charge redistribution
effects both efficiently and accurately
38,39
, we have performed simulations
on structures containing 5,000 and 12,168 atoms (one of the largest fully
self-consistent calculations ever performed). The 5,000 atom calculation was
carried out by iteratively refining a compact real-space Wannier basis with
respect to a primary plane-wave basis, whereas in the 12,168 atom calculation
the real-space basis was pre-optimized for isolated atoms, and thereafter fixed.
In order to capture both the polar [121] and non-polar facets of the observed
quantum-dots-in-nanowires, our simulation cells consist of fully-periodic slabs
(1.3 nm thick, along the [1
¯
11] direction) of an effective [1
¯
21] wire. Simulations
at the interface with the GaAs outer shell (Fig. 5) and with the Al
0.3
Ga
0.7
As
nanowire core were separately carried out (see Supplementary Information),
using norm-conserving pseudopotentials, the local-density approximation
40
, and
random alloying at each stated concentration.
Received 26 June 2012; accepted 21 December 2012;
published online 3 February 2013
References
1. Shields, A. J. Semiconductor quantum light sources. Nature Photon. 1,
215–223 (2007).
NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 5
© 2013 Macmillan Publishers Limited. All rights reserved.