Strain assisted inter-diffusion in GaN/AlN quantum dots
C. Leclere, V. Fellmann, C. Bougerol, D. Cooper, B. Gayral et al.
Citation: J. Appl. Phys. 113, 034311 (2013); doi: 10.1063/1.4775587
View online: http://dx.doi.org/10.1063/1.4775587
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Published by the American Institute of Physics.
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JOURNAL OF APPLIED PHYSICS 113, 034311 (2013)
Strain assisted inter-diffusion in GaN/AlN quantum dots
C. Leclere,1,a) V. Fellmann,2 C. Bougerol,3 D. Cooper,4 B. Gayral,2 M. G. Proietti,5
H. Renevier,1 and B. Daudin2
1
Laboratoire des Mat
eriaux et du G
enie Physique, Grenoble INP - Minatec, Grenoble, France
CEA-CNRS Group, “Nanophysique et Semiconducteurs,” Universit
e Joseph Fourier and CEA Grenoble,
INAC, SP2M, 17 rue des Martyrs, 38054 Grenoble, France
3
CEA-CNRS Group, “Nanophysique et Semiconducteurs,” Institut N
eel, CNRS and Universit
e Joseph Fourier,
BP 166, F-38042 Grenoble Cedex 9, France
4
CEA, Leti, Minatec, 38054 Grenoble, France
5
Departamento de Fisica de la Materia Condensada, Instituto de Ciencia de Materiales de Aragon,
CSIC-Universidad de Zaragoza, Spain
2
(Received 24 October 2012; accepted 20 December 2012; published online 18 January 2013)
The structural and optical properties of high temperature-annealed superlattices of GaN quantum
dots embedded in AlN barrier have been studied by a combination of X-ray techniques (reciprocal
space mapping, multiwavelength anomalous diffraction, and diffraction anomalous fine structure),
high resolution transmission electron microscopy, and photoluminescence spectroscopy. Taking
advantage of the disentangling of the chemical and structural information provided by the
simultaneous use of X-ray absorption and diffraction data obtained in a synchrotron environment,
we provide quantitative determination of strain and composition for each different region of the
nanostructures. Eventually, it is shown that strain driven dot/barrier intermixing is present, mostly
on top of the dots. These observations have been confirmed by high resolution electron
microscopy. A blue shift of photoluminescence peak has been furthermore observed and assigned
to GaN/AlN intermixing suggesting a new path for engineering the emission wavelength of such
C 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4775587]
heterostructures. V
I. INTRODUCTION
Semiconductor quantum dots (QDs) have been a subject
of continuous interest for several decades due to their remarkable structural and optical properties. Such nano-objects are
generally grown either by molecular beam epitaxy (MBE) or
by metalorganic chemical vapor deposition (MOCVD), using
the Stranski-Krastanow (SK) growth mode during which
pseudomorphic deposition of dot-forming material on a mismatched substrate is followed by three-dimensional (3D)
island formation above a critical thickness of some monolayers. This growth mode has been extensively used to grow
self-assembled InAs,16 InGaAs,33 SiGe,48 GaN,11 and InGaN1
QDs. In the case of InAs, InGaAs, and SiGe, interdiffusion
with barrier material surrounding QDs is commonly observed
and has been found to contribute to elastic energy minimization process.4,5,56 By contrast, in the case of III-nitride QDs,
interdiffusion has been found to play a minor role. This is
spectacularly true in the case of GaN QDs embedded in AlN
barrier material. High resolution transmission electron microscopy (HRTEM) studies of stacking of GaN QDs embedded in
AlN have revealed no significant interdiffusion. Nevertheless,
a detailed study has established that capped dots were slightly
smaller than uncapped ones, due to the conversion of one
GaN monolayer into AlN, which has been assigned to a Ga/Al
exchange mechanism promoted by the energetically favorable
formation of Al-N bond.8,15
For arsenides and SiGe QDs, annealing is currently used
to further enhance interdiffusion between the dots and the
a)
Cedric.Leclere@grenoble-inp.fr.
0021-8979/2013/113(3)/034311/10/$30.00
barrier, as a tool for band gap engineering of the heterostructures.22,54,58 Regarding nitride materials, thermally assisted
interdiffusion also appears as an attractive tool for band gap
engineering of light emitting diodes (LEDs) in a wavelength
range spanning from visible to UV. More specifically, interdiffusion of GaN QDs embedded in AlN or AlGaN barrier
material could provide a solution for fine tuning of light
emitting devices in the UV region. To address this issue,
superlattices of GaN/AlN QDs annealed up to 1700 C have
been studied by X-ray diffraction, photoluminescence spectroscopy, and HRTEM. Remarkably, it is found that no significant dot/barrier interdiffusion was observed below
1300 C, evidence of the exceptional stability of GaN/AlN
heterostructures. For annealing temperatures higher than
1300 C, detailed analysis of reciprocal space maps (RSMs)
and anomalous diffraction reveals that interdiffusion is taking place, mostly localized on top of the dots. This is confirmed by HRTEM studies of the samples, which show that
the spatially localized interdiffusion is enhanced in the case
of vertically correlated GaN dots, as a further evidence that
it is strain-assisted. Eventually, it will be shown that annealing at temperatures as high as 1700 C, far from resulting
in the formation of a homogeneous AlGaN alloy leads to
the re-crystallization in solid phase of Ga-rich islands surrounded by an Al-rich matrix.
II. SAMPLE PREPARATION
A. PA-MBE
The samples used in this study were grown by plasmaassisted molecular beam epitaxy. After standard degreasing
113, 034311-1
C 2013 American Institute of Physics
V
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034311-2
Leclere et al.
procedure, the commercially available 1 lm thick,
c-oriented, AlN/sapphire MOCVD wafers fixed with In on a
molybdenum sample holder were introduced in the growth
chamber and annealed at 350 C during 30 min to outgas
cleaning residues. Next, temperature was increased up to
about 750 C. An AlN buffer layer was first deposited by alternative supply of Al and N during 5 min for sample A and
10 min for sample B, corresponding to an effective thickness
of 10 nm and 20 nm, respectively. Next, GaN QDs/AlN
superlattices were grown. GaN QDs were deposited under
N-rich growth conditions, whereas for Al barriers an excess
of Al was used to ensure flat interfaces. After deposition of
the barrier, the surface was left exposed to an N flux to consume the excess of Al. The formation of GaN QDs obeyed
the SK growth mode. A thin GaN wetting layer (WL) was
first deposited layer-by-layer, till a critical thickness of about
2.4 MLs, followed by an abrupt transition to threedimensional facetted islands.11 It is now well known that,
depending on the amount of GaN deposited and on the thickness of AlN spacer layer, GaN QDs may be correlated or
not.6,15 Vertical correlation, when present, has been shown
to result from the AlN barrier elastic deformation due to the
presence of the GaN QDs plane beneath, which itself results
in the preferential nucleation of new GaN QDs just above
those of the previous plane.9,53 In order to address the issue
of the influence of vertical correlation on GaN QDs annealing, two samples were examined in the present study; the
first (sample A, N1368) consisted of 100 planes of GaN
QDs, about 1.6 nm high, separated by 11.6 nm thick AlN barrier layers. As it will be shown later, both X-rays RSM and
HRTEM revealed that such GaN QDs were uncorrelated vertically. The second sample (sample B, N1473) consisted of
170 planes of GaN QDs, about 3 nm high, separated by
6.5 nm thick AlN barrier layers. Such GaN QDs were found
to present a high degree of vertical correlation. After the SLs
growth, an AlN capping layer was grown (50 nm) in order to
protect the surface during the post-growth annealing step.
B. Rapid thermal annealing
Annealing was performed in an induction furnace,
allowing a fast temperature ramp of 1500 C in 10 min. Samples were placed in a graphite crucible under nitrogen atmosphere at 800 mbar, to avoid oxydation and impurity
incorporation. Temperatures at the top and the bottom of the
crucible were controlled with pyrometers. For sample A,
30 min annealing at temperatures of 1100 C; 1500 C, and
1700 C has been used on different parts of the wafer and
one piece called “as grown” was kept unannealed as
reference.
III. X-RAY DIFFRACTION
A. Reciprocal space mapping
Two-dimensional RSM is a well known tool to investigate the structural properties of inhomogeneously strained
and/or chemically inhomogeneous systems such as epitaxial
heterostructures.14,39,50 The use of linear and 2D detectors
together with the synchrotron high photon flux, help reduc-
J. Appl. Phys. 113, 034311 (2013)
ing acquisition times by orders of magnitude. In the case of
the semiconductor epitaxial nanostructures, one can distinguish a number of different regions; substrate, interface, wetting layer, QDs, outer and inner regions of QDs, capping or
spacer layers, etc. Each region can have a different composition and/or different strain state and contributes to diffraction
at a different location in the reciprocal space. RSM gives a
general picture of the sample allowing one to distinguish and
study in detail the individual contributions. In particular, it is
possible to measure relative angular differences in the peak
position with respect to the substrate diffraction peak used as
reference.14 These relative peak positions in RSM give information on the strain state (elastically strained, partially or
fully relaxed) and provide a quantitative measurement of
lattice parameters of the different heterostructure
regions.7,26,28–30
RSM experiments were carried out at beamline BM02/
D2AM at European Synchrotron Radiation Facility (ESRF).
Intensity of asymmetric Bragg reflections was collected by
an 8-circle diffractometer (Euler geometry). Scattered intenTM
sities were recorded by a linear gas-detector (Vantec ) spanning over an exit angle range of about [02 ]. The incident
X-ray beam was monitored by a dedicated photodiode.43
Two mirrors focus the beam in the vertical plane, whereas
the horizontal focusing is achieved using a sagittal bending
of the second crystal monochromator. Beam size at the focal
point was about 0:15 0:3 mm2 , thus illuminating a large
assembly of QDs. Beam polarization was linear in the horizontal plane and the Q vector was in the vertical plane, i.e.
the incoming and diffracted beam polarization vectors were
perpendicular to Q (r-r channel).
RSM was collected close to 1122 and 1015 Bragg
reflections at 10 200 eV below the Gallium absorption edge
(10 367 eV). The 1015 reflection is sensitive to out-of-plane
strain, allowing one to enhance the sensitivity to out-of-plane
annealing effects.
The RSM close to 1015 reflection is shown in Fig. 1(a)
for sample A and in Fig. 2(a) for sample B. Reciprocal space
units H, K, and L refer to AlN wurtzite cell parameters
(aAlN ¼ bAlN ¼ 3:112 Å, cAlN ¼ 4:982 Å and a ¼ b ¼ 90 ,
c ¼ 120 ). In this frame, H ¼ 0.976 and L ¼ 4.804 correspond to relaxed GaN parameters (aGaN ¼ bGaN ¼ 3:189 Å,
cGaN ¼ 5:185 Å). The mismatch between AlN and GaN is
2.4% (respectively, 3.9%) along ½1010 (respectively,
[0001]). For the sake of clarity, Fig. 1(d) (respectively, Fig.
2(d)) shows a schematic representation of Figure 1(a)
(respectively, Fig. 2(a)). The AlN buffer exhibits a sharp signal at H ¼ 1.0 and L ¼ 5.0. The superlattice reflections with
H ¼ 1.0 (streaks) correspond to the stacking along the [0001]
direction of GaN WLs and AlN spacers. The GaN WL is
matched to the in-plane aAlN parameter.24,47 The superlattice
reflections spacing is related to the stacking period X by the
c
. It gives XA ¼ 11:6 nm for sample A and
relation X ¼ DL
XB ¼ 6:5 nm for sample B in satisfactory agreement with
growth conditions and transmission electron microscopy
observations.
Figures 1(b), 1(c) and Figs. 2(b), 2(c) show H-scans with
L ¼ 4.90 and L-scans with H ¼ 0.98 extracted from 1015
RSMs for sample A (Fig. 1(a)) and B (Fig. 2(a)), respectively.
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034311-3
Leclere et al.
J. Appl. Phys. 113, 034311 (2013)
RSM of sample A, as
FIG. 1. (a) 1015
grown, indexed with H, K, and L referring to relaxed AlN. Relaxed AlN and
GaN positions are shown as white spots
at the crossing of white dashed lines. (b)
(respectively, c)) are linear scans along
H (horizontal black arrow) (respectively,
L (vertical black arrow)) at L ¼ 4.9
(respectively, H ¼ 0.98) for as grown
(black), annealed at 1500 C (red) and
1700 C (blue) samples. Intensities have
been averaged over 3 points. (d) is a
scheme of the diffraction pattern in
the reciprocal space where AlN buffer,
GaN wetting layers and uncorrelated
GaN quantum dots contributions are
represented.
Black curves (respectively, red curves) correspond to as grown
(respectively, annealed at 1500 C) samples. Along the H axis,
the GaN QDs diffraction signal appears as a broad diffuse scattering peak located in between of relaxed GaN and AlN due to
the in-plane compressive strain state of the QDs.8 The broadening along the H axis is mainly due to the QDs size.
For sample A, the full width at half maximum (FWHM)
of the black curve in Fig. 1(b), DH 0:025, gives in the real
space dQD 12:7 nm which corresponds to the average
diameter of the QDs, in agreement with TEM observations.
Along the L axis, the black curve of Fig. 1(c) shows superlattice modulations on top of a broad peak. This corresponds to
a random vertical arrangement of the QDs in the growth
direction (there is no long range vertical correlation of the
QDs). The FWHM of the black (respectively, red) curve
envelope DL 0:35 (respectively, DL 0:20) gives in the
RSM of sample B, as
FIG. 2. (a) 1015
grown, indexed with H, K, and L referring to relaxed AlN. Relaxed AlN and
GaN positions are shown as white spots
at the crossing of white dashed lines. (b)
(respectively (c)) linear scan along H
(horizontal black arrow) (respectively, L
(vertical black arrow)) at L ¼ 4.9
(respectively, H ¼ 0.98) for as grown
(black), annealed at 1500 C (red) and
1700 C (blue), samples. Intensities have
been averaged over 3 points. (d) is a
schematic representation of the diffraction pattern in the reciprocal space
where AlN buffer, GaN wetting layers
and vertically correlated GaN quantum
dots are represented.
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034311-4
Leclere et al.
real space hQD 1:5 nm (and hQD 2:6 nm) which corresponds to the average height of the QDs for as grown and
annealed samples, respectively. Note that in the case of as
grown sample, the strain value along the c-axis determined
from the position of the broad peak maximum, (H ¼ 4.88),
shows that the QDs are compressed by the AlN barriers.
For sample B, the situation is different, the QDs are
larger and the AlN barrier is thinner. The diffraction signal
along the H axis (black curve in Fig. 2(b)) shows a higher inplane strain state in comparison with the QDs of sample A.
Also, the QDs diffraction signal along the L axis (black
curve in Fig. 2(c)) shows a well defined superlattice structure
due to the correlation of the QDs in the growth direction.
The position of the superlattice envelope maximum shows
that the QDs are stretched along the c-axis.
In Figs. 1(b), 1(c), 2(b), and 2(c) red curves correspond
to an annealing temperature of 1500 C and blue curves to
1700 C. One can observe that annealing strongly modifies
the L-scans for both samples. At 1500 C, the superlattice
structure is still well defined and the QDs diffraction envelopes shift to higher L values, closer to relaxed AlN. This is
a clear indication of Al/Ga intermixing. At 1700 C, the
superlattice is destroyed and the diffraction pattern exhibits a
single peak that could be interpreted as a signature of an
Al1x Gax N alloy with x ’ 0:1. We will show in Sec. V that
the sample is not a homogeneous alloy but consists of small
Ga-rich clusters whose diameters are of the order of 10 nm
that are coherently embedded in an AlN matrix.
The 10
15 RSM shows appreciable changes of the structural parameters upon annealing that clearly indicate local
atomic re-arrangement or atomic species diffusion. The next
step was to perform resonant X-ray diffraction experiments
to quantify the structural change of the samples at the nanoscale, with a special attention to the determination of the
amount of intermixing.
IV. RESONANT X-RAY DIFFRACTION
A. Diffraction anomalous fine structure
Multiwavelength anomalous diffraction, including diffraction anomalous fine structure, is based on resonant
photon-atom interaction, or anomalous effect, that takes
place when the photon energy is tuned across an X-ray
absorption edge. By fitting the DAFS spectrum cusp to the
MAD formula, one can determine the modulus of the partial
structure factor (Thomson scattering) of the anomalous (resonant) atoms, jFA j, of the total structure factor (excluding the
resonant scattering of A atoms), jFT j, and the phase difference uT uA , where uT (respectively, uA ) is the phase of
FT (respectively, FA). In the case of a binary alloy or if one
can assume a known crystallographic structure, the atomic
composition can be determined in iso-strain region selected
by the diffraction condition. Also, DAFS cusp fitting provides the scale factor and crystallographic phase shift for fitting the extended DAFS oscillations (see Sec. IV B).
The scattered intensity from the crystal structure can be
written by separating the resonant terms from the anomalous
atoms A
J. Appl. Phys. 113, 034311 (2013)
f 0 þ if 00 2
IðQ; EÞ / FF ¼ FT þ FA A 0 A ;
f
(1)
A
h
where Q is the scattering vector, Q ¼ 2p 2 sin
k , E the photon
0
energy, fA the Thomson atomic scattering factor, fA0 (respectively, fA00 ) the real (respectively, imaginary) parts of the resonant scattering factor (anomalous terms). In Eq. (1), the
Thomson scattering factors are calculated by Waasmaier and
Kirfel method.55 In practice, prior to the DAFS experiment,
fA00 were obtained from a fluorescence measurement20
recorded close to the 1122 reflection to keep the measurement geometry as close as possible to the diffraction one. fA0
values are calculated using a difference Kramers-Kronig
transform with the DIFFKK code.10 fA0 and fA00 are shown in
Fig. 3 and depend both on the environment of the resonant
atom and on the polarization of the incoming X-ray beam.
This anisotropy of anomalous scattering12,19,36,37,52 must be
taken into account when analysing diffraction data.
The MAD equation,18 giving the scattered intensity as a
function of the photon energy for a given scattering vector
Q, can be written as
h
2
IðQ; EÞ / jFT j2 cosðuT uA Þ þ bfA0 ðEÞ
2 i
þ sinðuT uA Þ þ bfA00 ðEÞ ;
(2)
Aj
where b ¼ f jF
0 jF j.
T
A
We measured DAFS spectra at energies close to the Gallium K-edge (A ¼ Ga) at two different points of the reciprocal space given by the Miller indexes: H ¼ K ¼ 0.98,
L ¼ 1.92 and H ¼ K ¼ 0.98, L ¼ 1.96 (see Fig. 4(a)).
These two diffraction conditions correspond to two different iso-strain regions that we call 4% and 2%. The labels
4% and 2% refer to the mismatch strain value along the cAlN
axis with respect to relaxed AlN (ezz ¼ cc
cAlN ). Energy scans
were performed across the Ga K-edge (10 367 eV), in a wide
energy range of about 800 eV, with an energy step size of
1
1 eV before the edge and 0.06 Å in the k-space of the
FIG. 3. Anomalous terms of the atomic scattering factor f 0 (blue curve) and
f 00 (black curve) for the A ¼ Ga atoms at energies close to the Ga K-edge,
obtained from a fluorescence spectrum (see text). f 0 is calculated from f 00
using a difference Kramers-Kronig method.
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034311-5
Leclere et al.
J. Appl. Phys. 113, 034311 (2013)
FIG. 5. Energy scan across the Ga K-edge (10 367 eV) at fixed (H ¼ 0.98,
K ¼ 0.98, L ¼ 1.92) (zz ¼ 4%) and (H ¼ 0.98, K ¼ 0.98, L ¼ 1.96)
(zz ¼ 2%) positions in the reciprocal space. Both experimental (open symbols) and best fit curves (solid lines) are shown for sample A as grown (open
circle) and annealed at 1500 C (open square). The best fit parameters are
reported in Table I.
FIG. 4. (a) 1122 RSM of sample A, as grown, indexed with H, K, and L referring to relaxed AlN. (b) Linear L-scan (vertical black arrow) at H ¼ 0.98
for as grown (black), annealed at 1500 C (red) and 1700 C samples. The
red segments show the region of interest (ROI) of the linear detector used
for L-scans and DAFS spectra measurement (Fig. 5). The DAFS curves in
Fig. 5 correspond to the diffracted intensity integrated along the two red segments centred at H ¼ K ¼ 0.98, L ¼ 1.92, and H ¼ K ¼ 0.98, L ¼ 1.96.
virtual photoelectron above the edge, keeping Q fixed as a
function of the energy. The background intensity was monitored in order to correct the data for the fluorescence and diffuse scattering signals. For each Q value, five energy scans
were recorded and averaged out.
Fitting of background-subtracted DAFS spectra (Fig. 5)
with Eq. (2) was performed by assuming a wurtzite structure
of space group symmetry P63 mc. Each metallic atom position was filled by gallium and aluminium atoms with a variable population xGa and ð1 xGa Þ, respectively. Only
geometrical parameters (a scale factor, a linear dependence
as a function of the energy to take into account the detector
efficiency) and xGa were fitted. Absorption correction was in
practice negligible. Best fits (solid lines) are shown in Fig. 5
together with the experimental curves and best fit results are
reported in Table I. They were obtained with a metal-polar
crystallographic structure, consistent with the Ga-polar orientation of GaN QDs grown on the Al-polar commercial
substrate. In Table I, one can see that the structural parameter b, uT uA and consequently the amount of Gallium
(xGa) do not change at a nanometer scale after the annealing
at 1500 C. However, a change of superlattice intensities is
observed in 1015 RSM, as shown in previous section. The
reason for such a discrepancy can be seen in Fig. 4(b): There
is barely no shift of the superlattice intensity envelope after
the annealing. This suggests that 1122 RSM lacks the spatial
resolution and chemical sensitivity to show the small structural changes which take place at the nanometer scale close
to the GaN QDs and AlN barrier interface, in comparison
with 1015 RSM. In other words, 1122 RSMs combined with
MAD cannot easily distinguish case (a) where the Ga and Al
atoms are well separated from case (b) where a moderate
atomic diffusion took place due to annealing, leading to
mixed Ga and Al atoms close to the interface. Then, to get
further insight at the atomic scale, we analysed of the
extended-DAFS oscillations which show up on the diffracted
intensity after the Ga K-edge, as shown in next section.
B. Extended diffraction anomalous fine structure
(EDAFS)
EDAFS is the oscillatory contribution to the diffracted
intensity signal which shows up above the edge spanning
over a wide energy range of hundreds of eV. Its origin is
TABLE I. Crystallographic phase difference u0 uA and scale factor SD obtained by fitting the cusps of DAFS spectra to Eq. (2). The Gallium content xGa
was obtained by assuming a perfect wurtzite structure.
Sample
Sample A as grown
Sample B as grown
Sample A at 1500 C
Sample B at 1500 C
h,k,l
Isostrained Region
(%)
b
u T uA
(rad)
xGa
(%)
u0 uA
(rad)
SD
0.98, 0.98, 1.92
0.98, 0.98, 1.96
4
2
0.05258
0.04272
0.130
0.159
106.062
65.262
0.0672
0.0696
2.79
3.44
0.98, 0.98, 1.92
4
0.05185
0.133
102.062
0.0673
2.83
0.98, 0.98, 1.96
2
0.04193
0.175
62.762
0.0698
3.50
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034311-6
Leclere et al.
J. Appl. Phys. 113, 034311 (2013)
analogous to extended absorption fine structure (EXAFS)
and has been described in detail.20,38,49,51 EDAFS oscillations contain the same atomic local scale information as
EXAFS since an atomic specie is selected by tuning the photon energy across its X-ray absorption edge (chemical selectivity). In addition, EDAFS provides the spatial and site
selectivity of diffraction. Its analysis is, in principle, more
complicated due to the contribution of both real and imaginary parts of the atomic scattering factor to the diffracted
intensity. Nevertheless, it has been demonstrated that it can
be analysed as EXAFS by fitting the experimental signal to
theoretical phases and amplitudes calculated by XAFS simulation standard codes.10,35 They have to be corrected by a
phase (u0 uA p=2) and amplitude factor (SD), which are
provided by DAFS cusp analysis (see Table I).
This approach has been already used successfully for
several semiconductors systems both with 2D morphologies
as heterostructures and thin epilayers and for self-assembled
nanostructures (QDs, quantum wells, nanowires, nanoislands).13,21,25,31,41,44,46,57 The great advantage of this
method is that it provides information on the very local
structure of the sample region selected by diffraction. Furthermore, the chemical selectivity of DAFS avoids the interference from nearby regions belonging to substrate or
capping layers even if these regions have, due to mismatch
strain, the same lattice parameter and thus contribute to diffraction at the same point of reciprocal space. One wants, in
this case, to determine composition at a local scale to investigate the diffusion mechanism of Al in the GaN QDs upon
annealing.
In the extended region above the edge, the anomalous
atomic scattering factor can be splitted into smooth and oscil0
00 0
00
00 00
þ Df0A
vj and fj00 ¼ f0A
þ Df0A
vj , where
latory parts: fj0 ¼ f0A
0
00
f0A þ if0A is the anomalous scattering of bare neutral atoms
00
00
is the contribution of the resonant scattering to f0A
.
and Df0A
The smooth atomic scattering factor writes f0A ðQ; EÞ ¼ fA0
0
00
þ f0A
þ if0A
. The real and imaginary components of the
complex extended diffraction anomalous fine structure
~
v ¼ v0j þ iv00j , are related by the Kramers-Kronig transforms
and the imaginary component v00j is related to EXAFS vj by
the following equation: vj ðEÞ ¼ Im~v ðQ ¼ 0; EÞ.
The diffracted intensity, to the first order in v0j ; v00j , writes
I ¼ FF I0 þ 2
00
Df0A
jFA jjF0 j
vQ ;
fA0
correspond to the orthogonal projection in the complex plane
of v0j ; v00j onto the total structure factor F0.40 If one averages
over all the photoelectron scattering paths of the same kind a
simple parametric expression for vQ is obtained
X
2 2
vQ ðkÞ ¼
Ac ðkÞe2k rc
c
p
sin 2khRic þ uc ðkÞ þ u0 ðkÞ uA ;
2
(4)
where k is the wavevector of the virtual photoelectron, hRic is
the average effective length of path c, and rc the bond-length
disorder (static and dynamic Debye-Waller factors).
The background subtracted oscillatory contributions of
the DAFS spectra, vQ , are shown in Fig. 6. Experimental
spectra of 4% and 2% regions are compared with each other
before and after annealing at 1500 C. No appreciable
change shows up for the 4% region. The spectrum of the 2%
region shows instead a change in shape upon annealing that
must be related to a local structural change of the Ga
environment.
EDAFS analysis has been carried out using FEFF8 code2
to generate theoretical phases and amplitudes for a 6 Å radius
GaN cluster taking into account beam polarization. In order
to account for interdiffusion of Al atoms in the QDs, Ga-Al
scattering paths were considered by calculating phase and
amplitudes for the same cluster where all the Ga atoms,
except the central absorber, were replaced by Al atoms. The
Ga-Ga and Ga-Al scattering paths are combined linearly
with a weight factor x that corresponds to the Al concentration. The ARTEMIS interface to the IFEFFIT package42 was used
to fit theoretical computations to the experimental data. The
best fit curves are shown in Fig. 6 as solid curves and the fit
results are summarized in Table II.
Fits were performed in k-space in the range (2–8 Å1 ).
The best fit parameters were: first neighbors Ga-N distances,
second neighbors Ga-Ga and Ga-Al distances, Debye-Waller
factors, energy origin of the virtual photoelectron and, most
important, the Al atoms fraction, 1 xGa , of the second shell
Ga absorber environment, that represents composition at local
scale. We did not include triangular MS paths including Ga,
(3)
where F0 ¼ jF0 jeiu0 and vQ is the first order extended DAFS
vQ ¼ SD
NA
X
I I0
¼ cosðu0 uA Þ
w0j v0j
I0
j¼1
þ sinðu0 uA Þ
NA
X
w00j v00j ;
j¼1
where SD plays as a normalization factor and u0 uA , as
a phase factor that can be obtained by fitting the smooth
DAFS background at the edge. The sum is in this case over
all the Ga sites j. w0j and w00j are crystallographic weights that
FIG. 6. Extended-DAFS oscillations extracted out of DAFS spectra of
sample A as grown (open circle) and annealed at 1500 C (open square),
measured at fixed (H, K, L) reciprocal space units, i.e., (0.98, 0.98, 1.92) and
(0.98, 0.98, 1.96), to which correspond 4% and 2% iso-strained regions,
together with the best-fit curves (solid lines).
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034311-7
Leclere et al.
J. Appl. Phys. 113, 034311 (2013)
TABLE II. Sample A. best fit results for interatomic distances of nearest
neighbours (NN) (Ga-N) and next nearest neighbours (NNN)(Ga-Ga and
Ga-Al) and atomic Ga fraction. Debye Waller factors (r2 ), which are not
reported, are equal to 5 103 Å2 for NN pairs and 8 103 Å2 for
NNN pairs, with relative errors of about 20%.
h,k,l
(r.s.u.)
dGaN (Å)
60:02(Å)
a (Å)
60:03(Å)
xGa
(%)
A as grown 2%
A as grown 4%
A at 1500 C 2%
0.98, 0.98,1.96
0.98, 0.98, 1.92
0.98, 0.98,1.96
1.92
1.93
1.94
100
90
60
A at 1500 C 4%
0.98, 0.98, 1.92
1.92
3.12(Ga-Ga)
3.13(Ga-Ga)
3.11(Ga-Ga)
3.11(Ga-Al)
3.13(Ga-Ga)
Sample
90
Al, and N atoms, the contribution of which does not affect the
fit results due to the low signal to noise ratio of the data.
Regarding the values found for interatomic distances, the GaN next neighbors distance is close to the typical value of bulk
GaN, as expected for III-V semiconductors compounds, in
which a bimodal distribution is found for bond lengths that do
not follow the Vegard’s law. Second shell distances are in
agreement, within the experimental errors, with the values
found for composition and obtained by diffraction spectra.
The main results that answer the question about the annealing
effect, are the value of Al concentration. The shape change of
the EDAFS spectrum corresponding to the QDs outer region,
is reproduced by increasing the fraction of Al atoms seen by
the Ga absorbers. This is a direct evidence that Al interdiffusion
at the interface QDs/embedding AlN layers takes place. The
GaN core region instead, is scarcely affected by annealing.
V. TRANSMISSION ELECTRON MICROSCOPY
X-rays diffraction techniques reported above, provide
detailed structural information on the effect of annealing of
superlattices of GaN QDs embedded in AlN. Due to the nature of this probe, the information is obtained through reciprocal space analysis and is averaged on a great number of
QDs. Then, in order to complete this panorama by a more
local and real space technique, high resolution scanning
transmission electron microscopy (HR-STEM) has been performed using an aberration corrected FEI-Titan ultimate
microscopes operated at 200 kV. For this purpose, crosssections of samples A and B, as grown and after annealing at
1500 C and 1700 C have been prepared by mechanical polishing followed by argon ion-milling using a Gatan-PIPS
equipment.
Figure 7(a) shows a HR-STEM image acquired of the asgrown sample B using a high angle annular dark field
(HAADF) detector. Here, the signal is sensitive to Z-contrast
and GaN and AlN appear as bright and dark regions, respectively. It can be seen that the superlattice structure is well
defined, consisting of 3 nm high GaN QDs on a wetting layer,
separated by 6 nm of AlN. Moreover, a correlation of the QDs
along the growth direction is clearly observed. After annealing
at 1500 C (Figure 7(b)), we observe that the columnar organization is preserved. However, the contrast between the matrix
and the QDs is not as strong as in Fig. 7(a), indicating that
interdiffusion has taken place, mainly above the top of the
QDs where brighter grayish zones are visible. In the case of
sample A, the separation between the successive GaN QDs
layers is larger than in sample B and the QDs are uncorrelated,
but interdiffusion also takes place after annealing at 1500 C.
Figure 8, corresponding to a HAADF-STEM image
taken along the ½1010 zone axis, clearly reveals that intermixing occurs above the dots and extends roughly over half
of the spacing between the dots layers (4.5 nm). The fact that
interdiffusion appears stronger above the dots confirms the
suggestion that it is strain-assisted.
Finally, annealing at 1700 C destroys the superlattice
superstructure, as shown in Fig. 9(a). Recrystallisation takes
place and GaN crystallites presenting well-defined facets are
formed. No dislocation or stacking faults appear between the
matrix and the crystallites. Strain maps for the in-plane
(½1120, Fig. 8(b)) and growth direction ([0001]) have been
calculated by performing geometrical phase analysis (GPA)
on the STEM image. As no deformation has been measured
relative to the reference region (AlN matrix), the GaN crystallites are in perfect epitaxy with the AlN regions and therefore fully strained.
VI. PHOTOLUMINESCENCE
The effect of thermal annealing on the optical properties
of the QD superlattices has been examplified by measuring
FIG. 7. HR-STEM HAADF images of
GaN/AlN QDs heterostructure (sample
B), as grown (a) and after annealing at
1500 C (b).
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034311-8
Leclere et al.
J. Appl. Phys. 113, 034311 (2013)
FIG. 10. Photoluminescence spectra at 4 K of as-grown sample A (black
curve) and for three different annealing temperatures: 1110 C (red curve),
1500 C (green curve), and 1700 C (blue curve).
FIG. 8. HR-STEM HAADF images of GaN/AlN QDs heterostructure (sam
ple A) after annealing at 1500 C. The zoom in inset shows that interdiffusion extends roughly over half of the spacing between the dots.
the photo-luminescence (PL) of sample A at cryogenic temperature (4 K), as a function of annealing temperature. A
frequency-doubled continuous argon laser emitting at
244 nm was used as an excitation source. For all measurements, laser power density was approximately 1 W cm2. PL
signal was analyzed by a 46 cm focal length spectrometer
equipped with a 600 grooves cm1 grating and detected by a
liquid nitrogen cooled charge coupled device camera.
Fig. 10 shows the PL spectra of sample A at varying
annealing temperatures. The spectral shapes of the as grown
sample and of the 1110 C annealed sample are very similar,
evidencing that the structural properties of the QDs are not
affected by a 1110 C annealing. It has to be noted that the
PL intensity is larger for the 1110 C annealed sample, which
would correspond to a reduction of point defects due to the
annealing. The sample annealed at 1500 C shows a luminescence which is clearly blue-shifted with respect to the
as-grown sample. While the structural data reported in the
present work do not allow one to be quantitative on the effect
of the QD morphological modifications on the QD transition
energy, the structural data shows that the 1500 C annealed
QDs undergo an effective vertical size reduction as the top of
the GaN QD interdiffuses with the AlN barrier above. This is,
thus, consistent with a blue-shift of the luminescence. In
order to fully account for the spectral shift upon annealing,
one would need to know the exact composition and strain
profiles within the QD, so as to take into account the confinement as well as the quantum confined Stark effect. It also can
be noted that the PL intensity decreases for the 1500 C
annealed sample. This is a clue that the annealing at these
temperatures starts to create non-radiative recombination centers. This view is further confirmed by the PL of the 1700 C
annealed sample which does not show any significant luminescence compared to the other samples. The GaN inclusions
isostrained with the AlN matrix (Fig. 9) do not show any significant luminescence. This can tentatively be attributed to an
increase in non radiative recombination associated with the
presence of point defects, possibly introduced into the GaN
islands during the recrystallization process.
VII. DISCUSSION
The experimental data reported in the present work have
put in evidence a thermally activated interdiffusion in the
GaN/AlN QDs system. First of all, it appears that such interdiffusion is observed in a temperature range far exceeding
the growth temperature of the GaN/AlN system in molecular
beam epitaxy conditions, namely, 730750 C. This result is
consistent with the well documented absence of intermixing
between GaN QDs and AlN barrier grown in usual conditions.3,15,45 In such conditions, it has been demonstrated that
capping of GaN QDs by AlN actually results in the conversion of the upper GaN layer into AlN, which has been
assigned to the stronger Al-N bond with respect to the Ga-N
one in the typical temperature range used for the growth of
GaN QDs superlattices.8 This phenomenon is strictly limited
to one monolayer, ruling out the interdiffusion as its physical
origin. Furthermore, a detailed HRTEM study of the GaN
FIG. 9. (a) HR-STEM HAADF image
after annealing at 1700 C. Well defined
GaN crystallites (bright) are visible in
AlN matrix (dark). (b) Corresponding
strain map from geometrical phase analysis showing that the crystallites are in
perfect epitaxy with the AlN matrix and
therefore fully strained. (c) High resolution image taken along the ½11
20 zone
axis showing Ga-rich islands embedded
in Al-rich matrix.
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034311-9
Leclere et al.
QD/AlN interface profile has shown that about 15% of Ga
and Al atoms appeared to be displaced at the AlN/GaN interfaces of the wetting layer connecting the GaN QDs, a feature
which has been tentatively assigned to interface roughness,
again ruling out the hypothesis of a thermal-induced interdiffusion process.3
The strain state of GaN QDs embedded in AlN has been
theoretically analyzed in the case of isolated23 and vertically
correlated45 planes of dots. In both cases, it has been found
that dots, which have the shape of truncated hexagonal pyramids, are in-plane matched to the AlN substrate while along
the c-axis a strain gradient has been predicted and experimentally measured.23 The strain gradient was found to be
particularly pronounced along the ½1103 facets and in the
upper angles of the truncated pyramid.
Remarkably, data reported in the present work have
established that GaN/AlN interdiffusion is preferentially
occurring on top of the dots and not below them, in spite of
the high degree of compressive strain experienced at the
base of the dots which are matched to the AlN matrix. In
other words, diffusion is found to be related to the tensile
strain state of AlN regions rather than to the compressive
strain state of GaN. Alternatively, it can be argued that interdiffusion is preferentially occurring in regions where the dot/
barrier elastic interplay is maximum, resulting in a simultaneous strain relaxation of both GaN and AlN.
Interdiffusion, which requires atomic displacements,
implies the transitory formation of vacancies and interstitials.
The formation energy of such point defects in AlN and GaN
has been the object of numerous theoretical studies during
the past decade. It has been established that nitrogen vacancy
is the most favorable defect to be found in p-type GaN, while
the Ga vacancy is expected to dominate in n-type GaN.34
The situation is very similar in the case of AlN,17 making
vacancies the dominant defects in III-nitrides. By contrast, in
both systems, interstitials have been found to be less favourable, differing from the situation found in GaAs, Si, or ZnSe.
The high energy formation of interstitials is indeed consistent with the high temperature necessary to trigger interdiffusion between AlN and GaN. We suggest that the strain state
of AlN and GaN at the top of the dots, implies both an
expansion of Al-N bond length and a compression of Ga-N
ones, contributes to reduce the formation energy of Al and
Ga interstitials, respectively. Indeed, it has been theoretically
predicted that defect formation energy should weakly
decrease when applying a hydrostatic pressure.17 This effect
is certainly negligible in the present case, which moreover
drastically differs from the hydrostatic pressure case. However, the formation of Al interstitials in expanded AlN above
the dots is likely to be more favorable, as an additional
option to relax the distorted bond lengths, by contrast to the
situation at the bottom of them where the formation of Al
interstitials in almost relaxed AlN is likely less favorable.
However, results reported in Fig. 9 are a clue that the
formation of an AlGaN alloy does not correspond to the ultimate stability stage. As a matter of fact, the thermal stability
of AlGaN with high Al content, namely, 72%, has been previously investigated by Kuball et al.27 These authors have
demonstrated that above 1150 C the bidimensional layer
J. Appl. Phys. 113, 034311 (2013)
they studied exhibited a tendency to decompose into two
phases; a low-Al containing one and a high-Al containing
one. These data are indeed consistent with the results
reported in Fig. 9(c); the observation, after annealing at
1700 C, of Ga-rich islands perfectly matched to their Alrich surrounding suggests a full thermally induced phase separation in the AlGaN resulting from GaN QD/AlN barrier
interdiffusion.
It has to be noted that the morphological shape of
recrystallized islands, namely, the flat Ga-polar surface and
the m-plane facets parallel to growth direction, is consistent
with the morphology of GaN bulk crystals.32 Then, assuming
that the recrystallization of highly compressed Ga-rich
islands in an Al-rich matrix as observed in Fig. 9(c) corresponds to thermodynamical equilibrium, the observed interdiffusion at lower temperature likely corresponds to the
evolution towards a local energy minimum.
However, at higher temperatures, high enough to trigger
the recrystallization of GaN islands, it is shown that phase
separation is dominating. These results suggest that the
behaviour under annealing of our GaN/AlN system results
from a competition between kinetical effects, namely, the
interdiffusion which contributes to a decrease of the elastic
strain in both AlN and GaN and thermodynamical effects
which tend to demix the AlGaN material, eventually leading
to the formation of Ga-rich islands fully strained by the
surrounding Al-rich matrix.
ACKNOWLEDGMENTS
We thank the French CRG at the ESRF for granting
beam time and for support at beamline BM2-D2AM. We are
very grateful to D. Chaussende for his advices and help for
operating the induction furnace at LMGP. M.G.P. acknowledges the support of Project MAT2001-03074 of Spanish
Ministry of Science and Innovation.
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