Transition from elastic to plastic strain release in core-shell nanowires revealed by in-plane X-ray diffraction

Abstract

We investigate the strain evolution and relaxation process as function of increasing lattice mismatch between the GaAs core and surrounding InxGa1-xAs shell in core-shell nanowire heterostructures grown on Si(111) substrates. The dimensions of the core and shell are kept constant. Measuring the 224 ̅ and 22 ̅0 in-plane Bragg reflections normal to the nanowire side edges and side facets, we observe a transition from elastic to plastic strain release for a shell indium content x > 0.5. Above the onset of plastic strain relaxation, indium rich mounds and an indium poor coherent shell grow simultaneously around the GaAs core. Mound formation was observed for indium contents x = 0.5 and 0.6 by scanning electron microscopy. Considering both the measured radial reflections and the axial 111 Bragg reflection, the 3D strain variation was extracted separately for the core and the InxGa1-xAs shell.

Full text

Transition from elastic to plastic strain
release in core−shell nanowires revealed by
in-plane x-ray diffraction
Ali Al Hassan
1,2
, Waheed A Salehi
1
, Ryan B Lewis
3,4
, Taseer Anjum
1
,
Christian Sternemann
5
, Lutz Geelhaar
4
and Ullrich Pietsch
1
1
Naturwissenschaftlich-Technische Fakultät der Universität Siegen, D-57068 Siegen, Germany
2
Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Hermann-von-
Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
3
Department of Engineering Physics, McMaster University, Hamilton, Ontario L8S 4L7, Canada
4
Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e.V.,
Hausvogteiplatz 5-7, D-10117 Berlin, Germany
5
Fakultät Physik/DELTA, Technische Universität Dortmund, D-44221 Dortmund, Germany
E-mail: ali.hassan@kit.edu
Received 12 November 2020, revised 25 January 2021
Accepted for publication 12 February 2021
Published 26 February 2021
Abstract
We investigate the strain evolution and relaxation process as function of increasing lattice
mismatch between the GaAs core and surrounding In
x
Ga
1−x
As shell in core–shell nanowire
heterostructures grown on Si(111)substrates. The dimensions of the core and shell are kept
constant whereas the indium concentration inside the shell is varied. Measuring the
2
24
¯and
2
20
¯
in-plane Bragg reflections normal to the nanowire side edges and side facets, we observe a
transition from elastic to plastic strain release for a shell indium content x>0.5. Above the
onset of plastic strain relaxation, indium rich mounds and an indium poor coherent shell grow
simultaneously around the GaAs core. Mound formation was observed for indium contents
x=0.5 and 0.6 by scanning electron microscopy. Considering both the measured radial
reflections and the axial 111 Bragg reflection, the 3D strain variation was extracted separately for
the core and the In
x
Ga
1−x
As shell.
Keywords: core−shell nanowires, elastic strain investigation, plastic strain relaxation,
synchrotron radiation, in-plane Bragg x-ray diffraction
(Some figures may appear in colour only in the online journal)
Introduction
Compared to planar heteroepitaxy, the formation of axial or
radial heterostructures in the form of nanowires has opened
up new horizons for the design of heterostructures in a more
efficient and less costly way [1–5]. One of the most beneficial
qualities of core–shell nanowires is surface passivation of the
core by the surrounding shell which can be utilized to
enhance the efficiency of photo-emission because it reduces
non-radiative surface recombination [6,7]and thereby
enhances the opto-electronic properties of the device [8–10].
Strain relaxation in core–shell nanowires has been thor-
oughly investigated in recent years, revealing higher sustain-
ability of elastic strain compared to planar heterostructures
[11,12]. Above a critical lattice mismatch between the core
and shell materials, the misfit strain can relax via the formation
of misfitdislocations[13,14], quantum dots [15,16]and
stress-driven surface roughening [17,18]. The aforementioned
strain relaxation mechanisms within the nanowire core–shell
system strongly depend on the diameter of the core, thickness
of the shell and the lattice mismatch between the core and shell.
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For instance, Treu et al have reported that a 10 nm thick
InAs
0.91
P
0.09
shell grows coherently around an InAs core.
However, an InP shell of the same thickness shows the for-
mation of dislocations [19]. Furthermore, it was revealed that
the photoluminescence emission of this core–shell nanowire
system exacerbates for higher P contents within the shell. This
indeed indicates that the investigation of the strain relaxation
mechanisms and critical composition of core–shell nanowires
are of paramount importance for the fabrication of high per-
formance devices with nanowire heterostructures.
Moreover, a novel strain relaxation process was recently
revealed by Lewis et al 2017 [20]for GaAs nanowire cores
surrounded by In
x
Ga
1−x
As shells. Based on lab x-ray dif-
fraction of the axial 111 Bragg reflection and transmission
electron microscopy measurements, it was demonstrated that
above a critical lattice mismatch, plastically relaxed mounds
form along the nanowire sidewall facets. The relaxed mounds
and a coherent shell grow simultaneously from the beginning
of In
x
Ga
1−x
As deposition such as, driven by strain relief,
incoherent mound growth is increasingly favored for higher
lattice mismatches. Furthermore, it was unveiled that the
mounds are indium rich compared to an indium poor shell.
However, Lewis et al did not measure the radial lattice
parameters preventing 3D strain analysis.
In this work, we complement the above-described mea-
surements by recording reciprocal space maps (RSMs)of the
2
24
¯and
2
20
¯Bragg reflections which are orthogonal to the
nanowire growth axis, and normal to the side edges and side-
facets, respectively from GaAs\In
x
Ga
1−x
As core–shell
nanowires with 20%x60% In. From these diffraction
maps, on the one hand, we confirm the appearance of plastic
strain relaxation for the highest In content of 60%, resulting in
the simultaneous growth of indium rich mounds and an
indium poor In
x
Ga
1−x
As shell, in agreement with [20].
However, the formation of mounds is observed for indium
concentrations of 50% and above by scanning electron
microscopy (SEM). We extend on these findings by calcu-
lating the 3D strain of the GaAs core and In
x
Ga
1−x
As shell at
the edges and side-facets, revealing a strain variation of the
core which reaches its maximum for nanowires with 50% of
indium in the In
x
Ga
1−x
As shell. Notably, for an indium
concentration of 20%, the crystal lattice of the In
x
Ga
1−x
As
shell at the side-facets and edges undergoes 3D compression
whereas the GaAs core expands along and perpendicular to
the growth direction regardless of the lattice mismatch.
Experiment and results
The samples investigated in this work are GaAs/In
x
Ga
1−x
As
core–shell nanowires grown by molecular beam epitaxy using
the Ga-assisted vapor−liquid−solid growth on n-type Si(111)
substrates covered by native oxide. The core diameter and shell
thickness are kept constant at 140 nm and 18 nm respectively
whereas the nominal indium concentration inside the shell is
varied from 20% to 60% with steps of 10% for the five
investigated samples (samples 1–5). A detailed description of
the nanowire growth procedure can be found elsewhere [20].
SEM micrographs of nanowires from samples 1–5 are dis-
played in figure 1. The nanowires from samples 1–3displaya
smooth surface whereas nanowires from samples 4–5show
exterior presence of mounds. However, the number density and
relative size of the mounds is smaller for sample 4 (discussed
later).
The x-ray diffraction measurements were carried out on
as-grown nanowire ensembles at beamline BL9 [21]of the
DELTA synchrotron (Dortmund, Germany)with 1 mm
2
beam and photon energy of 13 keV. To access the radial strain
normal to the side facets and edges of the core and shell,
rocking scans were performed in the vicinities of the
2
24
¯and
2
20
¯in-plane Bragg reflections collecting the scattered inten-
sity distribution using a two dimensional 100 k Pilatus
detector placed 1 meter away from the sample. The experi-
ment was executed in grazing incidence geometry where the
angle of the incident beam with respect to the substrate sur-
face was set to zero and the diffracted intensities of the
2
24
¯
and
2
20
¯Bragg reflections were measured in the plane
perpendicular to the surface normal at Bragg angles at around
Figure 1. Panels (a)−(e)show SEM images of nanowires from samples 1−5, respectively. The scale bar in (a)is 1 μm and applies to all SEM
images.
2
Nanotechnology 32 (2021)205705 A Al Hassan et al

27.6°and 48.80°, respectively. The 2D intensity frames col-
lected at each rocking angle were integrated to compose 2D
RSMs of the respective Bragg reflections. More information
about the diffraction setup, and equations used to translate
from real space angular coordinates into reciprocal space
vectors can be found in [22]. From the width of a Si
2
20
¯
substrate reflection measured at the same beamline under
identical conditions (same beam energy, detector, sample to
detector distance and beam size)an angular resolution of
about 0.05°can be inferred.
RSMs of the
2
24
¯and
2
20
¯reflections are displayed in
panels (a)–(e)and (f)–(j)of figure 2, respectively, ranging
from samples 1 to 5 (from left to right). Reciprocal space
vectors
Q
z
224
¯and
Q
z
220
¯are defined along the scattering
direction of the measured planes in reciprocal space. In other
words,
Q
z
224
¯and
Q
z
220
¯are sensitive to the variation in the
spacing of the respective lattice planes. Reciprocal space
vectors
Q
xx
224
¯and
Q
xx
220
¯are defined along [
2
20
¯]and [
2
24
¯]
respectively, and are sensitive to the nanowire tilt along the
corresponding directions.
The scattering peaks, named A-E, in the RSMs of
figures 2(b)and (g)can be explained by the strain impact on
the lattice planes of different sections of the core–shell
nanowire system [22–24]. For better clarity, a schematic
correlation between the respective RSMs recorded for sample
2, and sketches of the core–shell nanowire cross-section
overlapped by the
2
24
¯and
2
20
¯lattice planes are illustrated in
figures 3(a)and (b). Peak A in the
2
24
¯RSMs originates from
the
2
24
¯lattice planes of the GaAs core and the In
x
Ga
1−x
As
side facets that are aligned vertically onto the side walls of the
core in figure 3(a). The two sub-peaks B, indicated by red
arrows at lower
Q
z
224
¯values, make an angle of 30°with [
2
24
¯]
and therefore originate from the
2
24
¯lattice planes of the
neighboring In
x
Ga
1−x
As side facets. The slight asymmetry in
the intensity of the split peaks B for samples 2–4
(figures 2(b)–(d)), clearly seen in figure 3(a)for sample 2,
Figure 2. Panels (a)–(e)and (f)–(j)show RSMs of the
2
24
¯and
2
20
¯Bragg reflections for samples 1–5 respectively. All maps are plotted using
the same color scale. The nominal indium concentration of each sample is mentioned on top of the each panel. Peaks A-E and M are
explained in text.
Figure 3. (a)and (b)Top rows show sketches of the core–shell
nanowire cross-section oriented along
Q
z
224
¯and
Q
,
z
220
¯illustrating the
lattice planes of the respective reflections. RSMs of the
2
24
¯and
2
20
¯
Bragg reflections of sample 2 are displayed in the bottom row. Peaks
A-E are explained in text.
3
Nanotechnology 32 (2021)205705 A Al Hassan et al

where the peak on the right is more intense than the left one,
can be attributed to the asymmetry of the (In,Ga)As shell i.e.
the opposing side facets of the shell contributing to the right
diffraction peak are thicker than the opposing side facets
contributing to the left diffraction peak. This slight asym-
metry can, in turn, result in a small nanowire bending which
is responsible for the slanting of peak A for samples 2–4. The
inhomogeneity of the shell may originate from the geometry
of the evaporation sources with respect to the substrate in the
growth chamber. Interestingly for sample 5, an additional
sub-peak, labelled by M, is visible at low
Q
z
224
¯values (see
figure 2(e)), presumably originating from the In
x
Ga
1−x
As
mounds (see figure 1(e)). The same is expected for sample 4,
as will be extended on later, but it is not visible due to the
smaller scanning range (figure 2(d)). We attribute peak C in
the
2
20
¯RSMs to Bragg diffraction from the
2
20
¯lattice planes
of the GaAs core. Sub-peaks D, making an angle of about 60°
with [
2
20
¯], are explained by diffraction from the
2
20
¯lattice
planes of neighboring In
x
Ga
1−x
As side facets. Peak E, indi-
cated by a red circle in figure 3(b), belongs to the
2
20
¯lattice
planes of the measured couple of In
x
Ga
1−x
As opposite side
facets that are aligned horizontally with the GaAs core.
Qualitatively, the central peaks appearing at
Q
z
224
¯
=54.5 nm
−1
and
Q
z
220
¯
=31.5 nm
−1
broaden along
Q
zand
Q
x
for increasing nominal indium concentration in the
In
x
Ga
1−x
As shell. The broadening along Q
z
reflects the higher
strain variation that the core undergoes whereas the broad-
ening along Q
x
resembles a higher angular tilt of the nano-
wires with respect to the substrate normal as the core–shell
lattice mismatch increases. The broadest peak is observed for
nanowires with 50% of nominal indium content. This is the
transition point from elastic deformation to plastic strain
relaxation via the formation of In
x
Ga
1−x
As aggregates found
by [20].
To estimate the strain variation in the core, the radial
2
24
¯
and
2
20
¯lattice constants and indium content of the
In
x
Ga
1−x
As shell, we integrate the
2
24
¯and
2
20
¯Bragg
reflections along Q
x
and fit the resulting Q
z
line profiles,
displayed in figure 4with multi-Gaussians.
The red dashed lines at
Q
z
224
¯
=54.5 nm
−1
and
Q
z
220
¯
=
31.5 nm
−1
in figure 4indicate the positions of the respective
unstrained lattice planes for GaAs. The cut vertical orange lines
represent the positions of unstrained
2
24
¯and
2
20
¯In
x
Ga
1−x
As
lattice planes for the nominal indium concentration of the sample.
The red curves represent peaks B and E in
2
24
¯and
2
20
¯
respectively. The most intense peaks in
2
24
¯and
2
20
¯are peaks A
and C. Their broadening originates from the strain variation
acting on the respective lattice planes of the GaAs core for peak
C, and from the
2
20
¯lattice planes of the core and the In
x
Ga
1−x
As
facets which are aligned vertically on the sides of the core (see
figure 3(a)) for peak A. Representing the lower and upper edges
of this variation by the green and blue Gaussians, the strain
variation can be calculated from the difference between these two
peaks. The values of the strain variation calculated accordingly
for the GaAs core for samples 1–5arelistedintable1. The pink
Gaussian peak along [
2
20
¯]represents sub-peaks D. Con-
ventionally, the Bragg peak of the substrate, supposed to be
unstrained, is used as a reference to calculate the absolute strain
in the nanowires. However, due to the absence of the Si peak in
the in-plane diffraction pattern, we set the right edge of the core
peak (colored in green in figure 4)to the position of unstrained
GaAs for both
2
24
¯and
2
20.
¯All other peaks have been shifted
subsequently. This is an approximation because the GaAs core is
affected by a small tensile strain induced by the surrounding shell
Figure 4. (a)and (b)show waterfall intensity integrations of the
2
24
¯and
2
20
¯RSMs in figure 2. The red dashed lines at
Q
z
224
¯
=54.5 nm
−1
and
Q
z
220
¯
=31.5 nm
−1
indicate the positions of unstrained GaAs. The cut vertical orange lines represent the positions of unstrained
2
24
¯and
2
20
¯In
x
Ga
1−x
As for the nominal indium concentration of the sample. The colored Gaussian fits are explained in text.
4
Nanotechnology 32 (2021)205705 A Al Hassan et al

which results in a tiny shift towards lower Q
z
values. However,
this effect is neglected. The In
x
Ga
1−x
As shell of the nanowires in
sample1iscompressedastheredpeakiscenteredatahigher
Q
z
224
¯value compared to the unstrained position assuming the
nominal In content, which is indicated by a vertical cut line. For
samples 2 (30% In)and 3 (40% In), the red Gaussian is almost
centered at the
Q
z
224
¯values of unstrained In
0.3
Ga
0.7
As and
In
0.4
Ga
0.6
As which leads to two possible explanations. The first
is that the In
x
Ga
1−x
As shell is fully relaxed whereas the second is
that the In
x
Ga
1−x
As shell is strained, but the tetragonal distortion
is at an angle, so the compression and expansion mostly cancel
out resulting in an average peak that is found at the unstrained
Q
.
z
224
¯However, the
2
20
¯Bragg reflection of the In
x
Ga
1−x
As shell
being visible at lower
Q
z
220
¯with respect to the unstrained value
(peak E)indicates that the In
x
Ga
1−x
As lattice, in agreement with
[20], is indeed strained and therefore negates the first explanation.
For sample 5 (60% of indium), two peaks colored in red and
cyan are visible along
2
24
¯and
2
20.
¯The cyan peaks are at lower
Q
z
224
¯and
Q
z
220
¯values compared to the unstrained position
whereas the red Gaussians are at higher ones. This indicates that
the In
x
Ga
1−x
As shell is indeed formed of two volumes with
different indium concentrations higher and lower than 60%. As
the nanowires of samples 4 and 5 show the formation of mounds
at the nanowire surface (see figures 1(d)and (e)),In
x
Ga
1−x
As of
sample 4 would be expected to be represented by two Bragg
peaks, similar to sample 5. However, the relatively lower number
density and smaller size of the In
x
Ga
1−x
As mounds of sample 4
(figure 1(d)) compared to those of sample 5 (figure 1(e)) indicate
the early stage of mound formation and thereby the smaller
impact the mounds have on the In
x
Ga
1−x
As shell. This will be
expanded on in the discussion part.
The percentage lattice difference of the strained (In,Ga)As
shell, mounds and GaAs core with respect to unstrained GaAs
along [
2
24
¯](
D
b%
zz
224 ()
¯)and [
2
20
¯](
D
a%
zz
220 (
)
¯)can be cal-
culated from the peak positions extracted from the Gaussian
curves (red and cyan for the (In,Ga)As shell and mounds,
respectively; blue for the GaAs core)using the equation below,
D==D =
=´
-
bfhkl afhklor 224 or 220
100, 1
zz
hkl
zz
hkl
QQ
Q
hkl hkl
hkl
exp 0,GaAs
0,Ga As
(¯)( ¯)
()
where
Q
hkl
0,GaAs is the position of unstrained GaAs along the
respective [hkl]direction in Q
z
and
Q
hkl
exp is the experimental
peak positions of the Gaussian curves. The results are plotted in
figures 5(a)and (b).
The strain variation of the GaAs core is calculated from
the blue curves using equation (1)since the green curves are
already shifted to the position of unstrained GaAs (
e
z
224
¯=
e
z
220
¯
=0), and the strain acting on the In
x
Ga
1−x
As shell and
mounds was calculated from the red and cyan curves repla-
cing
Q
hkl
0,GaAs by -
Q
hkl
0,In Ga As
xx1which is the position of
unstrained In
x
Ga
1−x
As along the respective [hkl]direction in
Q
z
. The numerical strain values are listed in table 1and
plotted in figures 5(c)and (d).
The colors of the data points in figure 5are correlated
with those of the Gaussian fits in figure 4. As the green curves
and cut orange lines in figure 4were attributed to unstrained
GaAs and In
x
Ga
1−x
As, the respective inplane strain values
being zero were represented by horizontally stitched green
and orange lines at
e
z
224
¯=
e
z
220
¯
=0(figures 5(c)and (d)).On
the one hand, looking at the separation between the blue data
points and green lines, the strain variation in the core reaches
a maximum of 1.02±0.29% and 0.96±0.21% along
2
24
¯
and
2
20
¯for the sample with 50% of indium content before
decreasing down to 0.44±0.34% and 0.37±0.23% for the
sample with 60% of indium. The values of the strain variation
for samples 1–5 are listed in table 1. On the other hand, the
strain acting on In
x
Ga
1−x
As is represented by the separation
between the red data points and the cut orange lines (figures 4
and 5). The red data points of samples 2–4 being centered at
positive
e
z
220
¯values (figure 5(d)) compared to
e
z
224
¯reveal that
the
2
20
¯lattice planes of the In
x
Ga
1−x
As shell undergo higher
expansion compared to the
2
24
¯lattice planes resulting from
the compression along [111]. A similar higher lattice expan-
sion along [
2
20
¯]has been observed by Balaghi et al 2019 [25]
for the GaAs cores when surrounded by thicker In
x
Ga
1−x
As
shells. Interestingly, for sample 1, the In
x
Ga
1−x
As shell is
compressed in all directions. For sample 5, the cyan and red
data points at higher and lower values compared to
e
z
224
¯=
e
z
220
¯
=0(see figures 4and 5)are both associated with
In
x
Ga
1−x
As. The first originates from an In
x
Ga
1−x
As volume
with an indium concentration higher than 60% whereas the
second shows a lower indium content. The TEM data for this
Table 1. Strain values along [
2
24
¯]and [
2
20
¯]for the GaAs core (calculated with respect to unstrained GaAs from the blue curves using
equation (1)) and the In
x
Ga
1−x
As shell and mounds (calculated with respect to unstrained In
x
G
1−x
aAs from the red and cyan curves using
equation (1), and plotted in figure 5. The strain values along [111]are taken from [20].
e
zz
224
¯(%)
e
zz
220
¯(%)
e
zz
111 (%)
In Blue–Green Red Blue–Green Red
20% 0.10±0.10 −0.62±0.92 0.05±0.12 −0.45±2.03 0.45
30% 0.55±0.63 −0.03±1.13 0.42±0.25 0.55±0.97 0.70
40% 0.44±0.38 −0.30±0.72 0.48±0.28 0.44±1.02 0.96
50% 1.02±0.29 −0.01±0.81 0.96±0.21 0.57±1.78 0.74
60% 0.44±0.34 0.96±1.22 (mounds)0.37±0.23 0.93±1.07 (mounds)0.46
−1.00±0.83 (shell)−0.63±3.71 (shell)
5
Nanotechnology 32 (2021)205705 A Al Hassan et al

sample from Lewis et al indicated that the mounds are indium
rich whereas the In
x
Ga
1−x
As shell, coherent to the core, is
indium poor. The error bars were calculated taking into
consideration the FWHM of the Gaussians as an input for
equation (1).
To get a better understanding of the 3D strain behavior in
the core and shell, we performed FEM simulations using a
single nanowire model composed of a 140 nm thick GaAs
core (blue colored volume in figure 6(a)) and 18 nm
In
x
Ga
1−x
As shell with indium concentration of 30% (colored
in red). More details about the numerical input, meshing
procedure (figure 6(b)) and calculation scheme can be found
in the FEM section of [24]. Iso-surface slices of the axial
strain are demonstrated in figure 6(c)where apart from the
upper section of the nanowire model, the core and shell share
the same lattice parameter. Line profiles of the strain com-
ponents
e
220
¯and
e
224
¯(see figure 3for orientation)extracted
through one pair of opposite side facets and edges are dis-
played in the panels (d)and (e)of figure 6, respectively. In
confirmation to our assumption, the In
x
Ga
1−x
As shell shows
lattice expansion larger than the expected nominal lattice
mismatch, as a result of the compression along the [111]
direction. Interestingly, the inner section of the GaAs core
shows slight expansion along [111],[
2
20
¯]and [
2
24
¯], faced by
compression as one approaches the core–shell interface. For
instance, for the nanowire model with 30% nominal indium
concentration, the inner volume of the GaAs core undergoes a
lattice expansion of 0.15% along [
2
20
¯]and a maximum lattice
compression of −0.20% at the core–shell interface, forming a
strain variation of 0.35%. This is in agreement with the strain
variation deduced experimentally from the difference between
the green and blue Gaussian peaks of 0.41%. This
experimental value might be overestimated because of nor-
malization of the GaAs peak (see above).
Discussion
The investigation of the strain behavior in nanowire hetero-
structures is essential for tuning the opto-electronic perfor-
mance of the device. For instance, the strain induced by
growing an In
x
Ga
1−x
As shell onto one side of a mismatched
GaAs core has been utilized to control the bending radius of
the nanowire [26]which would enable the realization of a
complex spatially varying strain field opening up new pos-
sibilities for elastic strain and band structure engineering
where the latter can be exploited to control the motion of
charge carriers within the nanowire [26–28]and therefore
tune its optical properties [29]. Moreover, GaAs nanowire
cores exhibit reduction of their bandgap by up to 40% when
overgrown with lattice-mismatched thick In
x
Ga
1−x
As
shells [25].
Nevertheless, for high lattice mismatches (indium content
50% and above),In
x
Ga
1−x
As deposition around a thick GaAs
core results in the simultaneous growth of an indium poor
coherent shell and indium rich In
x
Ga
1−x
As mounds [20]
(figures 1(d)and (e)). In the present work, this finding is
confirmed by the presence of two In
x
Ga
1−x
As diffraction
peaks along [
2
24
¯]and [
2
20
¯]for sample 5 (red peak for the
coherent shell and cyan peak for the mounds in figures 4and
5). The lattice spacing of the mounds calculates to 5.9537
A

corresponding to a mismatch of »5.3% which is above the
theoretical lattice mismatch considering 60% of indium by
1%. This reflects that the mounds are indeed indium rich
compared to the In
x
Ga
1−x
As shell. The average indium
Figure 5. (a)and (b)display the percentage lattice difference of the strained shell, mounds and GaAs core with respect to unstrained GaAs
along [
2
24
¯](Db%
zz
224 ()
¯)and [
2
20
¯](Da%
zz
220 (
)
¯). The spacing between the red dots and the orange cut lines represent the strain acting on the
In
x
Ga
1−x
As shell as explained in the text below figure 4. The blue and green data points represent the right and left edges of the diffraction
peak which originates from the core (figure 4). The cyan data points represent the In
x
Ga
1−x
As mounds for 60% of indium. The strain
variation of the core and the strain acting on the In
x
Ga
1−x
As shell and mounds along [
2
24
¯]and [
2
20
¯]are plotted in panels (c)and (d).
6
Nanotechnology 32 (2021)205705 A Al Hassan et al

concentration extracted from the cyan diffraction peaks in
2
24
¯
and
2
20
¯using Vegard’s law is around 75%, which is reported
to reach up to 80% in [20]. The indium enrichment of the
mounds coincides with an indium depletion of the neigh-
boring shell regions. The red Bragg peaks representing the
coherent In
x
Ga
1−x
As shell translates into a mean indium
concentration of 45%. However, the homogeneity of the
indium distribution within the mounds depends on how
indium diffuses from the shell into the mounds. In contrast to
sample 5, sample 4 showed only one diffraction peak attrib-
uted to the shell and centered at the position corresponding to
50% of indium. This could be due to the short scan range in
reciprocal space. However, an additional peak would be
expected to be relatively less intense compared to that of
sample 5. This could be attributed to the early stage of mound
formation resembled by the relatively low number density and
small size of the mounds (figure 1(d)) compared to those of
sample 5 (figure 1(e)). Indeed, Lewis et al measured the
intensity of the relaxed In
x
Ga
1−x
As signal from the 111 Bragg
reflection, demonstrating a constant value for 20%–40% of
indium (attributed to parasitic growth on the substrate)and
then an increase in the integrated intensity from 50%. The
intensity between 50% and 60% doubles, reflecting the
increasing mound volume with increasing In content.
The GaAs core undergoes a strain inhomogeneity,
induced by the surrounding In
x
Ga
1−x
As shell, reflected by the
broadening of its Bragg reflection along the scattering direc-
tions,
Q
z
224
¯and
Q
.
z
220
¯As the indium content within the
In
x
Ga
1−x
As shell increases from 20% to 50% (increasing
lattice mismatch with constant core and shell dimensions), the
strain variation acting on the core increases from
(0.10±0.10%)to (1.02±0.29%)along [
2
24
¯]and from
(0.05±0.12%)to (0.96±0.21%)along [
2
20
¯]. Interestingly,
as the nominal indium content increases to 60% (Sample 5),
the GaAs core relaxes as the strain variation drops down to
(0.44±0.34%)along [
2
24
¯]and to (0.37±0.23%)along
[
2
20
¯]. Absolute strain reduction has been observed axially for
Figure 6. (a)–(c)show the core–shell configuration of the nanowire model, the mesh used and the slices of the axial strain along the nanowire
axis, respectively. Panels (d)and (e)are line profiles of the strain components
e
220
¯and
e
224
¯extracted through the side facets and edges for
samples 1–3, respectively.
7
Nanotechnology 32 (2021)205705 A Al Hassan et al

the GaAs core in [20], and can be explained by the favored
growth of the mounds rather than a coherent shell for an
increasing core–shell lattice mismatch. The thinner the shell
is, the less is the amount of strain induced on the core.
The In
x
Ga
1−x
As shell at the side-facet acts as a thin layer
deposited on top of a GaAs substrate, which compresses
along [111]and [
2
24
¯](
c
band
111 In,Ga As
220
()
¯)to match the in-
plane lattice spacing of the GaAs core (
c
band
111 GaA
s
220
¯). This
biaxial compression translates into expansion of In
x
Ga
1−x
As
along [
2
20
¯](
a
aIn, G As
220
()
¯). This, indeed, has been experimentally
validated and illustrated in figure 5(red data points). How-
ever, for the nominal indium concentration of 20% (sample
2), the In
x
Ga
1−x
As shell seems to exhibit hydrostatic or tri-
axial lattice compression, which is not understood. The
complete opposite is expected for the GaAs core, which is
supposed to undergo only slight expansion, due to its much
larger volume, which increases when approaching the hetero-
interface. Moreover, supported by the FEM simulations in
figure 6, the GaAs core is expected to expand in all directions,
being pulled apart by the surrounding lattice mismatched
shell. Indeed, the GaAs core is simultaneously expanded
axially and radially near the hetero-interface at the side-facets
(blue data points in figure 5). Similar behavior has been
reported before for thin GaAs cores surrounded by a relatively
thick In
x
Ga
1−x
As shell [25].
Hetero-epitaxy of strained layers gives access to strain
engineering. However, radiative recombination takes place at
defect free strained layers only. Plastic strain relaxation asso-
ciated with the formation of dislocations and other defects
creates sources for non-radiative recombination of charge car-
riers [30]and reduce the luminescence intensity [31]. Con-
sidering Stranski-Krastanov growth mode known for lateral
hetero-structures, there is a critical thickness beyond which
misfit dislocations are created acting as non-radiative centers
within the complete layer. In this study we demonstrate that in
the case of GaAs/(In,Ga)As radial nanowire hetero-structures
there exists also a critical indium concentration which changes
the epitaxial growth. However, it is shown that a part of the
shell remains coherently strained without dislocations where
the strain is released through the formation of In rich mounds at
the edges of the shell side-facets [20]. In consequence it means
that the strained part still can provide radiative recombination
as functional element of a respective optical device.
Conclusions
In summary, sharing the same lattice parameter axially, the
GaAs core and the In
x
Ga
1−x
As shell have different radial
lattice spacings. This makes measuring in-plane Bragg
reflections by XRD, namely
2
20
¯and
2
24
¯which are normal to
the nanowire side-facets and edges, the perfect technique to
perform a detailed investigation of the 3D strain behavior and
variation in the core and the shell separately. Accordingly, we
observed an increase in the average strain variation acting on
the GaAs core when increasing the indium content from 10%
to 50%, and strain relaxation for 50% and 60%. In addition,
for indium concentrations of 50% and 60%, simultaneous
growth of relaxed indium rich mounds and an indium poor
coherent shell takes place. These were represented by two
diffraction peaks along [
2
24
¯]and [
2
20
¯]for the sample with
60% of indium. However, one diffraction peak centered at the
position corresponding to 50% of indium was evident for
nanowires with nominal indium content of 50% in the shell,
presumably due to the small volume of the mounds near the
onset of mound formation and thereby the negligible impact
on the shell. Furthermore, the lattice planes of the In
x
Ga
1−x
As
shell showed relatively higher expansion along [
2
20
¯]com-
pared to [
2
24
¯]. Therefore, this technique is ideal for the
investigation of the strain evolution and relaxation mech-
anism in nanostructures which can be correlated with further
optical measurements.
Acknowledgments
The authors would like to thank A-K Bluhm for the acqui-
sition of SEM images and M Höricke as well as C Stemmler
for maintenance of the molecular beam epitaxy system used
for growth. We thank the DELTA machine group for pro-
viding synchrotron radiation at beamline BL9 and acknowl-
edge Michael Paulus for support and discussions.
Data availability statement
The data that support the findings of this study are available
upon reasonable request from the authors.
Funding
This work was supported by the Deutsche For-
schungsgemeinschaft (grant no. Pi217/38). R.B.L. is grateful
for additional funding from the Alexander von Humboldt
Foundation.
ORCID iDs
Ali Al Hassan https://orcid.org/0000-0002-2924-4215
Ryan B Lewis https://orcid.org/0000-0002-7216-3541
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