Revealing misfit dislocations in InAsxP1−x-InP core–shell nanowires by x-ray diffraction

InAsxP1−x nanowires are promising building blocks for future optoelectronic devices and nanoelectronics. Their structure may vary from nanowire to nanowire, which may influence their average optoelectronic properties. Therefore, it is highly important for their applications to know the average properties of an ensemble of the nanowires. Structural properties of the InAsxP1−x-InP core–shell nanowires were investigated using the coplanar x-ray diffraction performed at a synchrotron facility. Studies of series of symmetric and asymmetric x-ray Bragg reflections allowed us to determine the 26% ± 3% of As chemical composition in the InAsxP1−x core, core–shell relaxation, and the average tilt of the nanowires with respect to the substrate normal. Based on the x-ray diffraction, scanning, and transmission electron microscopy measurements, a model of the core–shell relaxation was proposed. Partial relaxation of the core was attributed to misfit dislocations formed at the core–shell interface and their linear density was estimated to be 3.3 ± 0.3 × 104 cm−1.


Introduction
The A III B V semiconductor nanowires (NWs) are one-dimensional nanostructures based on such materials as indium phosphide (InP), indium arsenide (InAs), and indium arsenide phosphide (InAs x P 1−x ).They have attracted increasing attention due to their unique properties related to surface and quantum confinement effects allowing application for transistors, solar cells, single photon sources, lasing, sensors, qubits or thermoelectric materials, and light-emitting diodes [1][2][3].
There are still many challenges to grow NWs, to design p-n junctions, to control the composition and structure of their alloys (InAs x P 1−x ), and to manufacture metallic contacts to them.As an additional difficulty, the typical structure for the InAs x P 1−x NWs is a mixture of zinc-blende (ZB) and wurtzite (WZ) phases called polymorphism [3,4].In the present work, we do not discuss polymorphism of the NWs, which was investigated elsewhere [5,6].Here, we assume, based on the electron microscopy and x-ray diffraction studies, that the structure of the NWs is pure wurtzite.
Semiconductor NWs are commonly studied using different experimental techniques such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), cathodoluminescence (CL), etc [3,7,8].Most of these methods are usually local, require destructive sample preparation or could provide information only about the surface of the NWs.In the present work, a non-destructive x-ray diffraction method was used to study InAs x P 1−x -InP core-shell NWs.The x-ray diffraction on NWs can be performed to study crystallographic properties of a single nanostructure by the x-ray beam focused down to few micrometers or even to nanometer scale [9][10][11][12].In this case, information is obtained only for one object of the ensemble of nanostructures.Therefore, an additional investigation of averaged properties may be needed [5,13].For this purpose, large x-ray beams of about hundreds of microns may be useful to study many illuminated semiconductor NWs.
This research aimed to investigate the structure of an ensemble of InAs x P 1−x -InP core-shell NWs grown on (111) InP substrate using a combination of coplanar x-ray diffraction, SEM, and TEM measurements.

Sample
The InAs x P 1−x -InP core-shell NWs were grown in [0001] direction on (111)B InP ZB substrate in a low-pressure (100 mbar) metal-organic vapor phase epitaxy reactor at the center for nanoscience 'NanoLund' at Lund University.The growth of the core of the NWs was performed with the gold (Au) seed particles with a diameter of 40nm that were deposited in an aerosol particle generator [14].
During the growth of the InAs x P 1−x WZ cores, following the methods in [15] the reactor temperature was set to 420 °C and the growth precursors used were phosphine (PH 3 ) with a molar fraction c PH 3 =6.2× 10 −3 , trimethylindium (TMIn) with a molar fraction χ TMIn =7.1 × 10 −6 and arsine (AsH 3 ) with a molar fraction c AsH 3 =2.75× 10 −5 .These molar fractions were fixed to define a content x of InAs in the range of 24%-28%.Additionally hydrogen chloride (HCl) with a molar fraction χ HCl =2.3 × 10 −5 was used to control radial growth [16] and hydrogen sulfide (H 2 S) was used as n-type dopant.The core of the NWs was grown in three steps having different hydrogen sulfide precursor molar fractions c H S 2 .This was done in order to achieve high n-type doping in the ends of the nanowire and low doping in the center, to enable fabrication of ohmic contacts for studies of the optoelectronic properties of the NWs.The dopant molar fraction c H S Next, the InP WZ shell of the NWs was grown at 550 °C for 8min, using only the source gases TMIn and PH 3 , with molar fractions c PH 3 =3.7 × 10 −2 and χ TMIn =4.0 × 10 −6 , respectively.The InP WZ shell is expected to grow epitaxially on the InAs x P 1−x WZ core.Schematic structure of a coreshell NW is shown in figure 1(a).Two InAs x P 1−x segments of the NW's core with the sulfur dopant content are marked as n 1 and n 2 .In the manuscript, we will use a Cartesian coordinate system xyz with the z-axis perpendicular to the surface of the substrate depicted in figure 1(a).

SEM measurements
The NWs were first investigated by the SEM measurements with an accelerating voltage of 10kV at Lund University.Initially, the sample with only the InAs x P 1−x cores was studied.Its SEM image is presented in figure 1(b).The diameter of the cores was measured to be about 45nm and the total length of about 4.5μm.The average density of the NWs was estimated from the seed particles density and the SEM measurements to be about 0.4μm −2 .
Further, the sample with the InAs x P 1−x -InP core-shell NWs was measured (see the SEM image in figure 1(c) and an enlarged image in figure 1(d)).The total diameter of the NWs in our experiment was measured to be 95±3nm.Therefore, the resulting shell thickness of the NWs is 25±2nm.
As one can see from figure 1(c), additional parasitic growth of InP droplet on the top of NWs has happened.The grown InP material has ZB structure, which was confirmed by TEM measurements (see the supporting information available online at stacks.iop.org/NANO/30/505703/mmedia).Comparison of figures 1(b) and (c) demonstrates a tilt of the coreshell NWs with respect to the substrate, which was already observed in previous works [12,17].In our study, this bending of the NWs is more probably due to the random geometry of the ZB droplets on top of the NWs.

TEM measurements
The TEM measurements of the NWs were performed at the national center for high-resolution electron microscopy (nCHREM) on a JEOL 3000F TEM equipped with a field emission gun and operated at 300 kV.The high-angle annular dark-field TEM image with a general view of an InAs 0.26 P 0.74 -InP WZ core-shell NW under investigation is shown in figure 2(a).This scan covers a relatively large area of the NW, but with a low resolution.
To resolve a local structure of the NW, the highresolution TEM (HRTEM) imaging was performed on several parts of the NW and an area with an atomic resolution is presented in figure 2(b).The HRTEM image demonstrates the presence of stacking faults in the InP shell, which are depicted in figure 2(b).These stacking faults correspond to polymorphism in the NWs and are a mixture of ZB and WZ phases [3,4].However, the number of ZB layers is minimal, and the NWs are, therefore, assumed to be pure WZ in our study.Furthermore, the stacking faults do not contribute significantly to the x-ray diffraction due to their low density.Presence of the stacking faults in the shell allows expecting that some of them are formed due to the misfit dislocations (MDs) located between the core and the shell of the NWs.

Laboratory x-ray diffraction
First, an x-ray diffraction study of the sample with the wavelength of 1.541Å(energy of 8.046 keV) were performed at a laboratory x-ray source at NanoLund, Lund University, Sweden.The scheme of the experiment is shown in figure 3(a).From the structure of the InAs x P 1−x core NWs and the InP substrate, two Bragg reflections in reciprocal space were expected, namely, 111 InP and 0002 InAs x P 1−x Bragg peaks.Here and further we will use three indices notation for ZB and four for WZ structures.An expected reciprocal space map (RSM) of the sample is schematically shown in figure 3(b).
The sample with only InAs x P 1−x cores was studied at the laboratory x-ray source by employing 2Θ−ω scan through the maximum of 111 InP Bragg peak.This scan in reciprocal space is marked as 'A' in figure 3(b) and is parallel to the Q z -axis of the corresponding Cartesian coordinate system (see figure 3(b)).The intensity distribution of this scan is presented in figure 3(c) (black curve) and demonstrates presence of the expected diffraction signals.Due to the dominant contribution of the InP substrate signal, intensity of the InAs x P 1−x NWs Bragg peak is suppressed.In order to enhance this signal, the second 2Θ−ω scan 'B' was performed at an offset angle γ=0.2°withrespect to the scan 'A', which corresponds to a shift in reciprocal space along Q x by δQ x =0.07 nm −1 (see figure 3(b)).The intensity distribution of the scan 'B' is presented in figure 3(c) (brown curve) and demonstrates a symmetric shape of the 0002 InAs x P 1−x Bragg peak.From the Q z =18.32nm −1 coordinate of the Bragg peak composition x of InAs in InAs x P 1−x alloy can be determined.The unit cell lattice parameters of the WZ InP and InAs NWs are known to be a InP =4.14Å and c InP = 6.80Åfor the WZ InP [18], and a InAs =4.27Åandc InAs =7.03ÅforWZ InAs [19].The InAs x P 1−x unit cell lattice parameter c InAsP obtained from the Q z peak position is 6.86Å.Since the NWs with only InAs x P 1−x core are fully relaxed, the composition x of InAs according to the Vegard's law for the ternary alloys [20][21][22] could be calculated as and the unit cell lattice parameters of the relaxed WZ InAs 0.26 P 0.74 core are a InAsP =4.18±0.03Å and c InAsP = 6.86±0.04Å.
Further, the sample with InAs 0.26 P 0.74 -InP core-shell NWs was investigated using the same experimental scheme (see figures 3(b) and (c)).Theoretical lattice mismatch between the InP shell and the InAs 0.26 P 0.74 core is These Q z coordinates correspond to the unit cell lattice parameters c Peak(1) =6.82±0.05Å, c Peak(2) = 6.84±0.08Å.The intensity of the Peak(1) is approximately two times higher than the intensity of the Peak(2) taking into account the ratio of the area below Gaussian distributions from the fit.In order to understand the origin of the NWs Bragg peak double structure, x-ray diffraction measurements at a synchrotron source were performed.

Experimental setup at a synchrotron
The synchrotron x-ray diffraction measurements were performed at a bending magnet single-crystal diffraction beamline at the synchrotron facility ANKA in Karlsruhe, Germany.The RSMs of the sample were recorded with a monochromatic x-ray beam at an energy of 12keV.Measurements were performed at a six circle diffractometer with four degrees of freedom for the sample and two degrees of freedom for the detector.The x-ray beam was focused to the center of the diffractometer down to the size of about 500×500μm 2 .All x-ray data were recorded with a microstrip solid-state linear detector Mythen 1K.The detector has a total number of 1280 channels with a channel size of 50μm×8mm and a pointspread function of one channel.The sample to detector distance in the experiment was about 0.7m, which corresponds to an angular resolution of about 0.004°per pixel [24,25].
The sample was measured in a coplanar x-ray diffraction geometry with the surface normal, an incidence and diffracted x-ray beams lying in the same diffraction plane [26].Taking into account the x-ray beam size and its incidence angle for these reflections, the average number of illuminated InAs 0.26 P 0.74 NWs was estimated to be about 10 5 .In the RSMs (see figure 4 .The vertical one that goes parallel to the Q z -axis through the origin of reciprocal space is a crystal truncation rod (CTR) [24,27].The CTR is absent in the RSM of the reflection 444 due to a low intensity of the reflection and a possible small misalignment of the sample surface.The second streak is inclined to the CTR at the Bragg angle of the corresponding reflection.This streak corresponds to a detector frame (position of the Ewalds sphere) with increased background due to the x-rays scattering on air.The parasitic background is a result of the raised x-ray scattering intensity from the substrate in the exact Bragg conditions and is called a detector streak (D) [24].
Experimentally measured distribution of intensity in reciprocal space along the CTR for all reflections is presented From the average period ΔQ z of 0.03± 0.01nm −1 , the corresponding thickness of this layer δ=207±51 nm was obtained using equation δ=2π/ΔQ z [26].
Further, the broadening of reflections in Q x direction was analyzed.The InAs 0.26 P 0.74 NWs could be considered as tilted and twisted blocks, and a mosaic block model could be applied for the analysis of their symmetric reflections broadening.Therefore, a Williamson-Hall (WH) plot, which is a plot of the full width at half maximum (FWHM) of reflections broadening in an angular Q x direction as a function of Q z -coordinate [21,28], can be used to determine an average tilt of the InAs 0.26 P 0.74 NWs [3,24].From the linear fit of the WH plot, an average value of the NWs angular tilt α and horizontal coherence length L can be obtained [21] ( ) ( ) • ( ) The WH plot was performed for both diffraction peaks Peak(1) and Peak(2) (see figure 4).The intensity distribution along Q x    Bragg peaks.Red points show positions of the Peak(1) and Peak(2) Bragg peaks.From their positions, the unit cell lattice parameter of the peaks Peak(1) and Peak(2) are found to be a Peak(1) =4.16±0.03Åand a Peak(2) =4.17±0.05 Å, respectively.Additionally, positions of the 1128 Bragg peaks of an InP, InAs, and the unstrained InAs 0.26 P 0.74 core in reciprocal space are presented in figure 6(b).All coordinates of the Bragg peaks are summarized in table 2.
From the obtained unit cell lattice parameters a Peak(1) and a Peak(2) , the experimental lattice misfit in [11 2 0]-direction between the relaxed InAs 0.26 P 0.74 core and the detected signal is where P=c/a is a ratio of the unit cell lattice parameters c and a of the structures.This tetragonal distortion of the structure is due to the strain between the core and the shell, but it is less than the value predicted by the model, which will be presented in the next section.

Model
We have experimentally investigated the InAs 0.26 P 0.74 -InP NWs using different methods.Now, we will model the strain field in the NWs to retrieve the theoretically expected Bragg peak positions from the core-shell structure of the NWs in reciprocal space.Further, various effects, which may explain the double structure of the Bragg reflections will be considered.Finally, we will propose a model explaining the origin of the Bragg reflections Peak(1) and Peak(2).

FEM simulations
In order to understand the intensity distribution in reciprocal space of SXRD and AXRD reflections, a 3D model of an InAs 0.26 P 0.74 -InP core-shell NW was developed using the finite element method (FEM).The modeling was performed by commercial software COMSOL Multiphysics 5.4.Material properties of the shell and core used for the simulations are summarized in the supporting information.
According to the Saint-Venant's principle [30], the influence of the ends of the NW on the strain field along its length could be neglected due to the length to diameter ratio of 47. .This value is different from the D 1 and D 2 calculated above.It can be explained by the fact that the model does not take into account the core-shell relaxation by defects.

Monte Carlo simulation of the diffracted intensity
The strain field in the core-shell NWs obtained from the FEM model and the experimentally obtained, from the WH plot, average tilt of the NWs with respect to the substrate normal were used to simulate the intensity distributions of SXRD and AXRD Bragg reflections of the NWs using the Monte Carlo (MC) method.In the MC simulations, the diffraction pattern of a single NW with the corresponding strain field components ε ii was simulated 10 5 times with the angular distribution obtained from the WH plot.This number of simulations was chosen to be approximately equal to the number of illuminated NWs.The resulting intensity distribution of the 0002 SXRD reflection is presented in figure 4(c) and the 1128 AXRD Bragg reflection is shown in figure 6(c).Both RSMs reveal the formation of only one Bragg peak despite the complex strain field components.
It was observed from the TEM and SEM images that the InP shell of the NWs is thinner in the bottom part, closer to the substrate (see the supporting information).This thickness difference may also lead to different relaxation of the coreshell material along the NWs and may lead to additional maxima of intensity in RSMs.In order to investigate the influence of this effect on the scattered x-ray intensity, the shell thickness variation function was obtained from the TEM measurements, and a model of the NW with InP shell thickness variation was developed.Further, the MC simulated RSMs based on the FEM and this model were compared.It was demonstrated that the effect of the shell thickness variation does not have any significant influence on the scattered x-ray intensity in reciprocal space (see the supporting information).

Discussion
We attribute the most intense diffraction signal Peak(1) registered in our x-ray coplanar diffraction experiments to the scattering from the InAs 0.26 P 0.74 WZ core and InP WZ shell adapted to each other along the growth direction of the NWs.This assumption was made based on the fact that the InP shell thickness of the NWs in our experiment was below the critical one for MDs formation.The second less intense diffraction signal Peak(2) is originated most probably from the partially relaxed core due to the relaxation of strain between the core and the shell.
The main effect, which may explain this partial relaxation of the core-shell interface of the NWs and presence of two Bragg peaks, assumes relaxation of the core due to MDs formation between the core-shell interface, which most probably leads to the formation of the stacking faults.In this case, the core is partially relaxed due to the strain field of these defects, and the MDs have the circular dislocation lines in the xy-plane on the core-shell interface with the Burgers vectors b equal to the unit cell parameter (c InAsP ) along the [0001] crystallographic direction [31].Lattice parameters a and c, calculated from the FEM model, are smaller than the experimentally obtained from the reflection Peak(1) (see table 2).That might also be due to the strain release by the dislocations between the core and the shell.
The schematic representation of the model explaining the partial relaxation in the NWs due to MDs formation on the core-shell interface is given in figure 7(c).In this case, the linear MD density can be estimated as [32]   and is equal to 3.3 ± 0.3 × 10 4 cm −1 .Taking into account the low density of MDs and the limited number of recorded HRTEM images, they may be easily missed in our TEM measurements.Moreover, the MDs are located at the core-shell interface and are covered by the shell in the TEM transmission geometry.Therefore, the TEM measurements can not provide information regarding the presence of MDs with the lattice mismatch of only ∼5×10 −3 , which demonstrates the power of the coplanar x-ray diffraction performed at the synchrotron.

Conclusions
In this work, structural properties of an ensemble of InAs x P 1−x -InP core-shell nanowires were investigated employing the coplanar x-ray diffraction geometry.Study of series of symmetric coplanar Bragg reflections allowed us to derive 26%±3% chemical composition of As in the InAs x P 1−x core.Further, the average tilt of the NWs with respect to the substrate normal was obtained to be 1.68°± 0.71°using the mosaic model and the Williamson-Hall plot.
Based on the results of x-ray diffraction, scanning and TEM measurements, a model of core-shell relaxation was proposed.The finite element model of the InAs x P 1−x -InP coreshell NW helped us to understand the strain field distribution in the NW and the intensity formation in reciprocal space of the asymmetric 1128 Bragg peaks.Further, we demonstrated that the observed shell thickness variation does not influence the x-ray Bragg peak formation by the Monte Carlo calculations.The second diffraction signal (Peak(2)) observed in the experiment was attributed to the partially relaxed core of the NWs due to a small number of MDs with the circular dislocation lines formed at the core-shell interface.Their linear density was estimated to be 3.3±0.3×10 4cm −1 .
Results of our study demonstrate the high sensitivity of the coplanar x-ray diffraction measurements to the MDinduced strain relaxation detection in the NWs and the average structural properties of an ensemble of nanostructures.We hope that this work will contribute to a better understanding of the structure of semiconductor NWs and will help to improve their growth procedure.

2 was initially 7 . 1 ×
10 −7 , after 4 min growth the c H S 2 was decreased for 3 min to a 1.1 × 10 −7 for lower doping content.Finally, the growth continued for 8 min with c H S 2 changed back to the value 7.1 × 10 −7 .

Figure 1 .
Figure 1.(a) Schematic presentation of an InAs x P 1−x -InP core-shell nanowire structure with a Cartesian coordinate system.Two parts of the NW have the same dopant H 2 S content marked as n 1 .The central part of the NWs, which has seven times lower H 2 S content marked as n 2 .The SEM images of the sample surface after growth of the InAs x P 1−x WZ core (b) and InAs x P 1−x -InP WZ core-shell nanowires (c).(d) An enlarged SEM image of the InAs x P 1−x -InP core-shell nanowires.All SEM images are measured at a tilt angle of the sample surface of 30°.

Figure 2 .
Figure 2. TEM measurements of an InAs 0.26 P 0.74 -InP WZ core-shell NW.(a) High-angle annular dark-field (HAADF) TEM image with a general view of a NW under investigation.(b) High-resolution TEM image of a part of the NW with atomic resolution.(a) The investigated part of the NW is shown as a red square.The HRTEM image demonstrates presence of stacking faults in the InP shell, which are marked as stacking faults.

3
Taking into account the core-shell relaxation[23], similar Bragg peak at a different position in RS was predicted for the InAs 0.26 P 0.74 -InP core-shell NWs.Unexpectedly, the WZ core-shell NWs 0002 Bragg peak in 2Θ−ω scan 'B' revealed double maxima structure marked as '1' and '2' in figure3(c) (magenta curve).Positions of the peaks were obtained by a fit of the x-ray diffraction curve with three Gaussian functions shown in figure 3(d).Parameters of the Gaussian functions are Peak(1): Symmetric x-ray diffraction (SXRD) at a synchrotron At the synchrotron source a series of full SXRD RSMs of 111/0002, 222/0004, 333/0006, and 444/0008 Bragg reflections were measured and are presented in figure 4(a).
(a)), several maxima of diffraction intensity are visible.The most intense diffraction signal originating from the InP substrate is marked as InP in figure 4(a).Two broad Bragg peaks along Q x direction are attributed to the signals from the InAs 0.26 P 0.74 -InP core-shell NWs.The intensity streak along Q x direction in the vicinity of the InP Bragg peak well pronounced in the reflection 111 (see figure 4(a)) is attributed to the signal from the parasitically grown InP droplets on the top of NWs (see figure 1(d)).This signal is invisible in other reflections due to the lower intensity value in comparison to the substrate scattering.Additionally, two streaks of intensities crossing the InP Bragg peak are present in the RSMs in figure 4(a)

Figure 3 . 3
Figure 3. (a) Scheme of the laboratory x-ray diffraction experiment.The incident k i and the outgoing k f x-ray wave vectors define the scattering vector Q=k f −k i .Cartesian coordinate system Q Q Q x y z in reciprocal space has axis parallel to the xyz axis of the coordinate system in real space (see figure 1(a)).In the scheme, ω is the incident angle and 2Θis the angle between vectors k f and k i .(b) Reciprocal space scheme of the 0002 InAs x P 1−x -InP core-shell NWs and 111 InP substrate Bragg reflections.The sample was scanned by 2Θ−ω scans through the maximum of 111 InP Bragg peak marked as 'A' and along a direction 'B' inclined by an angle γ=0.2°withrespect to the scan 'A', which corresponds to a shift in reciprocal space along Q x by δQ x =0.065nm −1 .(c) The intensity distributions of the scans 'A' and 'B' of the samples with only InAs x P 1−x WZ cores and InAs x P 1−x -InP WZ core-shell NWs.(d) Fit of the Bragg peaks 1, 2 of the InAs x P 1−x -InP core-shell NWs and InP with three Gaussian functions.

Figure 4 .
Figure 4. (a) Reciprocal space maps of the symmetric ZB/WZ 111/0002, 222/0004, 333/0006, and 444/0008 Bragg reflections in logarithmic scale.(b) Their intensity distributions along the CTR.For better representation each plot of the intensity distribution in (b) was shifted by one order of magnitude.Numbers '1' and '2' depict positions of the Bragg reflections Peak(1) and Peak(2).(c) Monte Carlo simulation results of the 0002 Bragg peak of the InAs 0.26 P 0.74 -InP core-shell NWs based on a NW model with the shell thickness variation (see for details the supporting information).Position of the 111 InP Bragg peak and the CTR are also shown in RSM.
direction in reciprocal space of all symmetric reflections after the subtraction of the CTR intensity are compared in figures 5(a) and (c).These intensity profiles were fitted with the Gaussian functions and obtained FWHMs were used in the WH plot shown in figures 5(b) and (d).From the WH plots of the symmetric reflections, average slopes of 1.69°±0.14°and1.68°±0.71°,and intersection value of the linear function with the ordinate −0.016±0.012nm −1 and −0.051±0.049nm −1 were obtained using equation (4).The mean slope of 1.68°±0.71°isattributed to the average tilt of the NWs, while the intersection value could not be used for the coherence length calculation due to the high value of the systematic error in our measurements.The slope value is in a good agreement with the experimentally obtained tilt angles of semiconductor nanowires[12,17,29].Asymmetric x-ray diffraction (AXRD) at a synchrotron Coplanar AXRD RSM of 246 InP substrate and 1128 InAs 0.26 P 0.74 NWs reflections was recorded in order to determine the unit cell lattice parameters a of the Bragg peaks Peak (1) and Peak(2) from the lateral components Q x of their scattering vectors.Schematic comparison of symmetric and asymmetric RSMs shown in figure 6(a) demonstrates different positions of the Bragg peaks along Q x in the case of AXRD.The experimentally measured asymmetric RSM is presented in figure 6(b) (see the supporting information for the initial RSM).In the RSM, the D streak is inclined with respect to the CTR in an angle of about 63°, which equals to the sum of the Bragg angle of the 264 InP reflection (41.20°) and an angle of inclination of the diffraction planes with respect to the sample surface (22.21°).The intensity of the Bragg peaks is lower in comparison to the symmetric diffraction because of the twist of the NWs, which reduces the scattered intensity in the coplanar diffraction plane.Due to relatively high diffuse intensity in the vicinity of the substrate 246 InP Bragg peak, it is difficult to determine precise positions of the WZ Peak(1) and Peak(2) peaks directly.For better representation of the signals Peak(1) and Peak(2), the RSM is shown as a contour plot in figure 6(b).Red lines in the figure outline an elongation of the Peak(1), which is broad due to the tilt of the NWs with respect to the substrate observed in SXRD, and the Peak(2).The fact that these peaks have two components of the diffraction vector Q in reciprocal space and that Q z component is already known for both peaks allows precise determination of the second Q x component.The dashed horizontal lines in figure 6(b) show positions of the Q z coordinates of the Peak(1) and Peak(2)

Figure 5 .
Figure 5. (a) Peak(1) and (c) Peak(2) Bragg peaks intensity distributions of 0002, 0004, 0006, and 0008 reflections along the Q x direction after the subtraction of the crystal truncation rod intensity.Williamson-Hall plots of the Peak(1) (b) and Peak(2) (d) based on the FWHMs of the symmetric reflections.

c 2 ,
there is a tetragonal distortion of the structure corresponding to the Bragg peaks (1) and (2), which could be obtained as

Figure 6 .
Figure 6.Analysis of the asymmetric coplanar x-ray diffraction map.(a) Scheme of the ZB/WZ 246/11 28 Bragg reflections AXRD RSM in comparison with the ZB/WZ 444/0008 SXRD RSM.The AXRD measurement reveals the lateral components Q x of the scattering vectors.(b) Experimental AXRD RSM is presented as a contour plot (see the supporting information for the initial RSM).The red line in figure (b) outlines an elongation of the Bragg reflection Peak(1), which is due to the tilt of the NWs with respect to the substrate normal, while the red contour lines demonstrate the vicinity of the Bragg reflection Peak(2).The dashed horizontal lines show levels of Q z components and the red points positions of the Bragg reflections Peak(1) and Peak(2).Numbers '1' and '2' depict the peaks Peak(1) and Peak(2), respectively.Additionally, the 1128 Bragg peaks of an InP, InAs, the unstrained InAs 0.26 P 0.74 core (InAsP(WZ)), and the strained InAs 0.26 P 0.74 -InP coreshell obtained from the FEM model are presented in (b).(c) Monte Carlo simulation results of the AXRD Bragg peak based on the FEM model (see for details the supporting information).
4.Therefore, the length of the FEM model was chosen to be long enough to avoid the influence of the edge effects in the middle of the NW.Further, the values of the central part of the FEM model were used for the modeling.The strain field component ( ) FEM model presents the deformation of material along zdirection.Here u z (r) is the displacement field at each point r (x, y, z) of the NW.The 3D view of the ε zz (r) component is shown in figure7(a).As one can see, the central part is not affected by the strain field variation due to the edges of the model and was set further to the origin of the coordinate of the model.The 2D slices in xz and xy planes of the central part of the model with the strain components ε zz and ε xx , respectively, are shown in figure 7(b).The component ( the derivative of the xcomponent of the displacement field u x (r) and gives the deformation of the model along x-direction.The strain field component ε zz remains constant in the core and the shell along the NW length, while the ε xx component has complicated spatial distribution.Further, the average unit cell lattice parameters a and c were obtained from the FEM simulations, which are summarized in tables 1, 2 with the reciprocal space coordinates Q x , Q z of the corresponding Bragg reflection.The obtained Q x , Q z coordinates represent theoretically expected position of the defect-free InAs 0.26 P 0.74 -InP core-shell NWs Bragg peak in reciprocal space, which is shown in figure 6(b) for the 1128 Bragg peak.The tetragonal distortion of the unit cell lattice parameters c and a due to the strain between the core and the shell could be calculated from the FEM model and is =

Figure 7 .
Figure 7. 3D model of a strained core-shell NW with a partial relaxation.(a) The ε zz strain field component of the NW FEM model.The length of the model was chosen to be long enough to avoid the influence of the edge effects in the central part.(b) The strain field components ε zz and ε xx are shown as 2D slices of the model in the xz (y = 0) and xy ( = z length 2) planes, respectively.(c) Schematic presentation of a model explaining the partial relaxation in InAs 0.26 P 0.74 -InP core-shell NWs due to MDs formation on the core-shell interface.The MDs have circular dislocation lines in the xy-plane with the Burger's vector b parallel to z-axis and more probably lead to formation of the stacking faults shown in the model.

Table 1 .
The Q (2)alues of symmetric reflections and the unit cell lattice parameters c obtained from the Bragg peaks ZB InP, WZ Peak(1), Peak(2), and the FEM model.

Table 2 .
Coordinates Q z , Q x , and the unit cell lattice parameters a and c of the bulk ZB InP, WZ InP and InAs NWs, FEM model, and the Peak(1) and Peak(2) of ZB/WZ 264/11 28 Bragg reflections.