# Multimodal imaging of strain and light emission of core-shell InGaN/GaN wires under a submicrometer polychromatic X-ray probe

Beatriz de Goes Foschiani, Sergio Bongiorno, Odile Robach, Olivier Ulrich, Jean-Sébastien Micha, J. Eymery

► To cite this version:

Beatriz de Goes Foschiani, Sergio Bongiorno, Odile Robach, Olivier Ulrich, Jean-Sébastien Micha, et al.. Multimodal imaging of strain and light emission of core-shell InGaN/GaN wires under a submicrometer polychromatic X-ray probe. 2025. hal-05367785

HAL Id: hal-05367785

https://hal.science/hal-05367785v1

Preprint submitted on 16 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution - NonCommercial 4.0 International License
Multimodal imaging of strain and light emission of
core-shell InGaN/GaN wires under a sub-
micrometer polychromatic X-ray probe.

Beatriz de Goes Foschiani¹, Sergio Bongiorno, Odile Robach¹, Olivier Ulrich¹, Jean-Sébastien

Micha², Joël Eymery¹

1 Univ. Grenoble Alpes, CEA, IRIG, MEM, NRX, 38000 Grenoble Cedex, France

2 Univ. Grenoble Alpes, CNRS, UMR SyMMES, CEA-Grenoble/IRIG, 38000 Grenoble Cedex,
France

KEYWORDS

Wires, Laue diffraction, XEOL, InGaN/GaN core shell, strain, X-ray synchrotron

ABSTRACT

We present a combination of µLaue X-ray diffraction and X-ray excited optical luminescence (XEOL) techniques to map local strain, orientation, and light emission in metalorganic vapor phase epitaxy (MOVPE) core-shell InGaN/GaN multiple quantum wells (MQW) wires dispersed on silicon substrates. The components of the deviatoric strain tensor averaged along the beam footprint were quantified with a measurement precision better than 9 × 10⁻⁵ and an accuracy of approximately 4 × 10⁻⁴. This measurement quality is achieved by carefully calibrating the analysis chain with a Ge crystal and verifying it with measurements of the unstrained Si substrate reference. The µLaue mapping of the components of the deviatoric strain confirms the high crystal quality and the impact of the MQW shell grown only in the upper part of the GaN core, as evidenced by the local variations of the full width at half maximum of the diffraction peaks and of the lattice rotation tensor. The two deviatoric
tensors of the GaN core and InGaN/GaN shell can be measured independently and are in quantitative agreement
with three-dimensional finite element method (FEM) simulations. The structural information is correlated with
XEOL measurements, whose spectral analysis reveals the main contributions to light emission: the major blue
MQW emission from the m-plane at the top of the wires, with a gradient varying from 406 nm at the top of the
MQW to 397 nm at the bottom, with a secondary emission of a semipolar r-plane facet at ~470 nm; the near-
band-edge GaN signal at ~363 nm; and the usual yellow defect-band luminescence, centered at 560 nm. The
paper also highlights the potential of these techniques to obtain statistics on semiconductor heterostructures and
their automation capabilities for measurements and analysis.
Due to their unique properties and functionalities, nanostructures are essential for developing cutting-edge technologies, and accurate characterization is necessary to manage growth, understand properties, and optimize performance.¹⁻³ As a recent example, advanced characterization techniques such as micro-Laue diffraction (µLaue),⁴⁻⁷ X-ray fluorescence (XRF), and X-ray excited optical luminescence (XEOL) have emerged as powerful tools for investigating the structural and optical properties of nanomaterials at the nanoscale⁸⁻¹⁰. µLaue diffraction enables the mapping of deviatoric strain fields and rotations within crystals with high spatial resolution, providing crucial insights into their structural integrity and mechanical properties.¹¹ XRF provides information on elemental composition and sample alignment. Concurrently, X-ray excited optical luminescence facilitates the hyperspectral analysis of light emission from materials, offering valuable information on their optical properties and excitonic dynamics.¹²,¹³

In this context, previous studies have successfully applied XRF and XEOL techniques (including time-resolved analysis of emission time-decay) to investigate various nanostructures, including core-shell nanowires, revealing intricate details about their compositional features and optical behavior.¹²,¹³ Additionally, complementary techniques such as transmission electron microscopy (TEM), electron backscatter diffraction (EBSD), and cathodoluminescence (CL) have been employed to provide a comprehensive understanding of the nanostructure properties. The structural analysis performed with electrons has been demonstrated to be very efficient; however, it is limited in transmission electron microscopy (TEM) geometry by sample thinning, projection effects, and a small field of view. For a given sample orientation, only a few components of the deformation tensor can be obtained in an image or a diffraction pattern due to the limited measurement of the reciprocal space.¹⁴ Additionally, EBSD technique,¹⁴,¹⁵ which needs specific surface preparation, is precise and reproducible but lacks accuracy due to relative measurement to a sample reference frame: the orientations are determined relative to the sample's own coordinate system, not an external or universal frame.¹⁵,¹⁶ This structural information can be combined with
CL in scanning electron microscopes; however, implementing it in transmission microscopes is quite challenging and, again, limited by sample thinning.¹⁷

In contrast, the combination of µLaue microdiffraction and XEOL enables a nondestructive, bulk-sensitive, and fully quantitative investigation of the structural and optical properties of semiconductor nanostructures under realistic geometries. This multimodal synchrotron-based approach provides direct access to the deviatoric strain tensor while simultaneously mapping the corresponding optical emission with sub-micrometer resolution. By correlating the local strain state with emission properties, µLaue-XEOL characterization bridges the gap between structural and optical analysis, offering unique insight into strain-light coupling mechanisms that are inaccessible by conventional electron-based microscopy, paving the way for the design of next-generation optoelectronic devices.

This work also aims to contribute to methodological development in the field of materials science by presenting a comprehensive study of advanced nanostructure Laue diffraction characterization, with a special focus on the quantitative determination of strain tensors and associated error confirmed by finite element method (FEM) simulations. As a proof of concept, we have applied this methodology to GaN microwires covered at the top by InₓGa₁₋ₓN/GaN core-shell multiple quantum wells (MQWs) grown by metalorganic vapor phase epitaxy (MOVPE). It will also be demonstrated that fast scan imaging can deliver precise information and a statistical overview of the samples, paving the way for effective production control and rapid and systematic screening of optoelectronic materials and microstructures.

The multimodal characterization of the microwires was carried out on the BM32 beamline at the European Synchrotron (ESRF). A bending magnet produces a white beam with an energy range of 5-27 keV. A pair of Kirkpatrick-Baez (KB) mirrors, composed of two fixed-curvature, elliptical, perpendicular mirrors, is used for achromatic beam focusing down to approximately 300 x 300 nm (VxH) at the sample position. The sample, mounted on a scannable X-Y-Z stage tilted at 40° relative to the incident X-ray beam, is illuminated by the X-ray beam, and scattered beams hit a
plane detector to form an image in a single exposure (PhotonicsScience sCMOS, 2018x2016 pixels, 16-bit) (see Figure 1a). The recorded image is composed of one or several Laue patterns made of numerous diffraction spots, each originating from the diffraction on atomic lattice planes within the microwire. This instrument enables the simultaneous acquisition of µLaue diffraction images, fluorescence (Si drift Ketek detector), and XEOL data at each position of the sample. Indeed, XEOL instrumentation comprises an off-axis aluminum parabolic mirror that collects the luminescence signals resulting from the beam's interaction with the sample and focuses them onto a second parabolic mirror coupled to an optical fiber (reflective collimator). This signal is then dispersed by a diffraction grating and collected by a charge-coupled device (CCD-SCMOS, OceanOptics) with 1024 channels. Regarding fluorescence measurements, the distance between the XRF Si drift detector and the sample can be adjusted to select the appropriate element count rate. In this study, we measured the Ga K-alpha emission line within the 9.0–9.5 keV range, as illustrated in Figure 1c. This fluorescence signal serves as a real-time monitor of sample positioning and instrument stability during the scan. The higher intensity observed in the shell region is due to the added thickness of the MQW overlayer. This signal is also used as a mask to filter diffraction patterns. Indeed, the high crystallinity of the sample enables the production of diffraction patterns from the low-intensity tails of the incident beam, and maybe by secondary excitation. These patterns can be recorded from areas that are not directly illuminated by the main beam, and they must be filtered out. To do so, only diffraction patterns having the Ga Kα emission line intensity larger than a threshold of 450 (in arbitrary units for counts) are considered for the analysis in Figure 1c.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** (a) Schematic of the µLaue, XRF, andXEOL setup at the BM32 beamline at ESRF. (b) Schematic of the GaN microwires with InₓGa₁-xN/GaN core-shell multiple quantum wells at the top of the structure. The wires are grown via self-assembled Si-assisted growth by metal-organic vapor phase epitaxy on sapphire. (c) Ga Kα fluorescence mapping of a wire. (d) Scanning electron microscopy, view of mechanically dispersed wires on a (001) Si crystal.</figcaption></figure>

The schematic morphology of the MOVPE-grown wires is shown in Figure 1b. It highlights the surface crystallographic planes, the MQW regions, and the SiNₓ mask layer deposited at the stem. These heterostructures exhibit a hexagonal cross-section and a core–shell architecture, in which
the MQW shell forms on the upper part of the wires along the nonpolar m-plane {1-100} facets
of the GaN core. Following the growth method described in Ref. 18 and using specific surface
preparation under ammonia, the wires are N-polar and grow along the [000-1] direction. The GaN
stem is synthesized from trimethylgallium (TMGa) and ammonia at 1040 °C on a c-sapphire
substrate. During growth, silane gas is introduced for 300 s at a flow rate of 210 nmol min-1 to
promote vertical elongation. This heavy Si doping leads to the formation of a SiNₓ selective mask
at the base of the GaN stem. Once the silane flow is stopped, growth continues for an additional
200 s using the residual Si atoms present in the reactor. The resulting wires reach a total length of
approximately 20 µm, with a bottom diameter of about 1 µm that gradually increases toward the
top (see Figure 1c). The notation n⁺⁺- GaN refers to the highly Si-doped core, which provides a
high concentration of free electrons (>10²⁰ cm⁻³), whereas the n-GaN region is unintentionally
doped. A change in the growth conditions leads to the formation of 15 multiple quantum wells
(MQWs), corresponding to approximately 6 nm of In₀.₁Ga₀.₉N wells and 8 nm of GaN barriers.

The InGaN quantum wells are grown at 750 °C under a nitrogen atmosphere using triethylgallium (TEGa) and trimethylindium (TMIn), while the GaN barriers are deposited at 950 °C using TEGa.

The SiNₓ mask prevents the growth of GaN and InGaN alloys on the lower part of the wire,
ensuring that the MQW shell forms exclusively on the m-plane facets at the top of the structure.

The number of MQW periods was selected to enhance the XEOL optical signal and reinforce their
signature in the Laue diffraction patterns. The wire shown in the SEM image in Figure 2a
demonstrates this general morphology. Labels A, B, and C denote the MQW shell region; D marks
a transition zone where the mask is partially effective; and E corresponds to the area where the
SiNₓ mask completely suppresses growth.

A semipolar plane is observed in the A region at the top of the wire, which is attributed to the
usual r-plane (1-1 0 2) of the GaN lattice. This plane develops at the top core and is common in
these heterostructures.¹⁹ The B region with MQW has a regular morphology with well-defined
smooth m-plane facets. In the C region, a transition of the flat MQW growth occurs in a region
partially covered by the SiNx layer. Region D shows granular regions with small discontinuous overgrowths. It corresponds to a transition zone between the GaN core and the cladding. Finally, region E consists of the GaN core fully protected by the SiNx mask with no regrowth.

The wire cleaves at its base during mechanical scratching close to the sapphire substrate. As demonstrated by SEM views, some dislocations may be present at the base of the wire as a result of the lattice mismatch between GaN and the sapphire substrate. They correspond to weak points for cleavage and fracture. However, they are bent toward the surface, and usually, there are no extended defects in these wires.²⁰ Note that these objects have been selected as an example of a pure nanometric heterostructure governed by elasticity criteria, with no notable extended defects.

XEOL analysis at room temperature enables us to examine the distinct signatures originating from these regions within the 248-1038 nm detector range, as illustrated by the selection of spectral bands in Figure 2a from the panchromatic spectrum (Figure 2b). The acquisition time is 2.25 s at each position for XEOL. The beam excites volume elements through various optical excitation processes along the entire beam-free path (see the Supporting Information, Section S1 for a brief description of the recombination process). Then, the excited optical signal can be absorbed before it is extracted from the sample. The 355-375 nm emission wavelength refers to the GaN near-band edge (NBE) emission, primarily originating from the GaN core without MQWs (regions D and E). The 380-420 nm band corresponds to the efficient UV-blue emission from the MQWs, which highlights the signal from the nonpolar m-plane active zone, while the 450-490 nm band represents the emission from the MQWs grown on the semipolar planes, as seen in regions A and C of the wires. The 520-600 nm region corresponds to the yellow luminescence band (YL) associated with radiative recombination through defects. It is primarily observed in the cladding region due to the low-temperature growth of the GaN barriers.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** (a) Scanning electron microscopy (SEM) image of a GaN/InGaN core–shell wire (left) and XEOL emission maps for different wavelength ranges: 355–375 nm (GaN near band edge), 380–420 nm (m-plane MQW emission), 450–490 nm (semipolar MQW emission), 520–650 nm (yellow luminescence band), and 248–1038 nm (panchromatic signal). The maps highlight the spatial distribution of each spectral component along the wire. (see the description of the A-E</figcaption></figure>
labels in the text and growth conditions). (b) Panchromatic X-ray excited optical luminescence integrated over the wire and processed to enhance feature visualization is decomposed into four bandwidths (near band-edge emission, m- and r-plane MQW emission, and the yellow-luminescence defect band). Figure (c) details the analysis of the m-plane MQW emission (i.e., B-label in a). Spectral mappings taken at four wavelengths (397, 400, 403, 406 nm) show an emission gradient estimated at -1.6 nm/µm by performing a linear fit of the position of the maximum intensity along the m-plane MQW.

As shown in Figure 2c with four different mappings (at 397, 400, 403, 406 nm) within the UV blue emission of the m-plane MQW, a progressive wavelength blue shift of the maximum intensity is observed along the shell (B region) from ~406 nm near the top of the MQW to ~397 nm at the MQW bottom. The fitting can be performed along the shell axis, as demonstrated in Figure 2c, exhibiting an estimated linear gradient of approximately -1.6 nm/µm (or -11.3 meV/µm) from the top to the bottom. Given the relatively large well thickness (6 nm), quantum confinement effects can be ruled out, and this change can be directly attributed to the In composition.<sup>18,21</sup> Previous results analyzing the emission spectrum of the m-plane MQW<sup>22</sup> suggest that this shift can be attributed to a variation in the indium content. This variation is estimated from the emission values to range from 10% and 8% from the top to the bottom of region B.<sup>22</sup> Note also that the effect of strain on wavelength variation is quite small for deformation values smaller than 1% (See Ref. 22 for the calculation of the m-plane MQW emission and Ref. 23 for the measurements and calculation of the GaN NBE in highly bent microwires). The slight changes in In-composition and thickness are related to the three main mechanisms that explain how the materials are incorporated into the wires. Two of these contributions originate from gas-phase collection with direct impingement from the top -c facet and downward diffusion on the m-facets, as well as upward flow from sidewall facet diffusion. The third pathway corresponds to the flow from the neighboring substrate surface of the wires.<sup>24,25</sup> These kinetic arguments, combined with nucleation
conditions, also explain the size and composition distributions (see later) that may occur in an
assembly of self-organized wires.

Laue diffraction patterns, acquired concurrently with XEOL measurements, can be employed
for qualitative single-spot analysis and quantitative extraction of the deviatoric strain (DS) map to
establish a correlation between structural and optical properties. Figure 3a shows a representative
Laue pattern acquired in the shell region B with multiple indexed GaN and Si reflections (2 s
effective counting time). The peaks of the Si(001) substrate appear elongated along the Y-direction
of the pixel due to a thickness-broadening effect.²⁶ The first step in the analysis is to segment the
GaN and Si contributions. The Si pattern provides an internal reference that should not change
during mapping. It will provide a thorough evaluation of the precision and accuracy of the
complete analytical procedure, which utilizes the instrumental calibration derived from a reference
Ge crystal. The complete indexing diffraction pattern and detailed deviatoric strain tensor
calculations are provided in the *Supporting Information, Section S2*. Peak position refinement
analysis provides direct crystallinity information on orientation, strain, and structural integrity at
the illuminated point.²⁷ The lack of the precise energy value of a given spot prevents the calculation
of all six lattice parameters defining the crystallographic unit cell. Consequently, it is not possible
to determine the volumetric strain, but only the deviatoric strain tensor. It describes the unit cell
by two ratios of lattice constants b/a, c/a, and the angles α, β, and γ between unit cell basis vectors.
The spatial distribution, intensity, and shape of the spots provide information about local
crystallinity. Indeed, in a first approximation, neglecting instrumental broadening from beam
shape and divergence, and tilt of the sample, the Laue spots coming from a thin object should be
circular. Any deviations may result from the distribution of orientation and strain caused by defects
in the ideal crystal structure.

The presence of local structural variations can be identified by analyzing individual reflections.
As a first qualitative analysis, Figure 3b shows the reflection corresponding to the prismatic plane
(-4 4 -3) (estimated energy 7.19 keV) across regions A–E. Circular diffraction spots, such as those
observed in region E, indicate low defect density and high crystalline quality. Region D shows
slight distortions of the circular shape, corresponding to the onset of shell deposition. Region C,
which marks the transition between the microwire stem and the core-shell region, shows a more
severe shape distortion, due to the introduction of defects, roughness, and the overlap between
both core and shell diffraction spots. The A-B regions above the m-plane core-shell structure show
more pronounced distortion and broadenings with facet streaks and interferences. Remarkably, the
appearance of satellite spots can be attributed to the diffraction of the superlattice structure formed
by the MQW layers (see also the streaks centered on the spot, which indicate crystal facets).
Although a thorough examination of the satellite features is outside the purview of this study and
will require further in-depth research in the future, a rough estimation of the lattice periodicity of
the MQW is obtained from the angular distance between the satellites of the -2 2 0 Bragg peak
(see Supporting Information, Section S5). The estimated lattice periodicity value is approximately
14.1 nm at the edge center of the MQW. This value is consistent with the expected value given the
growth conditions. The set of GaN reflection positions for each Laue pattern is determined,
enabling a quantitative measurement of the strain and rotation tensors.²⁸ These positions are then
fitted to a structural model, which incorporates the geometry of the diffraction setup and the five
structural parameters (see the Supporting Information, Section S2). The analysis process can be
divided into several steps, following this sequence:²⁹ Initially, the detection geometry parameters
ensures that the detection geometry is consistent with the expected geometry. The calibration
ensures that the calibration parameters are calibrated using a known crystal. A
Ge(001) wafer is used because it provides a more circular spot than a silicon crystal, thanks to its
higher absorption. The calibration set is provided in the Supporting Information, Section S2. These
parameters are then used in subsequent analyses. The Laue pattern (set of Laue spots positions)
converted into scattering angles) is indexed to correspond with the experimental spots of a given
crystallographic unit cell and the theoretical reflections. This process establishes a raw orientation
matrix of the crystal being studied. The displacement of each diffraction spot is subsequently
calculated from its theoretical position in the absence of strain. Because the photon energy of each
reflection is unknown in polychromatic Laue diffraction, the hydrostatic strain component cannot be accessed.⁵,³⁰ The deviatoric strain is therefore obtained by refining the orientation and distortion of the unit cell, and the accuracy is improved by minimizing the discrepancy between the measured $m_i = (X_{m_i}, Y_{m_i})$ and calculated spot positions $c_i = (X_{c_i}, Y_{c_i})$ on the detector in pixel units. In this way, only distortional strain components are accessible, while hydrostatic contributions remain intrinsically invisible to the method.

To ensure the reliability and accuracy of the results, two quality parameters must be considered: the number of indexed reflections per pattern (NIR) and the residual mean pixel deviation (MPD) between the measured and refined positions on the detector. The MPD value is calculated using the following equation: $MPD = \frac{1}{NIR} \sum_{i=1}^{NIR} \sqrt{(X_{m_i} - X_{c_i})^2 + (Y_{m_i} - Y_{c_i})^2}$.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** (a) Left: example of a single diffraction pattern acquired on a GaN wire dispersed on (001) Si substrate (2 s counting time). Ordinates correspond to pixel numbers (2018x2016), and some indexations are indicated (see more details in the *Supporting Information, Section S2*). Right: evolution of the shape of the (-4 4 -3) GaN peak when crossing the wire at different heights corresponding to the labels of Figure 2a. GaN core and MQW shell maps of (b) the number of indexed reflections (NIR) used for the refinement, and of (c) the residual mean pixel deviation value (MPD), i.e., the fitting figures after determination by least-squares minimization of the orientation matrix and of the deviatoric strain tensor.</figcaption></figure>
The NIR mapping is shown in Figure 3c. The GaN core mean value is 110 (with a standard deviation of 29), and the MQW shell mean value is 18 spots (with a standard deviation of 11), larger than the theoretical minimum requirement of four reflections per pattern to extract the DS tensor.⁵ For the core, the NIR decreases at the border of the wire as less matter interacts with X-rays (NIR=14 for the worst case in the analyzed MQW area). The MPD mapping shown in Figure 3b has a mean value of 0.22 pixels and a standard deviation of 0.09 for the core region, and a mean of 0.49 pixels and a standard deviation of 0.17. This value reflects the reliability of the refinement process, as it is generally accepted in our setup that, for accurate strain determination, the MPD should not exceed 0.5–0.7 pixels. The increase in the mean MPD value observed at the border of the core map is likely related to larger structural heterogeneities, which are discussed later. In the shell region, lower NIR values and higher MPD are also expected because of the weaker diffraction spot intensity and their proximity to the core reflections, resulting in a reduced refinement quality compared to spots originating from the core. For reference, the Ge calibration (NIR = 96, MPD = 0.19) provided in the *Supporting Information, Section S2* can be used for comparison.

The deviatoric strain is extracted from the recorded patterns by selecting a reference value for the GaN lattice parameters, $a = 3.1881$ Å and $c = 5.1844$ Å,³¹ which are derived from the measurement of MOVPE homoepitaxial GaN growth. Estimation of the error bars associated with the analysis process in terms of accuracy and precision is achieved through a meticulous analysis of the monocrystalline Si substrate on which the wire is dispersed. As shown in the *Supporting Information, Section S3*, we achieved a measurement precision of less than $9 \times 10^{-5}$ for all components of the deviatoric strain calculated for the Si substrate, with an accuracy of approximately $4 \times 10^{-4}$.

The deviatoric strain maps are calculated separately for the GaN core and the InGaN/GaN MQW shell (see Figure 4). This separation was made possible by the slight but distinguishable shift observed between the diffraction peaks corresponding to the two regions, allowing independent
refinement of their respective orientation and strain tensors. Additionally, finite element simulations were conducted to enhance the understanding of the measured strain distribution.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
**Figure 4.** Deviatoric strain maps of the (a) GaN core and (b) InGaN/GaN MQW shell of the wire shown in the SEM image on the left. Four strain components are represented: biaxial strain $\varepsilon_{\parallel}$, axial strain $\varepsilon_{\perp}$, in-plane shear strain $\varepsilon_{xy}$, and out-of-plane shear strain $(\varepsilon_{xz} + \varepsilon_{yz})/2$, expressed in the GaN hexagonal basis (a, b, c). Note the small strain scale and the correspondence of the mappings with the (A-E) regions previously discussed in Figures 2 and 3. (c) Representative 3D finite-element simulations corresponding to Region B for a GaN core with a tapered radius and a single InGaN shell with 4.3% indium content, approximating the MQW superlattice as a homogeneous alloy. (d) Comparison between experimental and simulated profiles of biaxial and axial strain along the wire axis for the B region, showing good agreement between the experimental data and the FEM results. The homogeneous In-composition of InGaN/GaN homogeneous shell varies between 3.2-4.3% and the core radius between 0.89-0.98 µm.

Figures 4a and 4b present the deviatoric strain maps of the wire shown in the SEM image. The viewing geometry differs between the top-view SEM observation and the µLaue scan because of the 40° tilt of the sample relative to the incident X-ray beam, as illustrated in Figure 1a. For instance, the semipolar facet visible on the left side of the wire in the SEM image appears on the right side of the corresponding diffraction-based maps. The strain components are expressed in the hexagonal basis of GaN (x, y, z aligned with the a, b, c lattice vectors). The deviatoric strain maps were computed separately for the GaN core and the InGaN/GaN MQW shell. Four components are considered: the biaxial strain $\varepsilon_{\parallel} = (\varepsilon_{xx} + \varepsilon_{yy})/2$, the axial strain $\varepsilon_{\perp} = \varepsilon_{zz}$, the in-plane shear strain $\varepsilon_{xy}$, and the out-of-plane shear strain $(\varepsilon_{xz} + \varepsilon_{yz})/2$. As observed in the zoomed-in images, regions A and C correspond to semipolar facets displaying opposite shear patterns. In region A of the core, the presence of the semipolar facet produces large localized shear strains $\varepsilon_{xy}$ and $(\varepsilon_{xz} + \varepsilon_{yz})/2$ varying between -6.5 × 10⁻⁴ and 13 × 10⁻⁴, while in region C the shear values range from -8 × 10⁻⁴ to 3 × 10⁻⁴. Region B of the m-plane MQW exhibits homogeneous biaxial and axial strain with average values of approximately -3 × 10⁻⁴ and 6 × 10⁻⁴, respectively. In the 13–23 µm GaN
stem, both components relax toward values close to zero, which is in agreement with the reference value for the GaN lattice parameters. The shell components shown in Figure 4b exhibit opposite signs of in-plane and out-of-plane strains, with average values of approximately $\epsilon_{\parallel} = 7 \times 10^{-4}$ and $\epsilon_{\perp} = -14 \times 10^{-4}$. The strain signatures observed in the core and shell are consistent with compressive strain perpendicular to the c-axis and tensile strain parallel to it. This is in agreement with the larger lattice parameter of InN compared to GaN. The upper-right area of the map shows a lower number of indexed pixels, corresponding to semipolar MQWs, considering the 40° sample tilt. The shear components in region B (mean values $\epsilon_{xy} = 6 \times 10^{-4}$ and $(\epsilon_{xz} + \epsilon_{yz})/2 = 1 \times 10^{-5}$) are more difficult to interpret due to the absence of perfectly symmetrical facets (see Figure 5 and the related discussion). This rupture of symmetry can result in overarching tensile or compressive zones, as opposed to balanced distributions deduced from standard elasticity calculations. Figure 4c illustrates 3D finite-element simulations conducted with TiberCAD³²,³³ within the continuum elasticity framework (see the Supporting Information, Section S4 describing the FEM workflow). In these simulations, the MQW shell is approximated as a homogeneous InGaN layer with a mean uniform hexagonal geometry and an indium concentration that varies from 3.2 to 4.3% along the c-axis. This concentration follows the compositional gradient observed experimentally using available XEOL emission data. The GaN core was modelled as having a radius that evolves along the growth direction to reproduce the wire's tapered morphology (ranging from 0.89 to 0.98 µm). Within this framework, the strain distribution is obtained by minimizing the total elastic energy under mechanical equilibrium. Figure 4d shows that the simulated strain components ($\epsilon_{\parallel}$ and $\epsilon_{\perp}$) in the region of the m-plane MQW reproduce the signs and magnitudes of the experimental values, indicating good agreement between the two. The experimental axial strain ranges from approximately $5 \times 10^{-4}$ to $8 \times 10^{-4}$, while the biaxial strain varies from $-4 \times 10^{-4}$ to $-2 \times 10^{-4}$. The finite-element results reproduce this axial trend, confirming the structural origin of the observed strain evolution. However, this model does not account for the semipolar planes present in regions A and C or the expected asymmetry of the hexagonal cross-section¹,¹⁹,²⁰. Therefore, the slight
discrepancies between the experimental and simulated data can be attributed to the associated error
bars in the descriptions of the geometry and composition, as well as the presence of structural
defects such as stacking faults,³⁴ which facilitate local strain relaxation.

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Representation of the precession of the local **c** vector projected on the (u₀, v₀) plane perpendicular to the **c**₀ vector corresponding to the average value of -**c** in the wire.</figcaption></figure>

As mentioned above, it is also important to consider the lattice rotation tensor.³⁵ The epitaxial heterostructures under study are of high monocrystalline quality with no extended defects such as dislocations and grain boundaries, and therefore, the lattice rotations are quite small. Representing the rotation tensor (i.e., orientation matrix) is a difficult task. In Figure 5, we plot the angular deviation (i.e., precession) of the **-c** vector corresponding to the growth axis of the wire as an indicator. To this end, we averaged the orientation of this vector over all wire measurements to obtain a reference **-c**₀, which also defines its perpendicular plane with two lattice vectors u₀ and v₀. As shown in the Figure 5, the bottom of the wire (areas D and E) has a well-defined orientation that varies by less than 0.1° from the reference. The top of the wire (A-B-C) is also affected by the
core-shell heterostructure and exhibits a larger distribution of misorientation. Note that the bonding between the wire and the substrate is strong enough due to the large contact area, preventing movement under the beam (as confirmed by repeatability measurements), unlike what has been observed with smaller GaN wires.²⁷ These observations can be attributed to two main causes. First, the macroscopic orientation of the wire is driven by the van der Waals force between the wire and the Si substrate. This force is defined by the m-plane facets that interact with the (001) surface. However, the shape of the wire with its different misaligned m-plane facets (notably corresponding to the MQW over thickness and the bare stem) can introduce a bending mechanical moment between the bottom (D-E) and top (A-B-C) of the wire. Second, the in-plane section of the wire is not perfectly hexagonal, and the relative MQW thickness can differ on the six m-plane facets. TEM measurements have previously observed this effect²⁰, and can result in a mechanical twisting moment that is not uniform. This moment is responsible for broadening the orientation distribution at the top of the wire.

In addition to the wire previously discussed in detail (called $W_0$), the [Supporting Information, Section S6] provides information on measuring and analyzing the strain and light emission of three other wires ($W_{1,2,3}$) to estimate the variability of the heterostructures for different morphologies in terms of MQW lengths and shapes. The measurement time for each map is approximately 3 hours, and the entire analysis takes about 1 hour. Similar mapping trends can be observed, and quantitative results are summarized in Table 1. Note that the wire radius gradient along region A-B in $W_2$ is doubled, and this wire has a different morphology with a weak transition zone. However, the emission wavelength gradient remains in the range of 0.94 to 1.27 nm/µm for all wires. A comparison of the emission gradient and length in region A-B reveals a potential correlation between these two quantities, suggesting that wavelength control in these emitters imposes short MQW lengths. In terms of the deviatoric $\epsilon_{zz}$ strain gradient, a significant variability is indicated by the fact that the values of $W_0$ and $W_3$ are twice those of $W_1$ and $W_2$, and no significant correlations can be found with other geometrical and optical properties.
<table><caption>**Table 1.** Summary measurements of the morphological parameters of four wires with the emission wavelength gradient of the m-plane MQW and the deviatoric $ε_{zz}$ in-plane strain gradient along the growth axis z (see Figure 4c). The wire $W_0$ is discussed in detail in the text above.</caption><thead><tr><th>Wire name</th><th>W<sub>0</sub></th><th>W<sub>1</sub></th><th>W<sub>2</sub></th><th>W<sub>3</sub></th></tr></thead><tbody><tr><td>Total length (μm)</td><td>23.0</td><td>21.0</td><td>22.3</td><td>21.8</td></tr><tr><td>Bottom - top diameter (μm)</td><td>1.0 - 2.2</td><td>0.7 - 1.8</td><td>1.1 - 2.5</td><td>1.0 - 2.0</td></tr><tr><td>Wire radius gradient along region A-B (%)</td><td>3.8</td><td>3.5</td><td>7.5</td><td>3.5</td></tr><tr><td>Length of region A-B (μm)</td><td>8.8</td><td>7.6</td><td>8.8</td><td>5.4</td></tr><tr><td>Emission wavelength gradient (nm/μm)</td><td>1.34</td><td>1.05</td><td>1.27</td><td>0.94</td></tr><tr><td>Deviatoric ε<sub>zz</sub> strain gradient (×10<sup>-2</sup> μm<sup>-1</sup>)</td><td>0.75</td><td>0.38</td><td>0.31</td><td>0.63</td></tr></tbody></table>

In this study, we conducted a thorough characterization of GaN microwires containing InGaN/GaN multiple quantum wells grown on nonpolar facets without quantum Stark confinement effect. By combining µLaue diffraction, X-ray excited optical luminescence, and X-ray fluorescence with a sub-micrometer polychromatic X-ray beam, we achieved a spatially correlated analysis of the structural and optical properties of individual wires. Single-spot peak shape analysis enabled the qualitative detection of m-plane MQWs, the identification of r-plane facets, and the observation of subtle superlattice-induced features, highlighting the high sensitivity of the µLaue method to semiconductor heterostructures and periodic nanostructures. Meanwhile, hyperspectral XEOL mapping revealed wavelength emission variations at the sub-micrometric scale, associated with local changes in indium composition, MQW optical transitions, and point defects. A correlation was established between the In composition gradient in the quantum wells
(it ranges from 10 to 8% and exhibits a blue shift from top to bottom, respectively), and the measured deviatoric strain components of both the GaN core and the m-plane MQW shell contributions. The strain is tensile along the -c-axis and compressive in the perpendicular plane. Shear strain maps further revealed the spatial signature of semipolar facets. A precise calibration with a single Ge crystal and advanced analysis of the Laue diffraction patterns achieved a precision better than $9 \times 10^{-5}$ and an accuracy of approximately $4 \times 10^{-4}$, as verified using the Si substrate reference on which wires are dispersed. The quantitative values of the strain tensor were verified using the finite element method, in which the MQW shell was approximated as a homogeneous alloy.

Unlike conventional electron-based methods, such as TEM or EBSD, which are limited by sampling depth, angular coverage, and field of view, this multimodal, synchrotron-based approach is a non-destructive, highly spatially resolved means of extracting maps of the full deviatoric strain tensor, averaged over the probed volume. This capability is particularly relevant for complex nanostructures where anisotropic strain fields and compositional gradients play a decisive role in determining device performance. Ultimately, this proof-of-concept study not only showcases the capabilities of this synchrotron-based multimodal characterization but also demonstrates its potential for use in high-throughput screening of materials, process optimization, and growth control of optoelectronic micro and nanostructures, even for tiny deformations. By applying this approach to MOVPE-grown GaN/InGaN microwires, we demonstrate its potential to inform the rational design of next-generation nanodevices, where harmonization of structural precision and optical tunability is crucial at the nanoscale.⁴

■ ASSOCIATED CONTENT

**Supporting Information**

The Supporting Information (PDF) is available free of charge at [https://TTT/doi/XXX](https://TTT/doi/XXX). (Section S1) Experimental setup, instrumental calibration, and wire growth; (Section S2) Calibration procedure, data processing, and strain tensor extraction methodology; (Section S3) Error
estimation from substrate analysis; (Section S4) Finite element method (FEM) calculation;
(Section S5) MQW periodicity estimation from satellite peaks; (Section S6) Additional maps and
analysis: variability of strain and light emission; (Section S7) Raw data, software availability, and
repositories (data, Jupyter notebooks, and codes); (Section S8) References.

The data corresponding to this work can be downloaded from:

https://zenodo.org/records/17381927: F1.zip, F2.zip

https://zenodo.org/records/17064475: RefGe1.zip, F4.zip, F3.zip, Notebooks.zip, FEM.zip

■ AUTHOR INFORMATION

Corresponding Authors

Beatriz de Goes Foschiani – Université Grenoble Alpes, CEA, IRIG, MEM, NRX, 17 rue des Martyrs, 38000 Grenoble, France; [orcid.org/0000-0001-5814-9324](https://orcid.org/0000-0001-5814-9324); Email: [beatriz.degoesfoschiani@cea.fr](mailto:beatriz.degoesfoschiani@cea.fr)

Joël Eymery – Université Grenoble Alpes, CEA, IRIG, MEM, NRX, 17 rue des Martyrs, 38000 Grenoble, France; [orcid.org/0000-0002-4216-1166](https://orcid.org/0000-0002-4216-1166); Email: [joel.eymery@cea.fr](mailto:joel.eymery@cea.fr)

Authors

Sergio Bongiorno – Université Grenoble Alpes, CEA, IRIG, MEM, NRX, 17 rue des Martyrs, 38000 Grenoble, France; [orcid.org/0009-0007-4803-3898](https://orcid.org/0009-0007-4803-3898)

Odile Robach – Université Grenoble Alpes, CEA, IRIG, MEM, NRX, 17 rue des Martyrs, 38000 Grenoble, France; https://pubs.acs.org/0000-0003-2738-7279

Olivier Ulrich – Université Grenoble Alpes, CEA, IRIG, MEM, NRX, 17 rue des Martyrs, 38000 Grenoble, France;

Jean-Sébastien Micha – Univ. Grenoble Alpes, CEA, IRIG, DIESE, SYMMES, 38000 Grenoble Cedex, France; https://pubs.acs.org/0000-0002-2027-8283

ACKNOWLEDGMENT

The authors acknowledge the *Agence Nationale de la Recherche* (ANR) for its financial support
of the MAGNIFIX project n° ANR 21-ESRE-0011 and the management of the French government
grant PEPR-DIADEM/ESRF under the France 2030 program (reference ANR-22-PEXD-0011),
and *the European Synchrotron Radiation Facility (ESRF) for the provision of synchrotron
radiation facilities*. We also like to thank the French Collaborative Research Group of the ESRF
for assistance and support in using beamline BM32. In particular, we thank Samuel Tardif from
CEA for X-ray expertise, Olivier Geaymond and Lucio Martinelli from CNRS, Institut Néel, for
technical help, and Dominique Grand from CNRS, SERAS, for mechanical studies and mounting.
The authors also thank the MOVPE group at CEA, particularly Christophe Durand and Jean
Dussaud, for their help in growing the MOVPE sample.

References:

(1) Kapoor, A.; Guan, N.; Vallo, M.; Messanvi, A.; Mancini, L.; Gautier, E.; Bougerol, C.; Gayral, B.; Julien, F. H.; Vurpillot, F.; Rigutti, L.; Tchernycheva, M.; Eymery, J.; Durand, C. Green Electroluminescence from Radial M-Plane InGaN Quantum Wells Grown on GaN Wire Sidewalls by Metal–Organic Vapor Phase Epitaxy. *ACS Photonics* 2018, 5 (11), 4330–4337. https://doi.org/10.1021/acsphotonics.8b00520.

(2) Salomon, D.; Dussaigne, A.; Lafossas, M.; Durand, C.; Bougerol, C.; Ferret, P.; Eymery, J. Metal Organic Vapour-Phase Epitaxy Growth of GaN Wires on Si (111) for Light-Emitting Diode Applications. *Nanoscale Res. Lett.* 2013, 8. https://doi.org/10.1186/1556-276X-8-61.

(3) Bugallo, A. D. L.; Rigutti, L.; Jacopin, G.; Julien, F. H.; Durand, C.; Chen, X. J.; Salomon, D.; Eymery, J.; Tchernycheva, M. Single-Wire Photodetectors Based on InGaN/GaN Radial Quantum Wells in GaN Wires Grown by Catalyst-Free Metal-Organic Vapor Phase Epitaxy. *Appl. Phys. Lett.* 2011, 98 (23), 233107. https://doi.org/10.1063/1.3596446.

(4) Tamura, N.; MacDowell, A. A.; Spolenak, R.; Valek, B. C.; Bravman, J. C.; Brown, W. L.; Celestre, R. S.; Padmore, H. A.; Batterman, B. W.; Patel, J. R. Scanning X-Ray Microdiffraction with Submicrometer White Beam for Strain/Stress and Orientation Mapping in Thin Films. *J. Synchrotron Radiat.* 2003, 10 (2), 137–143. https://doi.org/10.1107/S0909049502021362.

(5) Chung, J.-S.; Ice, G. E. Automated Indexing for Texture and Strain Measurement with Broad-Bandpass x-Ray Microbeams. *J. Appl. Phys.* 1999, 86 (9), 5249–5255. https://doi.org/10.1063/1.371507.

(6) Barabash, R. I.; Ice, G. E.; Roder, C.; Budai, J.; Liu, W.; Figge, S.; Einfeldt, S.; Hommel, D.; Davis, R. F. Characterization of Growth Defects in Thin GaN Layers with X-Ray Microbeam. *Phys. Status Solidi B* 2007, 244 (5), 1735–1742. https://doi.org/10.1002/pssb.200675113.

(7) Purushottam Raj Purohit, R. R. P.; Tardif, S.; Castelnau, O.; Eymery, J.; Guinebretière, R.; Robach, O.; Ors, T.; Micha, J.-S. LaueNN: Neural-Network-Based Hkl Recognition of Laue Spots and Its Application to Polycrystalline Materials. *J. Appl. Crystallogr.* 2022, 55 (4), 737–750. https://doi.org/10.1107/S1600576722004198.
(8) Hageraats, S.; Keune, K.; Stanescu, S.; Laurent, J.-M.; Fresquet, W.; Thoury, M. Combining X-Ray Excited Optical Luminescence and X-Ray Absorption Spectroscopy for Correlative Imaging on the Nanoscale. *J. Synchrotron Radiat.* **2021**, *28* (6), 1858–1864. https://doi.org/10.1107/S1600577521009450.

(9) Levcenko, S.; Biller, R.; Pfeiffelmann, T.; Ritter, K.; Falk, H. H.; Wang, T.; Siebentritt, S.; Welter, E.; Schnohr, C. S. High-Resolution YEOL Spectroscopy Setup at the X-Ray Absorption Spectroscopy Beamline P65 of PETRA III. *J. Synchrotron Radiat.* **2022**, *29* (5), 1209–1215. https://doi.org/10.1107/S1600577522007287.

(10) Tolentino, H. C. N.; Geraldes, R. R.; Da Silva, F. M. C.; Guaita, M. G. D.; Camarda, C. M.; Szostak, R.; Neckel, I. T.; Teixeira, V. C.; Hesterberg, D.; Pérez, C. A.; Galante, D.; Callefo, F.; Neto, A. C. P.; Kofukuda, L. M.; Sotero, A. P. S.; Moreno, G. B. Z. L.; Luiz, S. A. L.; Bueno, C. S. N. C.; Lena, F. R.; Westfahl, H. The CARNAÚBA X-Ray Nanospectroscopy Beamline at the Sirius-LNLS Synchrotron Light Source: Developments, Commissioning, and First Science at the TARUMÀ Station. *J. Electron Spectrosc. Relat. Phenom.* **2023**, *266*, 147340. https://doi.org/10.1016/j.elspec.2023.147340.

(11) Ren, Z.; Cornelius, T. W.; Leclere, C.; Davydok, A.; Micha, J.-S.; Robach, O.; Richter, G.; Thomas, O. First Stages of Plasticity in Three-Point Bent Au Nanowires Detected by *in Situ* Laue Microdiffraction. *Appl. Phys. Lett.* **2020**, *116* (24), 243101. https://doi.org/10.1063/5.0012816.

(12) Martinez-Criado, G.; Segura-Ruiz, J.; Alen, B.; Eymery, J.; Rogalev, A.; Tucoulou, R.; Homs, A. Exploring Single Semiconductor Nanowires with a Multimodal Hard X-Ray Nanoprobe. *Adv. Mater.* **2014**, *26* (46), 7873–7879. https://doi.org/10.1002/adma.201304345.

(13) Salomon, D.; Messanvi, A.; Eymery, J.; Martínez-Criado, G. Silane-Induced N-Polarity in Wires Probed by a Synchrotron Nanobeam. *Nano Lett.* **2017**, *17* (2), 946–952. https://doi.org/10.1021/acs.nanolett.6b04291.

(14) Britton, T. B.; Hickey, J. L. R. Understanding Deformation with High Angular Resolution Electron Backscatter Diffraction (HR-EBSD). *IOP Conf. Ser. Mater. Sci. Eng.* **2018**, *304*, 012003. https://doi.org/10.1088/1757-899X/304/1/012003.

(15) Vilalta-Clemente, A.; Naresh-Kumar, G.; Nouf-Allehiani, M.; Gamarra, P.; di Forte-Poisson, M. A.; Trager-Cowan, C.; Wilkinson, A. J. Cross-Correlation Based High Resolution Electron Backscatter Diffraction and Electron Channelling Contrast Imaging for Strain Mapping and Dislocation Distributions in InAlN Thin Films. *Acta Mater.* **2017**, *125*, 125–135. https://doi.org/10.1016/j.actamat.2016.11.039.

(16) Ernould, C.; Taupin, V.; Beausir, B.; Fundenberger, J. J.; Maloufi, N.; Guyon, J.; Bouzy, E. Characterization of a Nanopipe Dislocation in GaN by Means of HR-EBSD and Field Dislocation Mechanics Analysis. *Mater. Charact.* **2022**, *194*, 112351. https://doi.org/10.1016/j.matchar.2022.112351.

(17) Kociak, M.; Zagonel, L. F. Cathodoluminescence in the Scanning Transmission Electron Microscope. *Ultramicroscopy* **2017**, *176*, 112–131. https://doi.org/10.1016/j.ultramic.2017.03.014.

(18) Koester, R.; Hwang, J.-S.; Salomon, D.; Chen, X.; Bougerol, C.; Barnes, J.-P.; Dang, D. L. S.; Rigutti, L.; de Luna Bugallo, A.; Jacopin, G.; Tchernycheva, M.; Durand, C.; Eymery, J. M-Plane Core–Shell InGaN/GaN Multiple-Quantum-Wells on GaN Wires for
Electroluminescent Devices. Nano Lett. 2011, 11 (11), 4839-4845.
https://doi.org/10.1021/nl202686n.

(19) Messanvi, A.; Zhang, H.; Neplokh, V.; Julien, F. H.; Bayle, F.; Foldyna, M.; Bougerol, C.; Gautier, E.; Babichev, A.; Durand, C.; Eymery, J.; Tchernycheva, M. Investigation of Photovoltaic Properties of Single Core-Shell GaN/InGaN Wires. ACS Appl. Mater. Interfaces 2015, 7(39), 21898-21906. https://doi.org/10.1021/acsami.5b06473.

(20) Kishino, K.; Ishizawa, S. Selective-Area Growth of GaN Nanocolumns on Si(111) Substrates for Application to Nanocolumn Emitters with Systematic Analysis of Dislocation Filtering Effect of Nanocolumns. Nanotechnology 2015, 26 (22), 225602.
https://doi.org/10.1088/0957-4484/26/22/225602.

(21) Orsal, G.; Gmili, Y. E.; Fressengeas, N.; Streque, J.; Djerboub, R.; Moudakir, T.; Sundaram, S.; Ougazzaden, A.; Salvestrini, J. P. Bandgap Energy Bowing Parameter of Strained and Relaxed InGaN Layers. Opt. Mater. Express 2014, 4 (5), 1030-1041.
https://doi.org/10.1364/OME.4.001030.

(22) Salomon, D. Croissance, propriétés optiques et intégration d'hétérostructures radiales InGaN/GaN autour de fils auto-assemblés de GaN crûs sur saphir et silicium, Université Grenoble Alpes, Grenoble, 2013. https://theses.fr/2013GRENY052.

(23) Sharov, V.; Pavlov, A.; Eliseyev, I.; Moskalev, M.; Komarov, S.; Novikova, K.; Alekseev, P.; Kapoor, A.; Eymery, J.; Durand, C.; Tchernycheva, M.; Davydov, V.; Mukhin, I. Nanoscale Welding and Strain-Engineered Photoluminescence of GaN Nanowires. Adv. Opt. Mater. n/a (n/a), e01821. https://doi.org/10.1002/adom.202501821.

(24) Eymery, J.; Chen, X.; Durand, C.; Kolb, M.; Richter, G. Self-Organized and Self-Catalyst Growth of Semiconductor and Metal Wires by Vapour Phase Epitaxy: GaN Rods versus Cu Whiskers. Comptes Rendus Phys. 2013, 14 (2-3), 221-227.
https://doi.org/10.1016/j.crhy.2012.10.009.

(25) Ruth, V.; Hirth, J. P. Kinetics of Diffusion-Controlled Whisker Growth. J. Chem. Phys. 1964, 41 (10), 3139-3149. https://doi.org/doi:10.1063/1.1725687.

(26) Tardif, S.; Gassenq, A.; Guilloy, K.; Pauc, N.; Osvaldo Dias, G.; Hartmann, J.-M.; Widiez, J.; Zabel, T.; Marin, E.; Sigg, H.; Faist, J.; Chelnokov, A.; Reboud, V.; Calvo, V.; Micha, J.-S.; Robach, O.; Rieutord, F. Lattice Strain and Tilt Mapping in Stressed Ge Microstructures Using X-Ray Laue Micro-Diffraction and Rainbow Filtering. J. Appl. Crystallogr. 2016, 49 (5), 1402-1411. https://doi.org/10.1107/S1600576716010347.

(27) Auzelle, T.; Biquard, X.; Bellet-Amalric, E.; Fang, Z.; Roussel, H.; Cros, A.; Daudin, B. Unraveling the Strain State of GaN down to Single Nanowires. J. Appl. Phys. 2016, 120 (22), 225701. https://doi.org/10.1063/1.4971967.

(28) Beamline BM32 ESRF. LaueTools GitHub, 2025. https://github.com/BM32ESRF/lauetools (accessed 2025-08-07).

(29) Petit, J.; Castelnau, O.; Bornert, M.; Zhang, F. G.; Hofmann, F.; Korsunsky, A. M.; Faurie, D.; Le Bourlot, C.; Micha, J. S.; Robach, O.; Ulrich, O. Laue-DIC: A New Method for Improved Stress Field Measurements at the Micrometer Scale. J. Synchrotron Radiat. 2015, 22 (4), 980-994. https://doi.org/10.1107/S1600577515005780.

(30) Abboud, A.; Kirchlechner, C.; Keckes, J.; Conka Nurdan, T.; Send, S.; Micha, J. S.; Ulrich, O.; Hartmann, R.; Strüder, L.; Pietsch, U. Single-Shot Full Strain Tensor Determination with
Microbeam X-Ray Laue Diffraction and a Two-Dimensional Energy-Dispersive Detector. *J. Appl. Crystallogr.* **2017**, *50*(3), 901–908. https://doi.org/10.1107/S1600576717005581.

(31) Leszczynski, M.; Teisseyre, H.; Suski, T.; Grzegory, I.; Bockowski, M.; Jun, J.; Porowski, S.; Pakula, K.; Baranowski, J. M.; Foxon, C. T.; Cheng, T. S. Lattice Parameters of Gallium Nitride. *Appl. Phys. Lett.* **1996**, *69*(1), 73–75. https://doi.org/10.1063/1.118123.

(32) Auf Der Maur, M.; Povolotskyi, M.; Sacconi, F.; Pecchia, A.; Romano, G.; Penazzi, G.; Di Carlo, A. TiberCAD: Towards Multiscale Simulation of Optoelectronic Devices. *Opt. Quantum Electron.* **2008**, *40*(14–15), 1077–1083. https://doi.org/10.1007/s11082-009-9272-7.

(33) *tiberCAD / DEVELOPER COMMUNITY*. http://www.tibercad.org/ (accessed 2025-10-14).

(34) Mancini, L.; Hernández-Maldonado, D.; Lefebvre, W.; Houard, J.; Blum, I.; Vurpillot, F.; Eymery, J.; Durand, C.; Tchernycheva, M.; Rigutti, L. Multi-Microscopy Study of the Influence of Stacking Faults and Three-Dimensional In Distribution on the Optical Properties of m-Plane InGaN Quantum Wells Grown on Microwire Sidewalls. *Appl. Phys. Lett.* **2016**, *108*(4), 042102. https://doi.org/10.1063/1.4940748.

(35) Boullier, A.-M.; Robach, O.; Ildefonse, B.; Barou, F.; Mainprice, D.; Ohtani, T.; Fujimoto, K. High Stresses Stored in Fault Zones: Example of the Nojima Fault (Japan). *Solid Earth* **2018**, *9*(2), 505–529. https://doi.org/10.5194/se-9-505-2018.