Structural and optical emission uniformity of m-plane InGaN single quantum wells in core-shell nanorods

Controlling the long-range homogeneity of core-shell InGaN/GaN layers is essential for their use in lightemitting devices. This paper demonstrates variations in optical emission energy as low as ~7 meV.m along the m-plane facets from core-shell InGaN/GaN single quantum wells as measured through high-resolution cathodoluminescence hyperspectral imaging. The layers were grown by metal organic vapor phase epitaxy on etched GaN nanorod arrays with a pitch of 2 m. High-resolution transmission electron microscopy and spatially-resolved energy-dispersive X-ray spectroscopy measurements demonstrate a long-range InN-content and thickness homogeneity along the entire 1.2 μm length of the m-plane. Such homogeneous emission was found on the m-plane despite the observation of short range compositional fluctuations in the InGaN single quantum well. The ability to achieve this uniform optical emission from InGaN/GaN coreshell layers is critical to enable them to compete with and replace conventional planar light-emitting devices. InGaN/GaN core-shell nanorod light emitting diodes (LEDs) have the potential to overcome the limitations of current-generation planar devices. Core-shell structures aligned along the [0001] c-axis can be grown with largearea {10-10} m-plane sidewalls to create dominant non-polar surfaces for growing LED structures, thereby eliminating the quantum confined Stark effect (QCSE) and its deleterious effect on the internal quantum efficiency, especially for wide quantum wells (QWs). The large surface area of high-aspect nanorods (NRs) brings the further advantage that carrier density in the active region is lower for a given injection current and so provides scope to reduce efficiency droop. In addition, core-shell LEDs also offer fast switching speeds due to the shorter carrier lifetimes in polarization-free structures for applications in short-range visible light communication. Realizing these advantages requires the formation of uniform InGaN/GaN QWs on the m-plane sidewalls of high-aspect-ratio NRs. However, the growth of such InGaN QWs on NRs often suffers from a gradient in InGaN composition and thickness along the non-polar length of the nanorods. While this phenomenon can be exploited for applications requiring broad absorption or emission bands, it will lead to strong emission wavelength shifts with drive current. More homogeneous emission is required in LEDs than has been reported and the current literature suffers from a lack of correlation between the structural and the optical properties of the core-shell structure. GaN cores can be obtained by bottom-up epitaxial growth or top-down etching of planar layers. Several approaches have been used to grow bottom-up NRs: VaporLiquid-Solid (VLS) growth, involving a catalyst droplet to trigger the vertical or oblique growth; self-assembled growth, requiring particular growth conditions such as low V/III ratio, silane doping or high temperature in order to enhance the vertical growth on nucleated GaN islands; and selective area growth, either combined with a pulsedgrowth mode, or via continuous-flow growth. Homogeneous GaN NR arrays have been obtained using selective area growth combined with a pulsed-growth mode, or via continuous-flow growth on either N-polar or Ga-polar substrates. These methods have the advantage of producing defect-free NRs beyond the initial nucleation step. The top-down approach, while creating the cores from defective planar templates, has the benefit of giving rise to highly-uniform GaN NR arrays as a result of controlled etching and facet re-growth processes. This is advantageous for fabricating devices with higher yield and easier scalability to production systems by reducing the demanding requirements of a bottom-up growth process. It is important to note that etched GaN nanorods, depending on their diameter and density, can also be free of dislocations. This paper reports quantitative structural and optical studies on InGaN/GaN core-shell structures grown on etched NR arrays. Long-range optical emission and structural uniformity of the InGaN m-plane QW was achieved on a 2000 nm pitch hexagonal NR array. Previous work showed that InGaN growth on the sidewalls of tall (4000 nm high), 400 nm diameter GaN nanorods with a 600 nm pitch resulted in a decreasing InN-incorporation on their m-plane sidewalls from top to bottom. Therefore the NR array geometry and pitch are useful parameters for optimizing the epitaxial growth of GaN/InGaN core-shell structures. The results reported here demonstrate that QW uniformity is not a limiting factor for this device architecture. EXPERIMENTAL SECTION GaN/AlN/Si NR arrays on silicon were fabricated using a top-down approach from conventional c-plane GaN-onsilicon templates grown by metal organic vapor phase epitaxy (MOVPE). The total III-nitride thickness, including AlN-based nucleation and alloy grading layers, was ~1.8 μm. Further information on sample fabrication and preparation can be found in the ‘Experimental Details’ section. The scanning electron microscopy (SEM) image in Figure 1 shows a cross-section through the GaN/AlN/Si NR array after plasma etching. The template has been etched completely through the III-nitride layers into the Si sub-

InGaN/GaN core-shell nanorod light emitting diodes (LEDs) have the potential to overcome the limitations of current-generation planar devices. Core-shell structures aligned along the [0001] c-axis can be grown with largearea {10-10} m-plane sidewalls to create dominant non-polar surfaces for growing LED structures, thereby eliminating the quantum confined Stark effect (QCSE) and its deleterious effect on the internal quantum efficiency, especially for wide quantum wells (QWs). The large surface area of high-aspect nanorods (NRs) brings the further advantage that carrier density in the active region is lower for a given injection current and so provides scope to reduce efficiency droop. 1 In addition, core-shell LEDs also offer fast switching speeds due to the shorter carrier lifetimes in polarization-free structures for applications in short-range visible light communication. 2 Realizing these advantages requires the formation of uniform InGaN/GaN QWs on the m-plane sidewalls of high-aspect-ratio NRs. However, the growth of such InGaN QWs on NRs often suffers from a gradient in InGaN composition and thickness along the non-polar length of the nanorods. [3][4][5][6] While this phenomenon can be exploited for applications requiring broad absorption or emission bands, it will lead to strong emission wavelength shifts with drive current. More homogeneous emission is re-quired in LEDs than has been reported and the current literature suffers from a lack of correlation between the structural and the optical properties of the core-shell structure.
GaN cores can be obtained by bottom-up epitaxial growth or top-down etching of planar layers. Several approaches have been used to grow bottom-up NRs: Vapor-Liquid-Solid (VLS) growth, involving a catalyst droplet to trigger the vertical or oblique growth; 7,8 self-assembled growth, requiring particular growth conditions such as low V/III ratio, silane doping or high temperature in order to enhance the vertical growth on nucleated GaN islands; [9][10][11][12] and selective area growth, either combined with a pulsedgrowth mode, 4,13 or via continuous-flow growth. 14 Homogeneous GaN NR arrays have been obtained using selective area growth combined with a pulsed-growth mode, 15 or via continuous-flow growth on either N-polar [16][17][18] or Ga-polar substrates. [19][20][21] These methods have the advantage of producing defect-free NRs beyond the initial nucleation step. The top-down approach, while creating the cores from defective planar templates, has the benefit of giving rise to highly-uniform GaN NR arrays as a result of controlled etching and facet re-growth processes. 22 This is advantageous for fabricating devices with higher yield and easier scalability to production systems by reducing the demand-ing requirements of a bottom-up growth process. It is important to note that etched GaN nanorods, depending on their diameter and density, can also be free of dislocations. 23 This paper reports quantitative structural and optical studies on InGaN/GaN core-shell structures grown on etched NR arrays. Long-range optical emission and structural uniformity of the InGaN m-plane QW was achieved on a 2000 nm pitch hexagonal NR array. Previous work showed that InGaN growth on the sidewalls of tall (4000 nm high), 400 nm diameter GaN nanorods with a 600 nm pitch resulted in a decreasing InN-incorporation on their m-plane sidewalls from top to bottom. 24 Therefore the NR array geometry and pitch are useful parameters for optimizing the epitaxial growth of GaN/InGaN core-shell structures. The results reported here demonstrate that QW uniformity is not a limiting factor for this device architecture.

EXPERIMENTAL SECTION
GaN/AlN/Si NR arrays on silicon were fabricated using a top-down approach from conventional c-plane GaN-onsilicon templates grown by metal organic vapor phase epitaxy (MOVPE). The total III-nitride thickness, including AlN-based nucleation and alloy grading layers, was ~1.8 μm. Further information on sample fabrication and preparation can be found in the 'Experimental Details' section. The scanning electron microscopy (SEM) image in Figure 1 shows a cross-section through the GaN/AlN/Si NR array after plasma etching. The template has been etched completely through the III-nitride layers into the Si substrate. Due to the physical etching and ion bombardment, the NRs are slightly tapered and suffer from sidewall roughness. It is therefore necessary to recover a smooth GaN surface using a GaN epitaxial regrowth step prior to subsequent growth of the InGaN layer. 22 The result of this first growth step is to produce faceted NRs typically bound by {10-10} and {10-11} planes with the latter intersected by a (0001) plane if the NR is truncated. If the starting GaN template is grown on a Si substrate, Ga melt-back etching of the latter must be avoided to achieve selective growth on the III-nitride surfaces only. Consequently, the etched NR array was first subjected to a high-temperature annealing (1050°C) in NH 3 atmosphere to achieve thermal nitridation of the Si surface.
The morphology of the GaN/AlN/Si NR array after GaN over-growth is shown in the SEM images of Figure 2 where it can be seen that growth only occurs on the exposed IIInitride surfaces. Further, the lateral steps and absence of obvious faceting on the AlN-containing layers indicates that the lateral overgrowth on these layers is substantially lower than on the GaN section of the NRs. After the GaN over-growth step, the NR morphology can be clearly resolved, consisting of six smooth m-plane facets {10-10}, six semi-polar facets {10-11} and a c-plane facet (0001) truncating the top pyramidal nanostructure.
Three samples of the faceted GaN NRs were then overgrown with an InGaN shell at temperatures of: 750°C, 700°C and 650°C respectively, followed by a GaN capping layer that is identical in all three samples. Further growth parameters can be found in the 'Experimental Details' section.

RESULTS AND DISCUSSION
Analysis of the structural properties of the InGaN shells involved performing cross-sectional scanning transmission electron microscopy (STEM) 25 and energy dispersive x-ray (EDX) spectroscopy. 26 Figure 3a shows a reconstruction of multiple high-angle annular dark-field (HAADF) STEM images, taken along the [11][12][13][14][15][16][17][18][19][20] direction, stitched together in order to show a complete set of facets of the GaN/InGaN core-shell. The structure shown in Figure 3a   showing the homogeneous thickness of the InGaN well from top to the base. Images showing b) the interface between semi-polar and non-polar m-plane c) the middle, and d) the base of the NR. e) Atomic resolution image of the m-plane InGaN/GaN interface for the sample grown at 700°C. The inset shows a magnified image of the interface between the GaN core and the InGaN QW. Scale bars in bd) are 50 nm. Images were taken along the [11][12][13][14][15][16][17][18][19][20] direction.
The thickness of the InGaN layer was found to differ from one facet to another. Starting at the top of the NR, the layer thickness was 20 nm on the residual (0001) c-plane, 8 nm on the upward facing {1-101} semi-polar facet, between 10-11 nm on the {10-10} m-plane and 11 nm on the downward facing {-1101} semi-polar planes. In comparison to QWs in a conventional c-plane MQWs LED, all can be classified as a wide single quantum well (SQW), being wider than the expected exciton Bohr radius. 27 Although not resolvable in Figure 3, accurate measurements of the InGaN SQW thickness, obtained every 20 nm along the entire 1200 nm length of the m-plane, reveal a slight increase of the thickness from the bottom to the top, from 10 nm to 11 nm up the NR. This 10% increase compares well with the 14% gradient of thickness reported elsewhere for a similar GaN/InGaN structure grown on a sparser GaN NR array. 28 Figure 3d, obtained from the lower part of the NR, also indicates an aggregation of InGaN at the interface between the etched AlN and the -c-plane. The thickness of the GaN cap layer was very thin, approximately 1 nm on the semipolar {10-11} plane and about 7-8 nm on the m-plane.
Atomic resolution images obtained of the m-plane InGaN/GaN QW grown at 700°C provided no evidence that dislocations are formed at the interfaces. A representative image is shown in Figure 3e. Thus, while the etched cores may contain threading dislocations the regrowth process appeared not to introduce new dislocations that could reduce the lifetime of carriers in the QW.
Further examination of the HAADF images shows that the morphology of the InGaN layers is strongly dependent on the growth facet. This can be seen most clearly in Figure  3b, showing the inter-section between the {1-101} plane and the m-plane. The {1-101} plane SQW remains smooth whereas the outer surface of the m-plane appears somewhat roughened. This was a feature of both 700°C and 650°C samples.
The InGaN alloy composition within the SQWs was examined by EDX spectroscopy. 26 Figure 4 shows typical EDX maps of the InN fraction for the {1-101} and m-planes for the samples grown at 650°C and 700°C. They clearly reveal the facet-dependence of the InN fraction and the relative degree of homogeneity. These EDX maps show that the InGaN SQW on the {1-101} plane is uniform in both the inplane and cross-well directions, whereas this is not the case for the m-plane SQW.  The lack of roughness on the {1-101} plane SQW indicates that the growth mechanism is not the same on the m-plane. The {1-101} planes evolve by a self-limiting process during the initial GaN facet recovery growth step performed after etching the NR cores whereas the m-planes evolve from the slightly tapered etched NR sidewalls. Incomplete recovery of the m-planes from the tapered sidewalls is equivalent to a slight mis-cut which could lead to a modification of the InN composition and dual emission. 29,30 Other factors that could contribute to the roughness of the InGaN shell include facet-dependent variations in the indium sticking coefficient and pseudomorphic strain. There is also evidence for increased InN incorporation at the apices between the facets, such as between {1-101} and m-plane. Understanding the complexity in the InGaN shell growth is the subject of ongoing investigation.
From an applications perspective, the longer range variations in InN fraction of the SQW are important. Therefore, the variation of InN content along the length of the rod was examined by taking EDX maps from near the top, middle and base of the m-plane facet and by comparing the average values within each map. Quantatitive analysis of the InN fraction down the length of the mplanes was achieved by creating cross-well average profiles from 80-100 nm segments at the different positions along the m-plane. This process resulted in the formation of radial profiles of the average InN mole fraction (see sketch in Figure 5a) at the top, middle and bottom of a typical coreshell NR, to provide a test for the long-range uniformity of the InN mole fraction rather than its local homogeneity.
Each row of pixels within the map was statistically analyzed to provide the average as well as the standard deviation as a measure of the uncertainty. Figure 5b shows crosswell profiles of the InN fraction in the SQW grown at 700°C formed on the m-plane measured at three different positions along its length. Within experimental error the profiles lie on top of each other, thus demonstrating the uniformity of the locally-averaged InN fraction down the entire length of the m-plane facet. Figure 5c shows the same is true for the sample grown at 650°C.
As a comparison, Figure 5d shows the cross-well profile for the semi-polar {1-101} facets measured at two locations for the sample grown at 650°C. The data confirm the result in Figure 3 that the SQW formed on the {1-101} facets is narrower than that formed on the m-planes. However, the InN incorporation on the {1-101} planes is higher at 21.5 at.% (peak value) compared to 18.6 at.% on the m-plane in the 650°C sample. The change of InN content with decreasing temperature on the {1-101} planes from 18.5 to 21.5 at.% is less pronounced than on the m-plane (10.3 to 18.6 at.%), but is similar to previous observations by Wernicke et al., which imply a saturation of InN fraction with reducing growth temperature, albeit at higher values of ~30 at.%. 31 This could be explained by the use in this work of TMGa rather than TEGa, since it does not decompose as efficiently at low temperature.
The estimated long-range variation in spatially-averaged InN fraction along the m-plane is ~0.4 at.% and lies within the experimental errors. This can be compared with the estimated short-range variations of ~2 at.% and ~2.5 at.% for 700°C and 650°C respectively, due to the In-rich fluctuations observable in Figures 4b-c. As such, the fabrication process reported here has resulted in the formation of InGaN/GaN SQW core-shell structures in which the mplane optical properties are likely to be more governed by the local, nanoscale properties of the SQW rather than by the vertical gradients in the InN mole fraction along the vertical axis of the NRs. The uniformity of the optical emission of the GaN/InGaN/GaN core-shell structures was assessed by room-temperature high-resolution cathodoluminescence (CL) hyperspectral imaging. 32 The measurement conditions can be found in the 'Experimental Details' section. The secondary electron images in Figures 6a-c show the field of view and measurement geometry for the CL hyperspectral datasets obtained. The mean cathodoluminescence spectrum for the whole field of view for the three samples grown at different InGaN growth temperatures is shown in Figure 6j. Two separated peaks can clearly be distinguished in each spectrum, with the more intense peaks being centered at 3.13 eV, 3.05 eV and 2.63 eV and the lower intensity peaks centered at 2.55 eV, 2.45 eV and 2.30 eV for the samples grown at 750°C, 700°C and 650°C, respectively. The decrease in growth temperature led to a clear red-shift of both peaks, as expected from the increase in the InN fraction with decreasing growth temperature found from the EDX measurements.
Integrating over each of these main peaks within the CL dataset allows maps to be generated that show the origin of the luminescence peak. These are shown in Figures 6d-e for the two peaks in the 750°C sample, Figures 6f-g for the 700°C sample and Figures 6h-i for the 650°C sample. By examining the spatial dependence of the emission, it can be seen that the higher-energy emission peaks arise from the m-plane while the lower-energy peaks arise both from the {1-101} plane facets and from the facet intersections, both m-planem-plane and {1-101} planem-plane (Figures 6c-i). Emission arising from the m-plane was always found to be brighter than that from either {1-101} plane facets or apices.
Several factors can contribute to the weaker intensity emission from the semi-polar plane. These include the presence of the QCSE, non-optimum growth conditions for this InN fraction and the higher number of structural defects that have been reported in similar structures. 6 There are a number of explanations for the lower-energy emission observed at the apices; firstly it is possible that between the m-planes very small a-plane facets have been created which have been shown to emit at lower energy than the corresponding m-plane, 33 though this is not seen in the SEM images. Secondly, strain relaxation will occur at the apices, which can lead to the preferential integration of InN, 34 as well as a reduction of the lattice deformation contribution to the fundamental energy band gaps of the materials comprising the local SQW. 35,36 In order to understand the further factors contributing to the lineshape of the emission from the m-plane facets, the normalized emission from the m-planes of several different nanorods within the field of view are shown in Figure 6k and 6l at 700°C and 650°C respectively. These figures show that m-plane emission from NR to NR is very uniform, and that the shape of the emission peak arises from effects within individual NRs.  photon energy as a result of a gradient in indium composition is often found, 5,38 for example, by as much as 230 meV.m -1 .
The weaker emission found at the base of the nanorod can be explained by the higher number of dislocations expected in this region. An indication of this can be seen in the contrast in the HAADF STEM image in Figure 3d where lines (indicated by white arrows) can be seen propagating from the core towards the m-plane.
Within the m-plane emission band resonances can be observed (dark red at 2.58 eV in Figure 7c) due to optical cavity modes (either whispering gallery or Fabry-Perot) which arise due to the nanorod geometry. 39 Individual spectra taken along the linescan (Figure 7d) show resonances appearing and disappearing along the length of the NR. The presence of these optical resonance modes in the CL spectrum makes it difficult to observe any underlying gradient in the energy of emission from the m-plane. To overcome this, we instead calculate the centroid energy over the energy range of this m-plane emission peak to provide a statistical measure of any shift in the peak. 40 This was calculated for a line-scan on each of the complete nanorods displayed in Figure 6 and is shown in Figure 8 against distance along the m-plane facet. For an individual nanorod the centroid energy oscillates, most likely due to the different cavity modes that come into and out of resonance. Neighboring nanorods have a similar overall dependence, but can have different sets of resonances. This leads to a set of oscillatory energies surrounding a linear mean dependence with distance, represented by the dashed lines in Figure 8. These lines indicate that the emission shifts to higher energy closer to the bottom of the nanorods, and this shift is more pronounced as the temperature decreases, from 7 meV.m -1 at 750°C to 36 meV.m -1 at 700°C to 40 meV.m -1 at 650°C. The cause of this shift is likely due to gas-phase diffusion on which the growth of InGaN on three-dimensional structures is expected to depend, whereby increased diffusion of the In precursors at the higher temperatures leads to an increase in the uniformity.  The optical emission energy from InGaN/GaN-based QWs will be determined by the bandgap of the InGaN well, the electron and hole confinement energies and any redshift caused by the QCSE. For the non-polar m-plane, there is no polarization field, therefore the QCSE is zero. An upper limit for the confinement energies can be obtained from the simple infinite QW model, = ℏ 2 2 2 ⁄ , using electron and hole effective masses of * ~0 .2 0 and ℎ * ~0 .8 0 and L being the thickness of the SQW. This gives a total confinement energy of ~24 meV for a 10 nm QW. Measurements of the QW width using HAADF STEM show the thickness changing from 10 nm to 11 nm along the ~1 m high m-plane. This variation is calculated to have only a small effect on the QW confinement energies of the order of a few meV and can be neglected with regards to the centroid emission energy variation, which is significantly greater, at around 50 meV as shown in Figure 8.  41 The calculated bandgap versus InN mole fraction curves are shown in Figure 9 alongside the two experimental data points from the non-polar m-plane for the two samples grown at 700°C and 650°C, as determined by CL and EDX as described above. The results in Figure 9 indicate that the QW grown is partially-relaxed. Comparing with the literature, strain measurements of In x Ga 1-x N/GaN core-shell NRs with x~30 at.% showed that they are almost fully strained for a thickness of 9 nm, whereas they are plastically relaxed through the generation of misfit dislocations for a thickness of 23 nm. 34 In contrast, the data in Figure 9 imply our structures are partially relaxed for lower InGaN layer thicknesses and InN fraction.
As no misfit dislocations were found through TEM analysis, it is unlikely that strain relaxation in the InGaN layer has occurred via plastic deformation, rather by elastic relaxation. An alternative explanation for the data in Figure  9 could be that the CL emission originates from the InNrich regions within the QW. This would mean that the experimental data points would shift to higher InN fractions by an amount reflecting the magnitude of the short-range variations, ~2-2.5 at.% as stated previously. Using half this peak-to-peak value for an estimate of the shift from the mean value currently used in Figure 9, the datum at 10.3% corresponding to the sample grown at 700°C would shift to 11.3 at.% and the datum at 18.6 at.%, grown at 650°C, would shift to 19.9 at.%. These shifts bring the data points closer to the line corresponding to Vegard's law for strained layers, but the conclusion that the QW is partially relaxed would still stand, at least for the sample grown at 650°C. More investigation is required to determine the exact percentage of relaxation state of the InGaN layer and the mechanism of relaxation that is involved.

SUMMARY AND CONCLUSIONS
In summary, InGaN/GaN core-shell structures with a single wide InGaN quantum well (SQW) were grown on arrays of etched GaN nanorods. EDX measurements of the QW confirmed a difference of InN homogeneity on the {1-101} planes compared with the m-planes. Nanoscalerange compositional fluctuations, with regions of higher and lower InN fraction, were found in the InGaN well on the m-plane while the InGaN well on the {1-101} plane was uniform. The long range InN fraction integrated on the m-plane SQW, from the top to the bottom of the nanorods led to a variation of just 7 meV.μm -1 in the layer grown at 750°C, but increased to 40 meV.μm -1 at a growth temperature of 650°C. Optical characterization demonstrated that homogenous emission arose from the m-plane despite the short range inhomogeneity within the QW. Finally, a comparison between calculated InN fraction from the emission peak and measured InN fraction indicated that the m-plane InGaN was partially relaxed, likely due to elastic relaxation since no misfit dislocations were seen in HRTEM.
To conclude, recent reviews of InGaN/GaN core-shell nanorods have highlighted the challenge and importance of controlling the long-range homogeneity along the length of the rod. 1,43 The results presented in this paper show that wide InGaN/GaN SQWs of uniform width and nearly-uniform volume-averaged composition can be grown over the entire ~1.2 m length of m-planes created from etched GaN cores arranged in a hexagonal array of 2 m pitch. However, nanoscale fluctuations of slightly raised InN mole fraction of up to 2-2.5 at.% occur in the InGaN layer, spaced at 20-30 nm intervals. Such excellent m-plane coverage by the InGaN shell was obtained for growth temperatures in the range 650-750°C on etched GaN cores demonstrating the existence of a wide growth parameter space for designing epitaxial InGaN/GaN coreshell NRs with near-uniform average emission wavelength from the m-plane sidewalls. Adopting a nanorod pitch of 2 m and simultaneously reducing the fill factor from 27% (used in our previous work) to 12% have contributed to the reported high uniformity in the m-plane optical emission. As such, these results conform to InGaN growth on threedimensional multi-faceted structures proceeding primarily by gas-phase diffusion. 44 Further work is required to determine the range of fill factors and pitch for which uniform composition can be achieved. Fundamentally this work shows that long-range homogeneity is achievable with the right NR array geometry.

EXPERIMENTAL DETAILS
A nickel-based metal mask of thickness 200 nm was created using a nanoimprint lift-off technique. 45 This resulted in a hexagonal array of metal dots of ~510 nm diameter with a 2000 nm pitch. The GaN/AlN/Si NR array was etched in an inductively coupled plasma (ICP) dry etch system (Oxford Instruments System 100 Cobra) using the following recipe: Cl2 flow -50 sccm, Ar flow -10 sccm, RIE power -120 W, ICP source power -800 W, chamber pressure -9 mTorr and temperature -150°C. 46 The MOVPE GaN regrowth step comprised 6 min of GaN growth at 1000°C and 100 mbar, using a TMGa flow rate of 8 sccm, a NH 3 flow rate of 5 slm and H 2 carrier gas.
The InGaN shell growth parameters for the three samples were identical apart from the temperature: pressure -300 mbar, TMGa flow rate -9 sccm, TMIn flow rate -200 sccm, NH 3 flow rate -5 slm, N 2 carrier gas. A GaN capping layer was grown on all samples with identical growth parameters for all samples: temperature -900°C, pressure -100 mbar, TMGa flow rate -8 sccm, NH 3 flow rate -5 slm.
Samples for TEM were prepared by a dual beam focused ion beam system. The nanorods were protected by a platinum layer prior to etching to reduce the damage that could occur with the use of an ion beam system. The samples for EDX measurements and atomic resolution STEM were prepared by a tripod polishing method using an Allied Tech Multiprep unit. Specimens were then ion-milled with a Gatan Precision Ion Polishing System (PIPS) using 1.5-5 keV argon ions for further thinning and removing the residue of polishing contamination from the specimens. Atomic resolution STEM images were acquired using a FEI TITAN 80-300 microscope that was equipped with a CEOS CESCOR spherical aberration (Cs) corrector in the probe forming lens and high-brightness FEI XFEG electron source. Atomic resolution HAADF STEM images were acquired at an accelerating voltage of 300 keV and probe convergence semi-angle of 17.9 mrad and collection semi-angle of 55-200 mrad. Energy dispersive X-Ray spectroscopy analyses were carried out using FEI Tecnai Osiris. This microscope was equipped with XFEG and Super X system EDS detectors. This detector comprises 4 Bruker silicon drift detectors (SDD) arranged symmetrically around the optic axis of the microscope for high collection efficiency and high count rate. Spectrum images were acquired at a spatial sampling of 2 nm/pixel and 200 ms/pixel dwell times with a probe current of approximately 0.5 nA, at an accelerating voltage of 200 keV. Using principal component analysis (PCA) and independent component analysis (ICA) (implemented in HyperSpy 47 ), two independent and uncorrelated components were identified in the spectrum images. The first component contains Ga and N X-ray peaks and the second component contain Ga, In, and N X-ray peaks. To obtain the composition of the InGaN shell, the intensities of Ga K and In L peaks were quantified using the Cliff-Lorimer method and the k-factor provided by the manufacturer of the EDX system (Bruker). The errors were also estimated from Poisson statistics. The ICA technique is capable of differentiating true spectra from the underlying noise efficiently and, as a result, noisy spectra can be tolerated. Using ICA technique, the required sample beam dose was therefore significantly minimized without compromising the accuracy of quantification.
High-resolution cathodoluminescence (CL) hyperspectral imaging measures the full emission spectrum from successive localized regions determined by the probing volume of a scanning electron beam in order to build up a multi-dimensional dataset containing spatial and spectroscopic information of the sample. The measurements were carried out at room temperature in a modified FEI Quanta 250 field-emission SEM with an accelerating voltage of 5 keV and had a spatial step size of 20 nm. Light was collected using an NA0.28 reflecting objective with its axis perpendicular to the electron beam, and focused directly to the entrance of the spectrograph using an off-axis paraboloidal mirror. We used a 125 mm focal length spectrograph with a 600 lines/mm grating and 50 µm entrance slit, coupled to a cooled electron multiplying charge-coupled device (EMCCD) detector. Further details of the experimental set-up can be obtained from Ref. 40 .
In order to determine a value for the InN fraction for the samples grown at 700°C and 650°C, the mean value of multiple EDX maps close to the center of the QW was calculated. These maps came from the top, middle and bottom of the m-plane. The standard errors on the mean value were all below 0.06 at.%. These errors can be neglected when compared with the experimental/instrumental error of 1.4 at.% and 2.0 at.% associated with the EDX measurements for the sample grown at 700°C and 650°C respectively. Therefore, the InN fraction and emission peak from the m-plane was determined as 10

Author Contributions
The manuscript was written through contributions of all authors. / All authors have given approval to the final version of the manuscript. / ‡These authors contributed equally.

Funding Sources
Financial support is acknowledged from the EPSRC, UK via Grant No. EP/I012591/1 "Lighting the Future" and Grant No. EP/M015181/1, "Manufacturing nano-GaN". Bowen acknowledges European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 320963 on Novel Energy Materials, Engineering Science and Integrated Systems (NEMESIS). This publication is supported by multiple datasets, which are openly available at locations cited in the reference section.