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Comparative analysis of electric potential in p-
GaN/InGaN/n-GaN nanowire LEDs

To cite this article: Anitha Jose et al 2025 *Nanotechnology* **36** 245702

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# Comparative analysis of electric potential in p-GaN/InGaN/n-GaN nanowire LEDs

Anitha Jose<fnref n="1" />,* ID, Arup K Kunti<fnref n="2" />, Nuno Amador-Mendez<fnref n="2" /> ID, Tiphaine Mathieu-Pennober<fnref n="2" />, Laurent Travers<fnref n="2" />, Cristina Cordoba<fnref n="3" />, Noëlle Gogneau<fnref n="2" /> ID, Maria Tchernycheva<fnref n="2" /> and Karen L Kavanagh<fnref n="1" /> ID

E-mail: anithaj@sfu.ca

Received 17 January 2025, revised 7 May 2025

Accepted for publication 12 May 2025

Published 2 June 2025

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

CrossMark

## Abstract

Recent advances in the development of deep ultraviolet, light emitting diodes (LEDs) have been reported for nanowire (NW) device geometries composed of nitride semiconductors. Typically, these involve arrays of NWs where the level of variation in the electrical and optical properties of individual NW LEDs is unknown. In this work, the electric potential distributions in axial p-GaN/InGaN/n-GaN NW LEDs grown by plasma-assisted molecular beam epitaxy are investigated using electron holography (EH). Two kinds of NWs are observed to grow simultaneously on the same substrate. One type exhibits a long, thin morphology and a varying diameter, while the other has a short, wide morphology with a uniform diameter. Although the bottom p-GaN and InGaN regions have similar lengths in both types, the top n-GaN region are five times longer in the first type. Photoluminescence spectra from arrays, show an InGaN emission peak ranging from 2.55 eV to 2.65 eV, which indicates an average In composition of 20 ± 3 percent. This is consistent with energy dispersive x-ray maps from individual NWs of both types, which reveal a core/shell InGaN/GaN structure with similar composition. However, the EH potential maps reveal a built-in junction voltage of approximately 3 V in the long, thin NWs, while the short NWs exhibit a drastic reduction, with a junction voltage of only 0.6 V. The difference is primarily attributed to the length of the short wire n-doped segment being too short to reach the flat potential of a complete p–n junction.

<figure><img src="image_2.png" /></figure>

<footnote n="1">¹ Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada</footnote>

<footnote n="2">² Centre for Nanoscience and Nanotechnology—C2N (CNRS / Université Paris-Sud), 91120 Palaiseau, France</footnote>

<footnote n="3">³ Department of Physics, University of Victoria, Victoria, British Columbia V8P 5C2, Canada</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
Supplementary material for this article is available [online](#)

Keywords: InGaN, electron holography, nanowire, p-n junction, built-in voltage

# 1. Introduction

Light emitting diodes (LEDs) with a wide range of tunable emission spectra are achieved with planar III—nitride hetero-structures, combining the alloys of GaN, InN, and AlN binary compounds with bandgaps 3.4 eV, 0.65 eV, and 6.2 eV, respectively. Nitride nanowires (NWs) are a promising alternative geometry for improved LED performance [1] particularly for the extreme ends of the optical spectrum (red and ultra-violet) accommodating greater lattice mismatch [2–6]. NWs offer enhanced light extraction efficiency and enable the creation of heterostructures in both axial and radial orientations. Furthermore, reports of NW transfer to flexible substrates provide opportunities for advanced lighting devices [7].

LED structures with high crystalline quality, the fewest visible defects, including dislocations and stacking faults, and well-defined heterostructural interfaces, result in the most efficient devices. When characterizing nitride NW LEDs, measurements typically involve averaging from the entire substrate. However, this approach can overlook significant variations that might exist between individual NWs. In some cases, the NWs exhibit a highly uniform morphology, whereas in others they may display a broader diversity in NW morphology, which can range from differences in length and diameter to variations in alignment and surface roughness. These discrepancies can lead to significant differences in performance between individual NWs.

Certain NWs within a sample may exhibit superior efficiency in terms of optical or electrical characteristics, while others may not perform as well. Average measurements will not accurately reflect the true potential of the best-performing NWs within the batch. Therefore, a more detailed, comparative analysis that involves examining the performance of individual NWs, is desired. This approach would allow researchers to isolate potential causes of reduced performance, such as defects or suboptimal geometries, that may be affecting the overall LED efficiency.

Structural and electronic characterization of individual NW heterostructures for LEDs is carried out using electron microscopy [6, 8] often in combination with cathodoluminescence, electron beam induced current (EBIC) [8, 9] and or *in situ* current-voltage (*I*-V) and capacitance-voltage (*C*-V) probing [3, 6]. Scanning and transmission electron microscopy (TEM), potentially combined with energy dispersive x-ray (EDX) spectroscopy, shows the overall uniformity of the grown NWs including their morphology, crystallinity and composition. CL and EBIC imaging are used to visualize conductive paths, optical emission, and minority carrier diffusivity, helpful in terms of yield and failure analysis [10].

The maps from nitride LEDs, established with these two techniques have demonstrated the impact of compositional gradients along the wire axis on the electrical and optical signals [9]. Finally, *in situ* *I*−*V* and *C*−*V* measurements on nitride LEDs access the carrier transport mechanisms, doping concentration, and net doping profiles [11] and provide information about the presence of acceptor-like defects in the active layer and problems associated with electron overflow [12]. These techniques help to optimize the doping and heterostructural design essential for low leakage currents and efficient carrier injection.

To confirm the presence of an internal potential profile at a NW junction and also to quantify its magnitude, one of the most accurate and direct methods is off-axis electron holography (EH) [13–15]. Carried out using TEM, EH maps the electron phase shifts resulting from transmission through a built-in potential at a semiconductor junction [16–18]. Subsequent theoretical modeling is used to fit the potential profiles and then determine carrier concentration profiles [19, 20]. When linked to the optoelectronic performance of devices, understanding how dopants are distributed allows for optimization of device properties, enhancing performance in applications such as light-emitting diodes, solar cells and lasers.

EH has been applied to many different semiconductors, including GaN-based heterostructures, both planar and NW geometries [21–26]. Due to their wurtzite structure, the nitrides are characterized by high piezoelectric coefficients, in comparison with other semiconductors crystallizing in the same structure, and the appearance of an internal polarization along the c-axis which can significantly influence a junction. Thus, 2D electron gas (2DEG) and an associated positive sheet charge were detected in planar GaN/AlₓGa₁-xN heterostructures and found to increase with aluminum composition [27]. Depletion regions from intentional doping have been shown to be significantly affected by internal piezoelectric potentials [28] and charge distributions from polarization effects at the heterointerfaces [27]. Direct EH measurement of the internal electric field at these interfaces was crucial for understanding the analysis of their electrical properties.

Another phenomena detected through EH measurements is the presence of lower than expected built-in voltages at nitride p-n junctions [23]. The factors proposed to explain this observation have included the presence of surface depletion layers from surface states, as well as non-uniform p-type dopant incorporation, effects of planar defects such as stacking faults and inversion domains, and interfacial polarization [23, 24].

Surface depletion layers are often attributed to the presence of intrinsic surface states or those generated by damage during
sample thinning for TEM using ion beam milling. In the case of NWs, sample preparation does not require ion beam milling, but their larger surface areas can lead to surface states originating mainly from covalent dangling bonds, impurities and chemical adsorbates incorporation [29, 30]. Potential profiles obtained from the smaller volume junctions under biased conditions also have smaller signal to noise ratios making junction detection harder [23].

In this paper, we have investigated axial p-GaN/InGaN/n-GaN heterojunction NWs grown by plasma-assisted molecular beam epitaxy (MBE) for LEDs. Scanning electron microscopy (SEM) and (TEM), combined with off-axis EH, established that the NW morphology, especially the length of the n-type top portion, from the same growth were correlated with the magnitude of the junction potential distribution observed.

## 2. Experimental

Heterostructural p-GaN/InGaN/n-GaN NWs were grown on conductive oxide-free Si(111) p$^{++}$ substrate by MBE equipped with a radio-frequency N plasma source. Prior to the NW growth, a 2.5 nm-thick AlN buffer layer was deposited at 620 °C following the procedure reported previously [31]. This buffer layer allows good control of the NW nucleation, density and orientation [32, 33]. The p-doped GaN:Mg NW base was grown at 775 °C with the Mg cell temperature fixed at 325°C, and under N-rich conditions with an N/Ga flux ratio of 1.36. The substrate temperature was then ramped down to 590 °C during a growth interruption to grow the tapered-shape axial InGaN active region with an In/Ga ratio equal to 1, within the N-rich growth regime [34]. Finally, n-type GaN:Si was grown at a low substrate temperature of 640 °C in order to avoid any degradation of the InGaN/GaN interfaces, with the Si cell temperature fixed at 1200 °C.

A secondary electron (SE) image of typical NWs on the Si substrate is shown in figure 1(a). The image indicates that there were two populations of NWs, distinguishable by their lengths and nucleation diameters, that grew simultaneously on the same substrate. One set were longer (by more than 1 µm) and spaced further apart, with a smaller initial diameter that tapered to a large diameter corresponding to the InGaN insertion position. In comparison, the other set is shorter (700 nm to 800 nm) and more densely spaced with a larger, uniform diameter. The diameter of the long wires as seen from the SEM image varied from (50 nm to 70 nm) in the wider region whereas the short wires had a larger variation in uniform diameter ranging from (60 nm to 100 nm). It is important to note that the short NWs have a propensity for coalescence, leading to the formation of defects at the coalescence interfaces [35, 36]. Coalescence defects have been reported to lower the LED efficiencies [37]. Therefore, the long NW morphology should be favored for an LED application. Based on the SEM images, we estimated the density of the long NWs as (11 ± 5) % of the total NW amount (the uncertainty is related to the difficulty

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Electron microscopy images of typical examples of the NWs studied in this work. (a) Cross-section SEM image obtained from the cleaved edge of the wafer. (b) BF-TEM images of cleaved short and long NWs. The red arrows indicate diffraction contrast presumably from strain in the InGaN regions. The growth order from the bottom to top, image (a) or right to left in (b) was p-GaN/InGaN/n-GaN.</figcaption></figure>

in distinguishing individual NWs in case of coalescence). The double population of NWs results from a two-stage nucleation process: one of thin, well-isolated NWs, and another of larger ones that are also closer together, thus having a higher risk of coalescing and forming even broader wires. We tentatively relate the double population of NWs to the adatom kinetics at the nucleation stage: indeed, this double population was observed when the growth temperature at the early stage was slightly too high. The work on optimizing the growth conditions is underway, aiming to reduce the temperature at nucleation while adjusting the fluxes accordingly.

The In incorporation and the homogeneity of the growth was probed by photoluminescence (PL) spectroscopy. PL characterization was performed on the NW ensemble at room temperature using a CW He-Cd laser (Kimmon brand, 325 nm wavelength, power measured at the sample surface equals 4 mW). The laser was focused on the NW sample surface into a spot of ≈2 µm diameter. The PL spectra were collected using a silicon CCD camera ('Sincerity' type) mounted on
a spectrometer (HR ‘Evolution’) at different points from the center to the edge of the wafer to follow the spectral variation of the InGaN emission.

The electrical activity of the p-i-n junction was probed using EBIC microscopy. In EBIC electron-hole pairs are locally generated by a focused electron beam. In structures with an internal electric field the electron-hole pairs created within or close to the field region can be separated and collected producing a measurable current. The EBIC experiments were performed in a Hitachi SU-8000 SEM using Kleindiek PS4 nan-manipulators equipped with tungsten tips to connect individual NWs to the external circuit, as was described previously [38]. To flatten the Schottky barrier at the NW/tip interface, an external bias was applied through a Stanford SR560 preamplifier controlled by a Gatan DigiScan system. For all experiments, the electron beam was set at a 5 kV beam acceleration voltage and 80 pA injected current. EBIC measurements were carried out on the two kinds of NWs.

NWs on the Si substrate were transferred to a holey-carbon Cu grid by mechanical abrasion, and electrostatic attachment. They were observed in a scanning transmission electron microscope (STEM) with an accelerating voltage of 200 kV (point-to-point resolution 0.23 nm) or (300 keV, point-to-point resolution 70 pm, aberration-corrected). Bright field (BF) images and selected area diffraction (SAD) patterns, spot mode, lattice images at higher magnification, as well as high-angle annular dark-field (HAADF) images using a scanning focused probe, were obtained.

Compositional analysis was carried out via EDX in a separate SEM (accelerating voltage and extraction current, 20 kV and 10 µA, respectively) with a cold field-emission gun and a windowless large angle EDX detector (Oxford Aztec Energy with X-MaxN 100 LE-100, 100 mm²).

Holograms were obtained at 300 kV (30% contrast and 2.5 nm fringe spacing) or at 200 kV (20% contrast and 4 nm fringe spacing) with a biprism mounted in the SAD holder. The biprism voltage and the exposure time were 140 V and 1.2 s, respectively. Care was taken to tilt the NWs so as to minimize contrast due to dynamical diffraction which leads to unintended phase shifts. A reference hologram from a vacuum region, was obtained 1 micron away from the sample to help eliminate any instabilities from the lenses or beam, during reconstruction of the hologram. Reconstruction was carried out using instructions added to the camera software (Gatan Digital Micrograph), which extracted separate amplitude and phase images.

Conventional TEM gives intensity variations sensitive to diffraction and density, whilst EH extracts the phase information from the transmitted electron wave. In the absence of magnetic fields and dynamical diffraction, the phase shift compared to passing through vacuum, $\Delta\phi$, for a uniform material is given by:

$$ \Delta\phi(x,y) = C_E \int_0^t (V(x,y,z)), \quad (1) $$

where $C_E$ is a constant depending on the beam energy equal to $e/\hbar\nu$ where e is the elementary charge, $\nu$ is the electron

<figure><img src="image_4.png" /><figcaption>Figure 2. High magnification, oriented TEM images to resolve lattice fringes, showing a comparison between long (a) and short (b) wires.</figcaption></figure>

velocity, t is the sample thickness, and the potential V, is a sum of contributions including the bulk mean inner potential (MIP), $V_0$, any built-in junction potentials, $V_{bi}$, and other potential sources in the specimen.

### 3. Results and discussion

Representative BF TEM images from each NW category are shown in figure 1 (b). The long wire example shown has a tapered shape with a diameter of 60 nm at the top region reducing to 40 nm at the bottom cleaved end. In comparison, the shorter NW has a uniform diameter of 70 nm. Diffraction contrast is visible in the top segment of the long NW likely due to strain. The contrast at the region where the diameter begins to increase in the long wire is due to the addition of InGaN in the NW, marked by the red arrow. (The region of very dark contrast in the thinner lower region of the wire should be disregarded since it is due to a broken piece of a different NW that became attached to this wire during transfer.) In the case of the shorter NW, within about 50 nm from the top, vertical strain contrast is visible (marked by the red arrow) which EDX will show is also associated with the InGaN region. In both cases, the InGaN region is 60 ± 5 nm long.

Figures 2(a) and (b) show higher magnification TEM images (300 keV) of a long and short NW, respectively, with the electron beam oriented parallel to the {0002} planes. The top region of the long NW has a high density of stacking faults (SF) when compared to the short NW. These defects
<figure><img src="image_5.png" /><figcaption>**Figure 3.** STEM images with EDX profiles from along the center of (a)–(b) long and (c)–(d) short NWs.</figcaption></figure>

result from the lower temperature (640 °C) used to grow the top layer of n-GaN aimed at preserving the abruptness of the InGaN/GaN interfaces. The InGaN region in both sets of wires generates strain deformation, which was also visible from the contrast in the BF images (figure 1(b)). The regions labeled in the figure with yellow arrows are based on this strain contrast and the EDX plots to be discussed later in figure 3.

Although the growth conditions are nominally the same, the short NWs must have grown more slowly, during at least some portion of the process. In both cases, the length of the InGaN region is about 60 ± 5 nm. The length of p-GaN region were approximately the same, with a length of 600 ± 5 nm and 650 ± 5 nm from the bottom for the short and long NWs, respectively. However, the n-type regions are very different. With respect to the top of the InGaN, the length of the n-GaN regions are approximately 50 ± 5 nm and 285 ± 5 nm, in the short and long NWs, respectively. Therefore, the ratio of the length of the n-GaN to InGaN regions, $L_{n-GaN/InGaN}$, is 0.8 and 4.8 for short and long wires, respectively.

Variation of the growth rates has been previously observed in the literature [39, 40] and explained via a combination of factors. During the NW elongation (so-called the steady state regime), the axial NW growth rate results from two ballistic Ga atomic flux contributions: the Ga species which directly reach the NW top facet, and the larger flux of Ga species adsorbed on the NW sidewalls and which then diffuse towards the NW top. The growth rate is thus driven by the adatom surface diffusion [41, 42]. In order to keep the InGaN/GaN interfaces abrupt, the n-doped GaN portion was grown at 640 °C. Compared to the usual growth temperature used for 2D-GaN layers (700 °C–750 °C) or for GaN NWs (765 °C–815 °C), at this lower growth temperature, the adatom mobility would be reduced. In addition, the growth was performed under N-rich conditions, leading to N surface saturation and thus also causing a lower adatom surface diffusivity. [43]. The combination of these two factors induced a reduction in the adatom kinetics at the top of the NW, i.e. on the adatom diffusion length with respect to the NW diameter [44, 45]. Thus, the time required for the nucleation of an additional layer taking place on the top of the larger NWs was increased, leading to an effective lowering of the growth rate, and thus to a reduced thickness of its GaN n-type top layer.

Lattice fringe measurements conducted in the GaN region of both NW types revealed a spacing of 0.521 ± 0.002 nm which corresponds to the expected d-spacing of (0002) planes. Upon incorporation of In, the d-spacing in the NWs is expected to be larger (lattice constant of relaxed InN is 0.567 nm) which could be used to estimate the In concentration based on Vegard's law. However, a change in lattice spacing in the InGaN regions was not detected, to within experimental error, indicating that the InGaN regions were compressively strained. This is consistent with the presence of a surrounding GaN shell, as discussed later from EDX map interpretation, which was confirmed to have spontaneously formed around the InGaN segment during growth [34].

STEM images and associated EDX line profiles along the length of the short and long NW are shown in figures 3(a)–(d). The position of In in each of the NWs, as per EDX profiles, are consistent with the diffraction contrast seen in the BF images. The regions with In concentration associated with the InGaN regions for both the long and short wire extended in length approximately 60 ± 5 nm. The average In atomic percentage, considering the change in the Ga signal, were (7 ± 1) % and (9 ± 1) % for the long and short wires, respectively. The calibration for this measurement was done by evaluating the dip in the Ga signal (equivalent to the amount of In incorporated) which was a constant value elsewhere. Assuming a uniform concentration, therefore, the average composition of the InGaN region in the long and short wire was In<sub>0.07</sub>Ga<sub>0.93</sub>N and In<sub>0.09</sub>Ga<sub>0.91</sub>N, respectively.

This estimated In composition could appear to be incompatible with the wavelength emission from PL results to be discussed. However, we have to consider that the EDX measurement probes the entire core–shell structure. The signature of the InGaN insertion and of the GaN shell are thus convoluted, reducing the effective In content quantification.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** EDX maps of Ga and In compositions from long and short NWs. Individual long NW (a)–(b) and 2 coalesced short NWs (c)–(d).</figcaption></figure>

Figure 4 shows Ga and In maps from an individual long NW, (a) and (b) (top end at left) whereas a coalesced set of 2 short NWs is shown in (c) and (d) (top ends at right). In each type of NW, In is detected within the expected region where a change in diameter occurred in the long NWs, and very close to the top end of the short NWs, in agreement with TEM images. The weaker green signal everywhere is presumed to be the background noise level. In both cases, the In concentration is present within a core region of the NW with a surrounding GaN shell.

The EDX composition from the line profiles in figure 3 have been thus recalculated by considering the GaN shell structure. Hence, in both short and long wires, the total diameter of the NW was approximately 1.6 times the core diameter. Taking into consideration, the hexagonal geometry of the NWs, the composition of In at the core was estimated to be 18 and 23 atomic percent for the long and short NWs, respectively.

PL spectra are shown in figure 5. These are plots of the average emission intensity each detected from a large number of NWs at locations across the whole substrate. They are

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Room temperature PL emission from NWs (excitation 325 nm) obtained at radial positions from the center to the edge of the wafer.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** SEM with EBIC images measured from (a) long and (b) short NWs. The color scale gives the EBIC current in each point in amps.</figcaption></figure>

dominated by the InGaN peak, which shifts from 2.55 eV (486 nm) in the central part of the wafer to 2.65 eV (468 nm) at the wafer edge. These energy values indicate an In concentration of $20 \pm 1$ atomic percent, based on an emission calibration from planar heterostructures [46], consistent with the results from EDX analysis.

The spectral range from locations across the wafer, reflects the effect of an inhomogeneity in the MBE heater on the InGaN composition, while the large InGaN peak width (FWHM of 200 meV) reflects compositional fluctuations from wire-to-wire. A weak GaN near- band edge emission is also observed peaked near 3.4 eV (365 nm) for all positions on the wafer. A broad shoulder seen at (3.1–3.2) eV arises from the donor-acceptor pair (DAP) transitions in the p-doped GaN.

Representative examples of EBIC maps from individual long and short NWs are shown in figure 6. An external reverse bias of a few volts was applied to the tip in order to overcome the Schottky barrier contact and to enhance the junction signal. Long thinner NWs (typically less than 70 nm in diameter) showed a localized EBIC signal in the top part of the wire with
<figure><img src="image_9.png" /><figcaption>**Figure 7.** (a) Phase image and (b) corresponding phase (purple dots) and potential (green dots) profile along the white arrow parallel to the long NW growth direction. The solid green line represents a simulated potential calculated using the Poisson's equation based on the depletion widths in the p and n sides.</figcaption></figure>

some statistical variations from wire to wire. The signal typic-
ally appeared starting from a 0.5 V applied bias. An example
of an EBIC map of this kind is shown in figure 6(a) for an
external bias of 2 V.

An EBIC signal extension of (50 nm–100 nm) is typical of
well-defined axial junctions [47]. In contrast, for the thicker,
shorter NWs (greater than 100 nm in diameter), the EBIC sig-
nal appeared only for a higher external bias (2.5 V–5 V) and
tended to span the large part of the length or even the entire
length of the NW, as shown in figure 6(b) for an applied bias
of 2.5 V. This extended signal is not expected in axial junction
NWs. It may originate from either the formation of a radial
junction over the entire NW length or from a resistive EBIC
signal due to the applied external bias. EBIC analysis alone
does not allow us to disentangle these two cases, however, EH
to be discussed found a much smaller built-in junction poten-
tial in the shorter NWs. And the top n-doped GaN segment is
only 50 nm long, much shorter than in the long wires. These
NWs may have been depleted due to surface band bending
thus leading to a p–i junction instead of a p–i–n junction. The
external bias applied to these structures leads to a broader field
extension and broader EBIC signal.

EH phase images (300 kV) from representative long and
short wires are shown in figures 7(a) and 8(a), respectively.
Corresponding average phase profiles (purple dots) along the
white arrows are shown below in the associated plots 7(b)
and 8(b) in each case. Both phase shift profiles were measured
relative to a vacuum reference set to zero radians. Moving from

<figure><img src="image_10.png" /><figcaption>**Figure 8.** (a) Phase image and (b) corresponding phase (purple dots) and potential (green dots) profile along the white arrow parallel to the short NW growth direction. The solid green line represents simulated potential calculated using Poisson's equation based on the depletion widths in p and n side.</figcaption></figure>

the nominally n-type GaN at the top of each wire through the
InGaN towards the nominally p-type GaN bottom, there is a
decrease in phase.

To estimate the NW thickness we evaluated the shape of
perpendicular phase profiles across either NW. For the long
wire, it was consistent with hexagonal NW volumes (sup-
plemental figure S1) with a flat region of constant phase in
the middle and sloping sidewalls. A hexagonal shape with
the incident beam perpendicular to a flat face of one of the
hexagonal facets fits the measured profile best. The thickness
of the NW was therefore, considered to be equal to 0.866 times
the corresponding diameter seen in the beam direction. For the
short NW, the profile was more similar to a circular one but
also showed faceted sides (supplemental figure S2).

The average potential profile along each NW axis was
calculated from the axial phase data (averaged within the
white rectangle in both cases) and estimated thickness, using
equation (1). For the short wire, since the diameter (and there-
fore the thickness) was uniform, the effect of thickness on the
phase was the same everywhere. In the case of the long wire,
since the diameter is changing along the length, the effect of
thickness was normalized at each point.

In order to accurately calculate the change in potential due
to the junction and any other potential sources, the variation
in the MIP due to composition must also be considered. We
have estimated the MIP for the InGaN regions using their average In concentrations obtained from STEM and EDX measurements and applying Vegard's law with known MIP values for GaN (16.89 V) and InN (18.90 V) [48]. Here the average In content was used and not the effective In content in the core since the region chosen for averaging in the phase image would imply to the average In composition rather than the composition in the core. This meant that the long wires with an average In<sub>0.07</sub>Ga<sub>0.93</sub>N composition had a MIP of 0.1 V greater than GaN, while the short wires with a slightly larger In composition at In<sub>0.09</sub>Ga<sub>0.91</sub>N have a MIP of 0.2 V greater.

The net variation in potential axially along the short and long wires, after normalizing their thickness contributions and assuming the MIP was radially uniform, is shown as the green profiles in figures 7(b) and 8(b), respectively. There is clearly a rise in potential from the p-region to the n-region confirming a junction. The built-in voltage measured from the difference from the n to p region in case of the long NW is 2.7 ± 0.1 V and only 0.6 ± 0.1 V for the short wire. Based on the location of In in both NWs, the depletion width on the n and p-type sides of the long wire were 30 ± 2 nm whereas for the short wire it was 22 ± 4 nm and 17 ± 4 nm, respectively.

We note that each type of measurement (STEM, SEM, EDX, EH, and EBIC) were carried out on different sets of wires. We are certain that the SEM morphology was similar over the central part of the wafer, where the analyses were performed, however, the exact locations of the NWs used for each of these measurement techniques were not identical. Correlated measurements using marks can potentially be envisioned for some of the characterization listed above, however it is a highly time consuming procedure and can be done on a small set of NW. Instead, we prefer to perform measurements on statistically representative NW sets coming from the central part of the growth wafer, where the NW morphology are similar.

Assuming uniform dopant concentrations, the depletion widths of the potential profiles of figures 7 and 8 indicated equal p and n-type carrier concentrations in the long wires of 6 × 10<sup>17</sup> cm<sup>-3</sup>, while the shorter depletion region in the short NW indicated a higher carrier concentrations of 1.2 × 10<sup>18</sup> cm<sup>-3</sup> and 9 × 10<sup>17</sup> cm<sup>-3</sup> for p and n-type, respectively. However, the expected built-in junction voltage for such dopant concentrations in GaN was not observed. There was also a significant difference in the measured built-in voltage in the long and short wires.

Potential simulations assuming uniform dopant concentrations were overlaid with the profiles in figures 7 and 8 (solid lines). They did not accurately fit the experimental data, particularly for the short NWs. This discrepancy suggests that the actual dopant distribution deviated significantly from the uniform model. Non-uniform radial dopant distributions is a possibility in MBE grown NWs [49]. In addition, in some cases the axial p-n junction profile can be distorted by lateral growth effects [47].

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Spontaneous (SP) and piezoelectric (PE) polarization in an N-face GaN/InGaN p-i-n structure.</figcaption></figure>

The calculation of potential from an EH phase shift assumes a certain thickness of the doped material. It is possible that the shorter NWs exhibited a smaller built-in voltage due to a lower and less uniform Mg dopant concentration. We hypothesize for the shorter NWs, that the p-n junction may be confined to a shell near the surfaces. This localized junction would explain the poor fit to the modeled results. The incorporation of Mg is highly influenced by surface attachment kinetics and facet p [49, 50]. However, it is to be noted that the length of the Mg-doped bottom region of the NWs were quite similar in short and long NWs. Therefore, unless the closer spacing of the shorter NWs inhibited dopant incorporation, (as sidewalls are favored over the top surface) both set of NWs should have been affected in a similar manner, whereas only short NWs showed a reduced built-in voltage.

Additionally, we must consider the possibility of lateral growth of Si-doped GaN occurring on the outside of the p-type regions of the NWs forming a lateral junction, potentially depleting carriers. Si dopants tend to favor axial growth in comparison to Mg dopant which tend to favor lateral growth. However, if this lateral doping effect were significant, it would have likely impacted both short and long NWs similarly. Therefore, while lateral junction formation might contribute to carrier depletion, it does not account for the observed differences in built-in voltage and dopant distribution between the shorter and longer NWs, as these effects would be present across both wire types.

Polarization in nitrides is another important factor affecting the potential distribution in the system. The InGaN layer when grown on a GaN template experiences significant compressive strain since InGaN has a larger lattice constant than GaN. It is known that NWs spontaneously nucleating on Si (111) by MBE predominantly exhibit N-polarity, although in some cases, careful chemical pretreatment can lead to a substantial fraction of metal-polar NWs [51]. Figure 9 shows a schematic diagram of the expected polarization direction in different epitaxial layers of an InGaN/GaN p-i-n structure with an N-polarization parallel to the [0001] direction. The built-in electric field in a p-n or p-i-n semiconductor device is directed from the positive n-type layer to the p-type layer. The net polarization-induced electric field is oriented from metal face to N face. In case of a compressively-strained InGaN in an N-face structure as shown in figure 9, the direction of
polarization induced field is opposite to that of the direction of
the p–n built-in field. This implies a field that partially cancels
the built-in electric field of the p–i–n structure [52].

Based on the In percentage obtained from EDX measure-
ments, the shorter NWs exhibited a slightly higher In percent-
age compared to the longer NWs. But based on the change in
diameter, strain from InGaN is more relaxed in the long, thin
wires. This suggests that the shorter NWs were more likely to
be influenced by strain induced polarization effects. Previous
literature indicates that polarization fields in structures such as
p–i–n AlGaN/InGaN/AlGaN can significantly affect the meas-
ured voltage [24].

Another possibility is the presence of inversion domains,
regions of Ga-polar growth surrounded by N-polar [39,
40, 53] These occur regardless of the substrate and could
affect the dopant activation. We observed a PL signature
of a GaN inversion domain boundary (IDB) reported at
3.45 eV [53], figure 5. However, we have not investigated
whether the short or long, or both NWs contributed to this
peak.

NWs with a similar bimodal growth morphology repon-
ted in literature have found that the shorter NWs were N-
polar whereas the thinner longer NWs were either Ga-polar or
formed a Ga-polar pipe surrounded by an N-polar shell [39].
The IDBs were imaged in the long, thin wires, either at the
intersection with a short NW matrix which led to completely
Ga-polar NWs, or within the long wire in case of a Ga-polar
pipe. The presence of IDBs in thin, long NW morphology
rather than short NWs has also been verified with cathodolu-
minescence (CL) measurements [39]. In our case, based on
SEM images, our long NWs do not result from the coales-
cence of several thinner NWs at their base, rather we more
likely have a Ga-polar pipe structure rather than a complete
Ga-polar thin NW. Further investigations are planned to con-
firm the presence of IDBs and then to understand their effects
on potential junction formation.

The primary difference between long and short NWs is the
difference in the length of n-region as mentioned earlier. The
n-segment is very short in the short NWs when compared to
the long NWs. It is likely that this n-type region was not able
to reach the flat potential. In other words, the n-region might
have been fully depleted forming an incomplete p-n junction.
Although, IDBs may have an impact on the carrier concen-
tration, the primary reason behind the difference in measured
built-in voltage was likely a depleted n-region in the short
NWs.

To summarize the discussion, the most likely hypothesis to
explain the discrepancy between the observed built-in poten-
tial in long thin and short thick NWs is the shorter top n-GaN
length in the short wires. This shorter length, together with
likely surface Fermi level pinning at the NW top surface, pre-
vented the p-n junction from reaching flat potential in the n-
GaN. Moreover, the shorter n-GaN segment would have been
strained by the underlying InGaN insertion, while in the longer

NWs the n-GaN segment reached relaxation. This would also
contribute to a different piezoelectric polarization.

4. Conclusions

Axial NWs of n-GaN/InGaN/p-GaN, p-i-n structure for LEDs,
were grown by MBE on silicon (Si) (111) p++ substrate.
Two distinct types of NWs were found to grow in parallel on
the same substrate differing primarily in their lengths. Such
double populations have been reported to occur at certain
lower growth temperatures such as in our case. While the p-
GaN and InGaN regions were approximately the same lengths,
the n-type top regions in the long wires were almost 5 times
longer in length compared to the shorter wires. This difference
has been attributed to a slower n-type growth rate and nucle-
ation density in the larger diameter short wires.

The In existed in a spontaneous core–shell structure in both
NW types, but was slightly higher in composition in the short
NWs (18 versus 23%). A change in diameter seen in the long
wires was associated with the In layer growth and strain relax-
ation in the subsequent n-GaN top layer. The short wires in
comparison saw no change in diameter and hence less lateral
strain relaxation.

Potential maps obtained using EH showed a significant dif-
ference in the measured built-in voltage, and estimated act-
ive carrier concentrations at the expected junctions in the two
types of NWs. In the long NWs a significant built-in voltage
of 2.7 V close to the expected value of 3.3 V was obtained
assuming uniform carrier concentrations of 6 × 10<sup>17</sup> cm<sup>-3</sup>. In
comparison, the shorter NW showed only a very small junc-
tion voltage (0.6 V). We conclude that the n-type region of
the shorter NWs, in close proximity to the top of the NW,
did not reach the flat potential necessary for the detection of a
p–n junction. Fermi level pinning may have contributed to the
formation of a fully depleted region.

Data availability statement

All data that support the findings of this study are included
within the article (and any supplementary files).

Acknowledgment

We gratefully acknowledge partial funding by the Natural
Science and Engineering Research Council of Canada
(NSERC) and the use of STEM facilities at SFU 4D Labs
and the Advanced Microscopy Facility at the U. of Victoria.
The sample fabrication, EBIC and PL measurements were car-
ried out within the C2N micro-nanotechnology platforms and
partly supported by the RENATECH network and the General
Council of Essonne.
ORCID iDs

Anitha Jose https://orcid.org/0000-0002-0129-2952

Nuno Amador-Mendez https://orcid.org/0000-0002-9493-5573

Noëlle Gogneau https://orcid.org/0000-0002-4881-1617

Karen L Kavanagh https://orcid.org/0000-0002-3059-7528

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