Demonstration of grain reorientation during GaN early stage coalescence grown by novel pendeo-epitaxy approach

Gallium nitride (GaN) is a wide bandgap semiconductor with applications in electronics and optoelectronics.^1–3 By alloying it with In to form InGaN of different compositions, light emission from red to ultraviolet can be achieved, enabling the fabrication of light emitting diodes (LEDs) covering a wide spectral range.^4,5 The epitaxial growth of GaN is typically carried out on foreign substrates, typically sapphire or silicon (Si) that generates dislocations in the GaN layers (dislocation density up to ∼10¹⁰ cm⁻²), which can cause a degradation in the emission efficiency of the optoelectronic devices as well as in their lifetime. The generation of such defects is due to the large lattice parameter mismatch between the substrate and the epitaxial layer and the independent nucleation of GaN grains. Different growth methods, such as epitaxial lateral overgrowth (ELO)^6,7 and pendeo-epitaxy (PE),^8,9 were developed to lower the dislocations densities, and values of the order of 5 × 10⁸ cm⁻² were reached for GaN on Si¹⁰ and 4 × 10⁸ cm⁻² for GaN on sapphire,¹¹ with dislocation densities being reduced further by a factor of two or three in the last few years. In parallel to the developments in large-area GaN growth, in recent years, GaN-based micro-LEDs have arisen as a solution for high resolution applications like augmented reality and virtual reality, where pixel size reduction is necessary. This has brought about new challenges related to the defects generated at the pixel's walls, during the necessary top-down etching process,¹² but also to the fact that with such dislocation densities, some pixels (i.e., some micro-LEDs) might have one dislocation or two, while others might have none, leading to potential inhomogeneities between different pixels.

To tackle these issues, we have implemented a novel pendeo-epitaxy approach that relies on the growth of GaN pyramids on top of GaN/AlN/Si(111)/SiO₂ nanopillars. At typical growth temperatures of around 1000 °C, the nanopillars are expected to twist and or tilt due to a softening of the SiO₂ layer¹³ at these temperatures. This should then allow a self-alignment of GaN layers during coalescence to finally obtain GaN platelets of sufficiently high quality for optoelectronic applications such as micro-LEDs. The results of previous dark field x-ray microscopy (DFXM) measurements conducted at the European Synchrotron Radiation Facility (ESRF) showed that with our growth method, we were able to obtain homogenous GaN layers in 1D pillar arrays (i.e., lines of pillars) with very low dislocation density (ρ = 1–5 × 10⁷ cm⁻²) as well as the oriented formation of pillar clusters in 2D (ρ = 1–5 × 10⁸ cm⁻²).¹³ As this growth technique does not require any etching step to obtain the pixels, it eliminates the etching damage during pixel definition, thus making these first results promising for the fabrication of micro-LEDs on micrometer-size highly oriented islands of GaN on silicon.

However, in order to completely comprehend and optimize this growth approach, it is crucial to examine the microstructural evolution during growth and to study, at the microscale and nanoscale, the coalescence process taking place. In this work, we investigate the coalescence phenomena by studying two samples: one with GaN pillars before coalescence (i.e., prior to the growth of the GaN pyramids) for reference, and a second one with GaN at the early stage of coalescence (not yet fully coalesced). To carry out a complete structural characterization and obtain a complete and reliable picture, we used three complementary techniques: (i) scanning x-ray diffraction microscopy (SXDM) at the ESRF, (ii) electron backscatter diffraction (EBSD), and (iii) cathodoluminescence (CL). In the following, we describe these three non-destructive methods, the studied samples, and present the results that describe the mechanisms at work during the early phase of growth of GaN. We show the transformation from misoriented GaN pillars before growth to well-oriented GaN layers after coalescence during the initial growth stages and present a clear visualization of grain boundary formation. The grain boundaries are characterized by the presence of geometrically necessary dislocations and by a strain gradient appearing between the domain's interior and the domain boundaries. Furthermore, we also introduce a model to determine the maximum initial misorientation between neighboring pillars for which they are still able to perfectly align themselves.

Gallium nitride (GaN) is grown on top of GaN/AlN/Si/SiO₂ etched nanopillars of 100 nm diameter, distributed in a hexagonal pattern with a pitch of 1.5 μm on a SiO₂ coated Si(001) substrate. The GaN, AlN, and Si(111) layers have thicknesses of 250, 120, and 50 nm, respectively, while SiO₂ is etched down to a depth of 300 nm using the nanoimprint lithography (NIL) technique combined with a lift-off step and followed by plasma etching. More details on the structure and etching process are presented in a previous publication.¹⁴ The growth of GaN on top of these pillars is performed by Metal Organic Vapor Phase Epitaxy (MOVPE) in a 3 × 2 in. close coupled showerhead (CCS) Thomas Swann reactor with trimethyl-gallium (TMGa) and ammonia (NH₃) as precursors for gallium and nitrogen, respectively. The entire growth process is explained in detail in Ref. 15. A schematic representation of the growth approach is shown in Fig. 1.

Two samples were studied: (i) a reference sample A that contains only GaN nanopillars before coalescence [prior to the pyramid growth, see Fig. 1(b)] and separated by 0.5 μm, and (ii) a sample B with GaN grown on top of pillars separated by 1.5 μm. The growth of GaN is deliberately interrupted before the platelet reaches full coalescence in order to characterize a sample with GaN at the early stage of coalescence [intermediate phase between Figs. 1(c) and 1(d)].

X-ray diffraction measurements were performed at the ID01 beamline at the ESRF in Grenoble, France, using a monochromatic nano-beam with a focal spot size of ∼65 × 65 nm² at an energy of 10 keV. The beam is focused at the rotation center of a diffractometer using a Fresnel zone plate (FZP) combined with a 50 μm molybdenum order sorting aperture (OSA), needed to remove high diffraction orders produced by the FZP.¹⁶ The diffracted signal is recorded by a two-dimensional (2D) Maxipix^™ detector (square of 4 chips, each of them 516 × 516 pixels with 55 μm pitch size).¹⁶ Samples A and B were examined with this technique. These measurements allowed us to compare the quality and orientation of GaN before and after coalescence.

For sample A, an area of 20 × 20 μm² has been scanned, and ω rocking curves were performed around the asymmetrical Bragg reflection GaN (105) with a step size Δω = 0.05° with an angular range of 59.5° < ω < 61° (i.e., each rocking curve consisted of 30 points). For every incidence angle $ω$ of the rocking curve, an x–y piezo scan was performed, and diffraction images were taken every 80 nm in the x direction (200 position) and 80 nm in the y direction (200 position) with t = 0.01 s. Therefore, by scanning 40 000 points (200 × 200) at each ω value with 0.01 s/point, which means a measurement duration of 3 h 33 min, we recorded 30 (x, y) maps, providing a final five-dimensional dataset.

For sample B, an area of 30 × 40 μm² has been scanned, and ω rocking curves were performed around the asymmetrical Bragg reflection GaN (105) with a step size Δω = 0.1° with an angular range of 58.5° < ω < 62.5° (each rocking curve consisted of 40 points). For every incidence angle $ω$ of the rocking curve, an x–y piezo scan was performed, and diffraction images were taken every 150 nm in the x direction (200 position) and 200 nm in the y direction (200 position) with t = 0.01 s. Therefore, by scanning 40 000 points (200 × 200) at each ω value with 0.01 s/point, which means a measurement duration of 4 h 44 min, we recorded 40 (x, y) maps, providing a final five-dimensional dataset.

To obtain the 3D reciprocal space map (RSM), mapping intensity variations across both 2θ and ω angles is required. We collected data solely through ω scans, but the 2D detector is able to simultaneously record the diffracted intensity at various 2θ angles which allows us to obtain a 3D reciprocal space map around the Bragg reflection for each probed (x, y) sample position from the data processing work. A detailed description of the experimental setup at the ID01 beamline can be found in Refs. 16 and 17.

Electron backscatter diffraction (EBSD) can identify different crystalline grain properties (size, orientation, and grain boundaries)^18,19 with high spatial resolution, down to the nanoscale. It consists of directing a focused electron beam at the sample surface and collecting the backscattered electrons (BSEs). The sample was tilted by 70° in the SEM to enhance the detection of backscattered electrons. EBSD mapping of the c-plane GaN layer has been performed on sample B (at the early stage of coalescence). The electron beam scans the surface of the sample over a discrete grid (rectangle in this work) with a fixed step size equal to 0.1 μm along x and y. As these electrons penetrate the crystal, they interact with the periodic arrangement of atoms within the crystal lattice, and since they have short wavelengths, they will fulfill the Bragg condition with respect to the atomic planes and will be diffracted out of the sample, and they are referred to as backscattered electrons (BSEs). The EBSD detector captures these BSEs resulting in the formation of parallel line pairs on the detector screen, which are referred to as electron backscatter patterns (EBSPs). The EBSP consists of overlapping Kikuchi bands where each Kikuchi band corresponds to a set of planes.^20,21 The EBSP is used to identify the phase and the orientation of the crystal lattice at the point of the sample that generated the EBSP through Hough transform.^22,23 Hough transform identifies the positions of the Kikuchi bands by converting the bands with the highest intensity from lines to points called peaks.

Once EBSPs have been transformed into the Hough space, the indexation of the Kikuchi band can be achieved. Given the wurtzite geometry of GaN, and knowing the Kikuchi band positions, it is possible to calculate the angle between each pair of bands. The computed angles are compared with a predetermined list of interplanar angles between the atomic planes for GaN. If a coherent match between the two lists of angles is found, each detected Kikuchi band is assigned to a certain crystallographic, ultimately providing a crystal orientation as the original solution. Following the Hough transform, a more sophisticated Kikuchi pattern indexing method is used. It is based on kinematic simulation that would model the expected positions of the Kikuchi band. This will enable a refinement of the original solution and an improvement of the angular resolution. In the measurements performed in this work, the angular resolution is around 0.2°.²⁴ At each position (x, y), three frames were obtained with Δt = 15 ms for each frame and the average result was then analyzed. It is important to note that one of the limitations of this EBSD method is that it is only sensitive to the sample's surface, i.e., up to the first 10 nm below it. Another challenge with this method for the current sample is the non-conductive nature of the undoped GaN and, in particular, of SiO₂, which causes the electrons to accumulate in their location instead of being evacuated, which can lead to a localized charge buildup and, therefore, can shift the beam trajectory.²⁵ During our experiment, this issue was avoided by decreasing the beam tension to 15 kV, which reduced the number of electrons that remained present and, therefore, prevented a beam drift. Using the relative grain orientations measured at each scan position, further analysis of the obtained EBSD data determined the geometrically necessary dislocation (GND) densities at the grain boundaries.

To confirm the presence of the GND, cathodoluminescence measurements were carried out on the same sample area. CL is a powerful technique in the characterization of semiconductors and nanomaterials,^26,27 because it enables the identification and counting of dislocations in GaN even on large areas.²⁸ This phenomenon occurs when photons (light) are emitted from a material upon interaction with an electron. An electron beam is focused on the sample surface, and it penetrates into the material and leads to the excitation of the electrons within the sample into higher energy levels. These excited electrons will become unstable (in excited states) and eventually relax back to their lower energy states by releasing the excess energy in the form of photons (electron–hole recombination).²⁹ CL measures the emitted light at each point across the sample surface. Dislocations are centers of non-radiative recombination, which causes the luminescence intensity to be significantly reduced, and thus, dark spots to appear.³⁰ This allows dislocations to be identified. For the measurements conducted in this work, the used CL system is a GATAN MONO CL4 cathodoluminescence system. It is mounted on a Field Emission Gun Scanning Electron Microscope (FEG-SEM; JEOL JSM7000F at CRHEA, Valbonne, France). The CL signal is collected with a parabolic mirror and sent to a CCD detector. The panchromatic mode is used to measure the integrated light intensity over all wavelengths (from ∼200 to ∼900 nm) produced at each point of the surface during the scan of the beam. This mode is especially useful to detect the presence of non-radiative structural defects, such as dislocations. The CL mapping was performed on a 32 × 28 μm² area across the sample surface with a Δx = Δy = 0.1 μm and a beam tension of 3 kV.

Synchrotron-based scanning x-ray diffraction microscopy at the ESRF is a very powerful nondestructive characterization technique.³¹ Here, it was employed due to its ability to probe the crystal structure of the GaN layer through all of its volume, rather than just the surface, with a sufficiently good signal-to-noise ratio despite the small layer thickness³² and to examine thin GaN pillars due to the high intensity of the beam without the need of a flat surface on top. These characteristics allowed us to study both sample A, which only has the GaN pillars before regrowth and coalescence with a pitch of 0.5 μm, and sample B, where the growth is interrupted in the middle of the coalescence process.

Figure 2(b) shows the result of such a calculation for sample A, i.e., a 2D map of the angular deviation of the normal of the (105) planes in each pixel from the mean orientation, thus describing the local lattice rotation.

These results show the GaN pillars, before regrowth and coalescence, exhibit a variety of colors, indicating that they are misoriented with a relatively large distribution of orientations up to just over 1°.

The same data processing is applied on the data collected on sample B; the 2D map of the integrated intensity is shown in Fig. 3(a) and the 2D map of $Q → 105$ relative tilt is shown in Fig. 3(b). Here, it is evident that GaN pillars have coalesced into larger well-defined GaN domains with a unique and narrow orientation distribution within each domain. We note that the black regions seen in Figs. 3(b)–3(d) correspond to the uncoalesced GaN regions diffracting with extremely low intensity seen in Fig. 3(a), and, thus, they were masked throughout the data treatment.

To establish the reciprocal space coordinates of the (105) peaks, one-dimensional projections of the data along $Q x, Q y$⁠, and $Q z$ are computed and fitted to Gaussians. Other than the peak position, this fit also allows the determination of peak full width at half maximum (FWHM) at each (x, y) coordinate. The 2D map of FWHM along $Q z$ and $Q x$ for sample B is displayed in Figs. 3(c) and 3(d), respectively. Inspecting the figure, we notice a broadening of the peak along both $Q z$ and $Q x$ at the boundaries of the same grains identified in the relative tilt map in Fig. 3(b). This peak broadening implies a distorted lattice or the presence of a strain gradient between two neighboring GaN grains. Such broadening is introduced by (i) the presence of geometrically necessary dislocations required to accommodate the disorientation between two large rigid grains and/or (ii) by an elastic local strain introduced during the coalescence of grains. Therefore, the FWHM plots indicate the presence of dislocations or a strain gradient at the grain boundaries; however, we cannot determine whether both are present or just one of them, as the broadening is observed in both directions, which is why further characterization have been performed.

The relative strain map indicates the homogeneity of strain inside the GaN domains; however, it is hard to retrieve clearer and firm conclusions from this spatially resolved strain analysis since we do not have an absolute strain map.

To validate the SXDM results and to determine the number of dislocations between neighboring grains, we had to align them along the same crystallographic direction; EBSD and CL measurements are performed on the same area of sample B that was studied by SXDM. A scanning electron microscopy (SEM) image of the sample is shown in Fig. 5(a). Pillars with uncoalesced GaN on top (designated by red arrows) as well as coalesced GaN regions are seen. The data obtained from EBSD are processed using the MTEX Matlab toolbox.³⁵  Figure 5(b) shows the grain reference orientation deviation (GROD) map, which corresponds to the local misorientations of each pixel relative to the mean orientation; we note that the area colored in black is masked out because it corresponds to the non-indexed pixels with low signal. Please also note that the GROD maps seem to be compressed along the vertical axis compared to the SEM image. This could be due to a drift that occurred during the EBSD measurements or due to the difference in angle as the SEM was acquired with a flat sample.

Figure 5(c) shows the GROD axis map with the standard crystallographic triangle presenting the crystallographic axes used to describe the orientation of the grains; in other words, it indicates the rotational axis that each grain must turn around to align with the mean orientation.

We notice that large rigid GaN islands are formed in the early stage of growth: they are very well oriented within themselves [i.e., they present the same misorientation magnitude; the same GROD angle values in Fig. 5(b)], and they share the same rotation axis in Fig. 5(c). We observe the formation of GaN grains with extremely small GROD angles (<0.5°) and we can also see that certain grains exhibit a large misorientation of 4° compared to the mean orientation.

These results are in good agreement with those found in the SXDM measurements. However, in the GROD angle map [Fig. 5(b)], we are able to identify a larger number of islands and a greater angular deviation than in the relative tilt map by SXDM [Fig. 3(a)]. This implies that the ω angular range that was selected for the ESRF scans was insufficient and only permitted us to see GaN grains that were misoriented by a maximum of 2°. Therefore, conducting EBSD measurements prior to the synchrotron measurements would be extremely helpful to determine the ω angular range that should be considered during the SXDM experiments, allowing us to be more time-efficient by avoiding unnecessary angular measurements, while at the same time, detecting all grains, including those with significant misalignments in their orientations.

To accommodate the misorientations between adjacent domains, geometrically necessary dislocations (GND) are required, as the grain boundaries can be described in terms of arrays of dislocations for low angle boundaries (<10°) to accommodate the tilt and twist components.³⁶ Therefore, further analysis was performed to estimate the GND densities present at the grain boundaries.

We observe large GND values, around 2 × 10¹¹ cm⁻², present at the grain boundaries for GROD values higher than 2°, while areas with a misorientation lower than 2° present lower GND values, of the order of 10¹⁰ cm⁻². To validate the GND measurements, CL images were collected at the corresponding sample area; the results are shown in Fig. 6(d). The dark lines observed in the CL images (on the surface of flat grains) confirm the presence of large density of dislocations in the same regions for which the GND map showed maximum values [Fig. 6(c)], as indicated by arrows of matching colors.

We note that noise in measurement can lead to overestimated GND density, especially in slightly deformed grain structures and local measurements (small step size). In our case, this precision limit has set the lowest measureable GND density to 10¹⁰ cm⁻².

Nevertheless, this study confirms the growth of large GaN domains (3.9 μm) of homogeneous orientation with large dislocation densities at the interfaces between highly misoriented domains and reveals that the grain boundaries are the major issue.

Further data treatment allows us to analyze the tilt between neighboring pillars that, according to our measurements, contribute on average to forming grains that are well aligned within themselves. We can obtain the maximum tilt angle possible between adjacent pillars that would result in the formation of pillar domains similar in size to the GaN domains that form at the early coalescence stage. However, this size comparison will be made between pillar groups before coalescence, separated by 0.5 μm (sample A), and coalesced GaN grains grown on top of pillars separated by 1.5 μm (sample B). These different pitch sizes are used due to the lack of available data on structures with the same pitch.

First, we set a tilt limit between pillars and determine how many pillars would be contained in a group within this limit. The size of the groups of pillars is then analyzed for different tilt limit values. Figure 7(a) shows the tilt magnitude of the GaN pillars before coalescence (sample A) and Fig. 7(b) also shows the tilt distribution of the same sample but with a conversion from pillars to pixels spaced by 0.5 μm, meaning each pixel represents one pillar.

We define the pillars adjacent to the above-mentioned domains as the first neighboring pillars and choose a set of tilt limits from 0.2° to 0.04°. The test condition is that the tilt between two adjacent pillars is less than the tilt limit specified. In the next step, each pillar is considered as a starting point and the tilt between all its neighboring pillars is calculated. If the condition is satisfied, in other words, if the tilt between the two pillars is less than the specified tilt limit, these two pillars are considered to belong to the same pillar group. Figure 8 shows the pillar groups obtained for three tilt limit values (0.2°, 0.1°, and 0.04°). We note that the groups formed by one pillar only were removed from the maps.

We notice that for a tilt max = 0.2° [Fig. 8(a)], we have large groups of pillars formed much bigger than the measured coalesced GaN domain size, meaning that the tilt limit specified is too high. After decreasing the tilt limit, we have the formation of smaller groups verifying the condition.

The final step is to compare the sizes of these groups to the size of the GaN domains to find the maximum tilt that allows us to obtain groups of pillars similar in size to the experimentally measured GaN domains. To clearly display the groups, the experimental GaN domains are encircled by red contours in Fig. 9(a) and the pillar groups of tilt limits 0.1° and 0.04° are designated by red contours in Figs. 9(b) and 9(c), respectively.

However, as we mentioned in the introduction of Sec. III C, the GaN domains in Fig. 9(a) are grown on top of pillars separated by 1.5 μm while the GaN pillars in Figs. 7, 9(b), and 9(c) are separated by 0.5 μm. In order to properly compare the sizes, we assume that the distribution of orientation of the pillars before coalescence should be the same, whether they are separated by 0.5 or 1.5 μm, because regardless of the pitch, the pillars undergo the same etching process from the same 2D layer and independent nucleation of GaN. If we now consider that the pillars in Figs. 7, 9(b), and 9(c) are separated by 1.5 μm instead of 0.5 μm, while maintaining the same orientation, this means that the size of the pillar groups obtained from Figs. 9(b) and 9(c) should also be multiplied by three. This scaling occurs because the distance between the pillars directly influences the effective area occupied by each group. Therefore, with a tripled spacing, each pillar group will be three times larger in size. Consequently, the comparison with the GaN domain size from Fig. 9(a) will be relevant.

From Fig. 9(a), we find that the GaN domain’s mean size is 3.9 μm with a standard deviation σ = 1.3 μm. We note that GaN domains smaller than 1.5 μm were excluded from the calculation of the mean domain size and were not outlined in Fig. 9(a) because we consider that these groups are formed on top of a single pillar, and they were removed from the tilt limit maps shown in Fig. 8.

From Fig. 9(b), the size of pillar groups for a tilt limit of 0.1° is found to be equal to 1.7 μm on average, and that with a tilt limit of 0.04° is equal to 0.5 μm on average as seen in Fig. 9(c). Once multiplied by three, the size of the pillar group for a tilt limit of 0.1° becomes equal to 5.1 μm, which means that the tilt limit of 0.1° between neighboring pillars before coalescence allows the formation of group pillars slightly larger than the coalesced GaN domains which are 3.9 μm on average. This tilt can be generated due to the excess surface energy present on the interface of each GaN pyramid and because of SiO₂ that will become softer at a high growth temperature due to its viscoelastic properties,⁴² allowing the pillars to tilt/twist easily and GaN on the top to align. Additionally, we notice from Fig. 9(c) that each group consists of typically two to five pillars, so we would expect each GaN island to be formed on top of this amount of pillars.

GaN platelets grown by pendeoepitaxy at the early stage of coalescence and GaN pillars before coalescence have been characterized by SXDM at the ESRF, EBSD, and CL. A crystalline orientation map of GaN before coalescence and at the early stage of coalescence has been obtained and it has been shown that, with this novel growth approach, the initially misoriented GaN pillars transformed into well-defined and well-oriented GaN domains. The presence of dislocations at the grain boundaries has been confirmed with CL observations and estimated from the EBSD measurements, providing an upper bound for their local density of ∼10¹¹ cm⁻². In addition, the spatially resolved strain analysis highlighted the homogeneity of the strain gradients inside the GaN domains. Finally, we constructed a model that correlates the pillars' initial tilt before coalescence to the observed GaN domains’ size; thanks to this model, it was found that as long as the tilt between neighboring pillars does not surpass 0.1°, neighboring pillars contribute to forming a highly oriented crystalline domain. These results also illustrate the importance of combining EBSD, CL, and SXDM to provide complementary structural information on the evolution of GaN crystalline structures from pillars to well-defined coalesced domains. This study advances the understanding of the coalescence process at the nanoscale and highlights the potential of this novel pendeo-epitaxy technique in producing well-oriented GaN layers, which can be employed in the future in the production of micro-LEDs.

This work was supported by the French ANR PEGADIS (No. ANR-20-CE24-0022). The authors gratefully acknowledge both the European Synchrotron Radiation Facility for beam-time allocation at the ID01 beamline and the beamline staff for their full support during the measurements.

The authors have no conflicts to disclose.

Maya Wehbe: Formal analysis (lead); Investigation (equal); Software (equal); Writing – original draft (lead). Matthew Charles: Investigation (equal); Project administration (lead); Supervision (equal); Writing – review & editing (equal). Daniel Pino Muñoz: Investigation (equal); Supervision (equal); Writing – review & editing (equal). Kilian Baril: Resources (equal); Writing – review & editing (equal). Nabil Labchir: Resources (equal); Writing – review & editing (equal). Sebastien Labau: Resources (equal); Writing – review & editing (equal). Cecile Gourgon: Writing – review & editing (equal). Blandine Alloing: Writing – review & editing (equal). Pierre-Marie Coulon: Writing – review & editing (equal). Jesús Zuniga-Perez: Writing – review & editing (equal). Edoardo Zatterin: Software (lead); Writing – review & editing (equal). Patrice Gergaud: Investigation (equal); Supervision (equal); Writing – review & editing (equal).

The data from the ID01 experiment that support the finding of this study are available in ESRF at https://doi.org/10.15151/ESRF-ES-847479780, Ref. 43.