Observation of interfacial strain relaxation and electron beam damage thresholds in Al_0.3In_0.7N/GaN heterostructures by transmission electron microscopy Free

AlInN can be used in various electronic and optoelectronic applications. It is lattice matched to GaN at a composition of 18% indium (In) and is useful in RF and power electronics as a strain-free barrier on GaN for high electron mobility transistors¹ and in optoelectronics as distributed Bragg reflectors² or electron blocking layers.³ Its high-quality epilayer can also be a promising alternative to InGaN and AlGaN^4,5 and is used as a part of thermoelectric and spintronic devices.^6–8 AlInN has a direct bandgap with a range of 0.65–6.1 eV, which includes the vast majority of the solar spectrum, making it useful for solar cells and is tunable by controlling its metal composition. In-rich AlInN ternary alloys have attracted interest for multijunction tandem solar cells.^9,10 Of particular interest is the 70% In alloy which has an optimal bandgap to use as a tandem solar cell, of 1.7 eV, when combined with silicon. However, studies on In-rich AlInN, especially structural properties including transmission electron microscopy (TEM), are not well investigated as compared to other III-nitrides (GaN, AlN, and InN) or their ternary alloys (InGaN and AlGaN).^6,11–13 Historically, there were challenges in growing AlInN by traditional molecular beam epitaxy (MBE) or metal organic chemical vapor deposition (MOCVD) due to conflicting issues of (1) decomposition and phase separation for high temperature growth and (2) low adatom surface mobility for low temperature growth. The first challenge is due to the large lattice mismatch between InN and AlN, resulting in AlInN having a large miscibility gap, similar to InGaN.^14–16 The second challenge is due to the fact that, in traditional MBE, for example, InN dissociates at temperatures above 450 °C, while AlN requires over 800 °C to achieve good quality. Likewise, in MOVPE, temperatures in excess of 700 °C are preferred to crack ammonia and provide adequate adatom mobility but also result in decomposition. Due to this trade-off, the In-rich AlInN growth previously required compromises involving intermediate temperatures where the surface adatom mobility for aluminum is too low to yield good film quality.¹⁷ 

Metal modulated epitaxy (MME) has proven useful for this challenging material in improving crystal quality by enhancing adatom kinetics even at lower growth temperatures (below 425 °C) than those traditionally used in plasma assisted MBE (PAMBE) and MOCVD and by mitigating the decomposition of In–N bonds and the desorption of In adatoms. This technique utilizes periodic, shuttered growth to modulate the Al and In metal fluxes, being simultaneously opened and closed periodically while nitrogen is supplied constantly. When the metal shutter is open, a metal-rich adlayer is accumulated and the surface diffusion is enhanced. While the shutter is closed, the metal on the surface is consumed into the film, terminating each cycle in a dry, nitrogen-rich surface. MME offers the ability to optimize the metal adlayer coverage and to prevent droplets from persisting during the growth by its precise control of the shuttering time.^15,18–24 Specifically for AlInN growth, MME was shown to improve both symmetric and asymmetric x-ray diffraction (XRD) figures of merit by as much as 11× over prior studies for a composition of 70% In.¹⁸ It also facilitates growth in the two-dimensional growth mode resulting in smooth surfaces (0.44 nm RMS roughness) with spiral mounds that decorate threading dislocations rising from atomically flat surfaces and extremely strong photoluminescence not common in films of this composition. As detailed in Ref. 18, the film quality has been improved compared to the prior literature by the MME low temperature growth method. The present paper seeks to identify by what mechanism, is the improved quality obtained.

Toward this goal, the observation of the bulk or interfacial structure of AlInN/GaN would help to understand the mechanisms by which MME improves the film quality. The (scanning) transmission electron microscope [(S)TEM] technique is a useful method for investigating the topographies, morphologies, crystallographic information, and composition of AlInN, not only for the surface structures but also for the bulk/interfacial structures in high resolution up to the atomic level. It also enables the investigation of defect structures and strain structures, as well as their mechanisms. Thus, (S)TEM is the ideal tool to directly observe the bulk/interfacial mechanisms underlying the successful growth of In-rich AlInN by MME from our previous study. Scanning nanobeam diffraction or four-dimensional STEM (4D-STEM) can be used to measure the local strain field or the lattice expansion via local lattice parameters. However, (S)TEM can itself cause damage and induce phase separation if not performed under proper conditions.^25–27 Of the TEM reports of AlInN,^11,26–29 most focus on AlInN around the GaN-lattice-matched composition of ∼18% In, and electron-beam induced degradation of AlInN is not well investigated. Only a few reports exist for imaging In-rich AlInN to our knowledge.^9,30–33 The electron beam radiation can cause permanent damage to the foil of the sample during the measurement, such as ionization damage, sputtering, decomposition, phase separation, and atomic displacement.^34–39 Among reports about high-energy electron-beam damage for III-nitrides,^40–42 one report suggests that the ejection of nitrogen atoms from wurtzite InN by 100 keV electron beam is observed in (S)TEM.⁴² 

The present work focuses on the investigation of the bulk and interfacial structure of the MME grown In-rich Al_0.3In_0.7N/GaN heterointerface from our previous work by Engel et al.¹⁸ and investigates the improved film quality compared to the prior literature by TEM and strain mapping calculated from 4D-STEM. Its potential false-defect observation by electron-beam damage in TEM is also examined by time-dependent TEM.

All films in the present study were grown in a Riber 32 radio frequency (RF) PAMBE reactor with the MME technique. Hydride Vapor Phase Epitaxy (HVPE) semi-insulating GaN templates grown on the top of on-axis c-plane sapphire with minimal step-edges are prepared in a 1 × 1 cm² size. The threading dislocation density is ∼5 × 10⁸ cm⁻² for this template. Two micrometers of tantalum are sputtered on the backside of the single side polished template in order to facilitate uniform heat conduction during growth. Right before transferring these substrates into the introductory chamber of the MBE system, two types of wet chemical cleanings were carried out; piranha cleaning with a solution of 3:1 volume ratio of H₂SO₄:H₂O₂ for 10 min at 150 °C and HF cleaning with a solution of 10:1 volume ratio of de-ionized water:HF for 5 s at room temperature, in order to reduce surface contaminants and oxidation. The templates were set into molybdenum blocks and transferred into an introductory vacuum chamber with a base pressure of ∼5 × 10⁻⁹ Torr. The transferring time was kept as low as possible in order to minimize oxygen exposure. The templates were thermally outgassed in the introductory and main growth chamber for 20 min at 200 °C and for 10 min at 650 °C, respectively.

All metal fluxes were provided by conventional effusion cells. A nitrogen plasma was provided by a Veeco UNI-Bulb RF plasma source with an RF power of 350 W and a nitrogen flow of 2.5 SCCM. 100 nm of unintentionally doped (UID) GaN was grown on the HVPE GaN template with a substrate temperature of 600 °C to obtain a high-quality growth interface for the subsequent AlInN growth. The GaN growth details are described elsewhere.^43–45 100 nm of AlInN was grown in a metal-rich condition with a target III/V ratio of 1.3. Both the Al and In shutter are simultaneously cycled at 2.1 s open and 2.1 s closed, while the nitrogen plasma was constantly impinging on the surface during the growth. This metal shuttering scheme helps to prevent phase separation by limiting the metal adlayer buildup to one monolayer of metal. This scheme was similar to what is also described in more detail for InGaN.^19,46 The AlInN film was grown at a substrate temperature of 350 °C, which is below the In desorption threshold temperature within the given system. The low growth temperature prevented both the decomposition of In–N bonds during growth and desorption of In from the surface.¹⁸ The details of AlInN conditions in addition to the similar conditions for our previous InGaN study are shown elsewhere.^18,19 The postgrowth XRD measurement was performed with a Philips X'pert Pro MRD to identify the composition of the AlInN film and the film quality. The measured composition matched the targeted composition set by in situ flux measurements normalized by ion gauge sensitivity, confirming the lack of In desorption. In situ reflection high-energy electron diffraction (RHEED) measurements, using an STAIB Instruments RH20S with an electron beam acceleration voltage of 20 kV combined with a k-Space Associates kSA 400 analytical RHEED system and a highly sensitive CCD camera, were utilized to monitor the growth rate and III/V ratio during growth.

The grown film was prepared for the cross-sectional TEM (XTEM) investigation by mechanical thinning and dimpling, followed by intermittent Ar⁺ milling with a 10 s period with 50% duty cycle at 4.5 kV for initial setup, 3 kV then finished at 2.0 kV using a Gatan precision ion polishing systems. An FEI Tecnai F30 super-twin field-emission-gun TEM operated at 300 kV was used to acquire the TEM images, electron diffraction patterns, and 4D-STEM images. Local-strain-field maps were calculated from nano-electron-beam diffraction patterns from 4D-STEM datasets. The electron-beam current densities for all TEM images are measured at the bottom fluorescence projected screen. All the TEM images are taken under electron-beam current densities of 2.5–5.7 A/cm² in order to minimize and quantify the damage induced by the electron beam. These values were selected because they are comparable to or lower than the threshold current density of 35 A/cm² for the previously observed degradation of InGaN/GaN quantum wells.²⁵ In addition, all the images were taken in different regions of the foil in order to avoid cumulative beam damage during the measurement. The images were recorded using a Gatan One View camera, and the exposure time was set to 0.25 s, which was enough to attain bright TEM images. The second condenser lens aperture was set to 100 μm for TEM and electron diffraction patterns and 10 μm for 4D-STEM images. The measured beam current density for 4D-STEM was 3.0 × 10⁻² A/cm². 4D-STEM is acquired within a 100 × 54 pixel array and 0.02 s per pixel in order to minimize the electron beam exposure. Strain-field maps were calculated from the nanobeam diffraction patterns obtained in 4D-STEM, using gatan gms3 software after ensuring that there is no overlap in the diffraction spots that could confuse the analysis. While direct measurement of the actual beam size was not possible in our experimental setup, it is estimated to have a 4.3 nm radius based on the diffraction image for the GaN substrate. The pixel step size is set up to be 0.64 nm. The calculation method is shown elsewhere.⁴⁷ Time-dependent TEM was necessary to ensure that the electron beam did not damage the films. The frame size and pixel exposure time were selected to be 512 × 512 and ∼0.3 s per frame, respectively.

Figure 1(a) shows a dark-field (DF) STEM image aligned close to the $⟨112¯0⟩$ zone axis. A nanobeam is focused with a convergent angle of 1.25 mrad and is scanned over the square area. Two-dimensional electron diffraction patterns are contained in each pixel and are summed up in a 4D-STEM image as shown in Fig. 1(b). 100 × 54 (width × height) pixels are contained in Fig. 1(b) with a scan time of 0.02 s for each pixel. Figure 1(c) is an electron diffraction pattern taken at the single-pixel point of C as indicated in the GaN layer in Fig. 1(b), and Fig. 1(d) is taken at the pixel point of D as indicated in the AlInN layer. The shifting of the diffraction spots from the center spot between each diffraction pattern shows the change in the interplanar distances; thus, the information of local lattice expansion or a strain map can be obtained. The projection pole was confirmed along the $⟨112¯0⟩$ in each 2D diffraction pattern. Vectors from the central spot to the diffraction spots of $⟨11¯00⟩$ (m-direction) and $⟨0002⟩$ (c-direction) were identified as the u vector and the v vector, respectively. The lattice expansion (or strain map) for the u vector (E_uu) and the v vector (E_vv) is calculated and shown in Figs. 1(e) and 1(f), respectively. The calculation used for the strain map based on the shifts of diffraction spot is shown elsewhere.⁴⁷ Figures 1(g) and 1(h) show the histogram of the strain versus pixel number obtained in Figs. 1(e) and 1(f), respectively. From Fig. 1(g), a strain difference of 5.4% ± 1.8% along the m-direction is observed between the AlInN (upper) layer and the GaN (lower) layer. The standard deviation of each of the two Gaussian-shaped distributions for AlInN and GaN was determined. These standard deviations, σ_GaN and σ_AlInN, were doubled to account for the double-sided variation of a Gaussian and summed to provide a total standard error in the strain estimate of 1.8% around 1.0%–3.5%. This implies that the interplanar distance along the m-direction of AlInN and GaN is different by 5.4% ± 1.8% between the two layers. Using a similar procedure for the c-direction (v-vector), we measure 5.2% ± 1.3%. We can compare this measured strain to the theoretical strain by assuming the interplanar distance for the m-plane for GaN is $dGaN=aGaN32$⁠, where a_GaN is the lattice parameter in the a-direction: 3.189 Å, and for Al_0.3In_0.7N is $dAlInN=aAlInN32$⁠, where a_AlInN for 70% In is 3.417 Å based on literature references.^48,49 Thus, the calculated strain between Al_0.3In_0.7N and GaN for m-direction (u vector) and c-direction (v vector) is 7.16% and 6.59%, respectively. The theoretical c lattice parameters for GaN and AlInN are 5.185 and 5.527 Å, respectively.^48–50 

Results of XRD reciprocal space mapping (RSM) from our previous report¹⁸ show that the composition of the AlInN film was 70% In. On comparing the measured and theoretical lattice constants, we find that the AlInN film is 75% ± 25% relaxed toward $⟨11¯00⟩$ (m-plane) if it is 70% In as found from XRD previously. We note that as Gerthsen et al.^51,52 showed that for InGaN, estimates of the In composition from thin 2D TEM samples are subject to large errors due to an unknown strain state in the thinned direction versus thick direction implying the lack of knowledge of fully relaxed versus biaxially strained state. These small theory versus experiment differences in the interplanar strain, within the calculated error, are likely due to the low resolution when the 4D-STEM was taken and the uncertainty in the bidirectional strain state of 2D TEM samples. Higher resolution 4D-STEM scans cannot be taken because this more involved diffraction mapping takes a longer time when taken under higher resolution, damaging the film from the electron beam exposure. Therefore, shorter scanning time with low resolution was prioritized rather than longer scanning time and high resolution.

The most noteworthy feature in these two figures is that there is a very thin layer, less than 2 nm, of intermediate interplanar-distance material along the AlInN/GaN interface as shown in Figs. 1(e) and 1(f). This implies that the interface has a very thin layer of strained material, suggesting that the critical thickness of Al_0.3In_0.7N is very thin, and the strain above this critical thickness is nearly fully relaxed, which is in good agreement with our previous study in which the RSM data from XRD showed that the grown AlInN are fully strain relaxed compared to the underlying GaN layer.¹⁸ Similar cases have been studied for the InGaN/GaN interface in previous studies,^15,53,54 and misfit dislocations were observed for high-In content InGaN/GaN interfaces with a very thin critical thickness. Thus, misfit dislocations are predicted to exist herein. According to a previous report, because of the large lattice mismatch between GaN and high-In InGaN, plastic relaxation occurs so early in growth that dislocations have no vertical direction to glide resulting in a near planar dislocation network.⁵⁴ The strain map results suggest that the growth away from the heterojunction happens under strain relaxed conditions. This feature is reported to improve the film uniformity and reduce the defects including threading dislocations and stacking faults above the interface.⁵³ The reduced defect density will increase the minor carrier lifetime; therefore, it can improve the performance in solar cell applications which are a device target of this particular composition.

Figure 2 shows XTEM images in the two-beam condition $g=⟨11¯00⟩$ under bright-field [Fig. 2(a)] and DF mode [Fig. 2(b)], close to the $⟨112¯0⟩$ pole with an electron-beam current density of 4.1 A/cm². This beam alignment is known to highlight edge type dislocations but is also convenient to highlight stacking faults. In order to minimize the beam damage, the measurement time was limited to ∼60 s per scan region. This excessively low current density makes the acquired images less clear than standard XTEM of more robust materials but is on par with images obtained from careful InGaN investigations.^15,53,54 Intrinsic basal stacking faults (BSFs) that lie on the ${0001}$ plane are normally observable in TEM images with $g=⟨11¯00⟩$⁠.^55–57 However, no such intrinsic BSFs were observed. Edge and mixed type dislocations normally observable at this alignment were also not observed in the bulk of the AlInN film within the range of the measurement (1200 × 100 nm²). This result of sparse dislocation density correlates with the sparse dislocations observed at the surface in prior AFM studies of the same films.¹⁸ The bright and dark contrasts shown in the film are considered to be low-angle grain boundaries associated with slight crystal rotations along the c-axis.^53,58 The darker spotty contrast, which is seen more in the GaN film, is considered an artifact of Ar⁺ milling during the sample process. Moiré fringes are observed at the AlInN/GaN interface, proving the generation of misfit dislocations, explaining the method of relaxation of the AlInN observed in the 4D-STEM analysis.^15,53 This Moiré fringe is an interference effect at the interface of two overlapping crystals with some levels of interplanar-distance mismatch.^59–61 There are several studies of misfit dislocations for highly mismatched InGaN/GaN interfaces, where the grown film is thicker than the critical thickness, resulting in strain relaxation.^62–64 It is also reported that the Moiré fringes in MME grown InGaN/GaN heterointerface resulted from strain when the film thickness exceeded the critical thickness in the first monolayer during growth.^15,53 Thus, like MME grown InGaN, high-In AlInN appears to relax via the same misfit dislocation mechanisms, resulting in higher film quality above the misfit array. To our knowledge, this is the first observation of Moiré fringes in an AlInN/GaN interface.

Moiré fringes can be used to determine the lattice mismatch of the films at the heterointerface, and then with some bidirectional strain assumptions of relaxation, to determine the composition of the ternary III-nitride samples grown on GaN.^53,65 The relationship between distance D of the fringe and interplanar distances along $⟨11¯00⟩$ direction in the GaN (d_GaN) and AlInN (d_AlInN) is

where D is measured as 3.9807 ± 0.1000 nm, and the lattice constant difference of Δa = a_GaN – a_AlInN = 0.121 ± 0.005 Å is obtained. From this difference, the In composition is estimated as 70.8%–73.7%, which is in good agreement with the XRD results from the previous study of 70% In.¹⁸ This TEM result identifies the mechanism for which the MME growth technique can grow high-quality In-rich AlInN films so as to fully strain relax the heterointerface with GaN by generating misfit dislocations.

XTEM images in the two-beam condition $g=⟨112¯0⟩$ and $g=⟨0002⟩$ are taken in different regions from Fig. 2 and are shown in Figs. 3(a) and 3(b), respectively. The electron beam current density is measured as ∼4.4 A/cm². The image for $g=⟨112¯0⟩$ normally highlights edge/mixed type dislocations and the image for $g=⟨0002⟩$ normally highlights screw/mixed type dislocations. Again, threading dislocations were not observed within the measured range and the resolution in the bulk of the film, and the bright and dark contrasts shown in the film are considered to be low-angle grain boundaries associated with slight crystal rotations along the c-axis^53,58 as discussed above. This conclusion arises from considering three other possibilities for the origin of the contrast: (1) compositional variations of AlInN, (2) residual local strain from lattice mismatch with GaN, and (3) electron-beam damage in the film. (1) and (2) are not supported by the XRD RSM results taken around the $(101¯5)$ reflections in our previous report,¹⁸ which has shown a sharp peak at the reciprocal position of Al_0.3In_0.7N and has shown that AlInN is fully strain relaxed from GaN substrate. However, the strain map shown in Figs. 1(e) and 1(f) depicted some strain variations in the AlInN film. Therefore, (2) local residual strain could possibly be a factor in the contrast. Given the local nature of the strain, this may not be observable in the XRD RSM but is seen in TEM/STEM. The sample foil thickness in the measured region in Fig. 3 was comparably thick, ∼90 nm—limited to large size by the tendency of the beam to degrade thin material as discussed later. Therefore, the effect of (3) can be ruled out with the electron-beam current density as discussed later. While local strain variations cannot be completely ruled out, the relatively thick foil size possibly emphasizes the contrast affected by the low-angle grain boundaries projected through the thick foil of the film. This is qualitatively supported by the low surface intersecting threading dislocation density observed in AFM studies of the same films in Ref. 18.

To compare the upper measured bound of relaxation to the critical thickness theory and to determine which theory is most appropriate for AlInN/GaN, calculations of the critical thickness have been implemented using various models^66–69 and compared with previous experimental results measured by XRD RSMs,^18,70–72 shown in Fig. 4. Due to the limited resolution resulting from the low beam current density necessary to avoid the electron-beam damage in the film, and by complex contrasts from various factors including low-angle grain boundaries, there are difficulties in directly measuring the burgers vector of these AlInN films from TEM images. However, only three models account for the reported strain states shown in Fig. 4: Srinivasan with b = a, Srinivasan with b = (a + c)/2, and Fischer for b = a. Since the Srinivasan model is most appropriate for the wurtzite system, a Burgers vector of b = a is consistent with previous reports.^53,73 But mathematically this is almost identical to the use of b = (a + c)/2 as found in Kim et al.,⁷⁴ which cannot be ruled out from the existing literature data. We note that some prior calculations used b = (a + c)⁶⁹ and b = c could be used. However, each of these two choices results in unrealistically large critical thicknesses (micrometers) for very large lattice mismatched films (In > 40%). As expected, the critical thickness resulted in larger values toward the In fraction of x = 0.17−0.18, where Al_1−xIn_xN possesses the same lattice constant as GaN. Cubic crystal models such as Matthews–Blakeslee introduced the force balanced model, which considers misfit stress balancing with the dislocation line force.⁶⁶ People and Bean introduced the energy balanced model, considering the areal strain energy density associated with the film thickness balancing with the one associated with an isolated screw dislocation from a free surface.⁶⁷ Fischer et al. suggested a theory for strain relaxation in metastable heteroepitaxial structures, placing an image dislocation outside the crystal and canceling the real misfit strain at the surface for lattice mismatched epilayers.⁶⁸ Hexagonal crystal models such as Srinivasan et al. among others took the Peierls force into account in addition to the former force balance conditions for the case of low growth temperature and low threading dislocation densities that closely matches our growth situation.^53,69 Unfortunately, Srinivasan's and People's models have a numerical instability as the critical thickness approaches 0 making them only applicable for smaller ranges of In than those examined here. Thus, as was done for InGaN/GaN previously, we calculate these models up to the In composition with stable results and then roughly extrapolate their trends above the In composition range.^53,68 The experimental results from previous reports^18,70–72 showed that some of AlInN films grown pseudomorphically are plotted under the calculated curves and some with strain relaxed are plotted above the curves. Our strain fully relaxed sample with x = 0.7 (plotted as a triangle) has consistency with all calculated models using b = a and b = (a + c)/2. Since our TEM results have not depicted threading dislocations nor V-defects in our measured area range, but do show misfit dislocations, the models by Fischer et al. and Srinivasan et al. should be more suitable for the AlInN/GaN case although Srinivasan's conditions more accurately match the growth conditions and crystal structure of AlInN. The critical thickness for x = 0.7 by Fischer's model is ∼17 Å (1.7 nm), which is in good agreement with the strain map in Fig. 1 showing the intermediate layer thickness being less than 2 nm. Srinivasan's model is estimated as 3.7 Å, close to a monolayer thickness of 2.7 Å for Al_0.3In_0.7N. Thus, the calculations from the two models by Fischer et al. and Srinivasan et al. support the assertion that the AlInN film relaxes in the range of a monolayer or two as suggested by the TEM results in Fig. 2 where Moiré fringes are observed along the heterojunction. This misfit relaxation is also reported as the favorable mechanism in InGaN under large lattice mismatch instead of relaxing through V-defects or threading dislocations as is favorable for lower lattice mismatches.^53,62,75,76 Thus, misfit dislocations should appear when the critical thickness for plastic deformation is on the order of a few monolayers and when the growth mode remains two-dimensional. These conditions are met by the MME technique, where long adatom migration lengths due to the metal-rich surfaces lead to 2D growth.

Since prior InGaN relaxation of quantum wells has been argued to be the result of TEM electron-beam damage,^25–27 it needs to be ensured that the results shown above are not an artifact of damage due to electron-beam exposure. Bright-field mode time-dependent TEM was measured every 60 s for 620 s (∼10 min) in a newly exposed region of the same sample, in the two-beam condition $g=⟨11¯00⟩$⁠, and the results are shown in Figs. 5(a)–5(d) at various electron-beam irradiation times. The electron-beam current density was measured as 2.5 A/cm², 60% of the current density used for Figs. 2(a) and 2(b). Therefore, 100 s of beam irradiation time has equivalent beam dose as used in the previous measurements. No obvious damage from the electron-beam irradiation was observed from Figs. 5(a)–5(d). Thus, it is confirmed that there is no beam induced damage in Figs. 2(a) and 2(b). The dark and bright contrast in the film is considered to be the low-angle grain boundaries as explained above.

The examination of electron-beam damage is also undertaken in the two-beam condition $g=⟨0002⟩$⁠. The bright-field time-dependent TEM image with this condition is shown in Figs. 6(a)–6(d). The electron beam current density is measured as 5.7 A/cm². No screw/mixed type threading dislocation is observed within the range of the measurement. All four images depict cluster features in AlInN. This is likely argon milling damage but is also possibly due to the electron beam exposure during the search of target region after inserting the sample into the TEM equipment and/or during the calibration of beam conditions for Figs. 2 and 5. During the time-dependent measurement, no change in these clusters was observed (the cluster stayed the same through this long-time beam irradiation). These images were taken on the region with a thick foil of the sample, limiting resolution. However, when projecting the thinner sample foil region, clusters with darker contrast started to generate very quickly. Figures 7(a)–7(h) taken under the two-beam condition of $g=⟨0002⟩$ and the same beam current density of 5.7 A/cm² display images of this phenomenon taken over time. Figure 7(a) shows the first scan of the beam irradiation (5 s). This cluster generation started to be observable around 20 s as shown in Fig. 7(b). Some clusters kept generating and drifting in the AlInN film, and at 75 s, some clusters started to merge as shown in Fig. 7(c). Moiré fringes appeared inside one cluster at 100 s (shown by an arrow) in Fig. 7(d). At 255 s, the cluster with the arrow merged with a neighboring cluster as both the clusters drifted toward each other as shown in Fig. 7(e). Figure 7(g) at 370 s shows the point where Moiré fringe in two big clusters is observed (arrows). And finally, the last scan of this in situ TEM measurement at 420 s is shown in Fig. 7(h).

This generation of clusters is evidence of decomposition by local beam heating or ionization/displacement damage by electron beam irradiation, etc.^34–36 As the AlInN film is degraded, precipitated regions, possibly of metal with nitrogen removed, form clusters as shown in Figs. 7(c)–7(h). Some previous studies suggested that there is In clustering, or a composition fluctuation within In-rich InGaN in InGaN/GaN quantum wells^25–27,77 during the electron-beam exposure. The Moiré fringe in the clusters implies that, after the drifting and merging, the cluster is stabilized as a crystal with a different interplanar distance as compared to the surrounding crystal film. To our knowledge, the clusters as shown here in In-rich AlInN have not been revealed in any reports, though it is similar to what has been reported for InGaN.^25–27,77 The damage threshold current density was estimated using time-dependent TEM to be ∼5.7 A/cm², significantly lower than from prior studies of InGaN which was found to be 35 A/cm²,²⁵ but damage strongly depended on the thickness of the TEM foil examined as the same current density did not show degradation in the thicker regions described previously. Using a drilled hole in the thin region and using sample rocking, we estimate the thickness of the thin region to be ∼90 nm. By most TEM standards, this “thin” region prone to damage is substantially thick, indicating that extremely thick samples of AlInN are needed for damage-free analysis. Unfortunately, these thicker samples result in degraded quality TEM images.

Bulk and interfacial structures and the quality of MME grown Al_0.3In_0.7N grown atop GaN are investigated via strain mapping from 4D-STEM and XTEM in an attempt to explain the 11× improvement in XRD structural figures of merit compared to the prior literature. 75% strain relaxation along the $⟨11¯00⟩$ (m-plane) direction is detected within ∼2 nm of the AlInN/GaN heterojunction, suggesting a very abrupt and almost complete relaxation mechanism. TEM measurement in the two-beam condition $g=⟨11¯00⟩$ showed Moiré fringes, indicating that the sudden strain relaxation occurs by misfit dislocation generation at the interface, allowing the film above these misfits to be grown in higher quality with reduced threading dislocations and stacking faults. Calculations of critical thickness support these results and suggest for Al_1−xIn_xN/GaN heterojunctions the critical thickness is ∼3.7–17 Å. These two measurements by 4D-STEM and TEM coupled with the critical-thickness calculations confirm that MME grown In-rich AlInN creates misfit dislocations that improve overall film quality. These results are in good agreement with and provide an additional mechanistic explanation of our previous study by Engel et al.¹⁸ 

Additionally, an electron-beam damage threshold dose for a 300 keV beam has been determined to be ∼28–115 J/cm² (∼5–20 s exposure for a 5.7 A/cm² current density) even for rather thick ∼90 nm TEM foils, making AlInN substantially more sensitive to damage than InGaN. Furthermore, there was an extreme sensitivity of the damage threshold to thickness not found in InGaN. The implications of this result suggest compromises in image quality (low current, short acquisition times, and thicker foils) must be made to ensure no electron beam artifacts exist in the images.

The authors are grateful to Yong Ding, Mengkun Tian, and Pralav P. Shetty who gave assistance in TEM and STEM and Alec M. Fischer for aid with the codes for the critical thickness. This work was supported by the Office of Naval Research (ONR) Multi-Disciplinary Research Initiative (MURI) entitled, “Leveraging a New Theoretical Paradigm to Enhance Interfacial Thermal Transport In Wide Bandgap Power Electronics” under Award No. N00014-17-S-F006 administered by Mark Spector and Lynn Peterson. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of ONR or MURI.

The authors have no conflicts to disclose.

Keisuke Motoki: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Zachary Engel: Resources (equal); Writing – review & editing (supporting). Christopher M. Matthews: Writing – review & editing (supporting). Habib Ahmad: Writing – review & editing (supporting). Timothy M. McCrone: Data curation (supporting). Kohei Harada: Data curation (supporting); Investigation (supporting). W. Alan Doolittle: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (lead); Validation (equal); Visualization (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.