Compositional Mapping of the AlGaN Alloy Composition in Graded Buffer Structures Using Cathodoluminescence

Herein, the use of cathodoluminescence (CL) hyperspectral mapping in the quantification of the AlGaN alloy composition in graded buffer structures is explored. The quantification takes advantage of the known parabolic dependence of the AlGaN bandgap on the alloy composition allowing the AlGaN near‐band‐edge (NBE) emission energy recorded from CL to be converted to a composition. The proposed quantification method is first applied to cleaved cross‐sections of two nominally step‐graded AlGaN buffer structures each containing five AlGaN layers with different compositions. By comparing the compositions obtained from CL to those calculated using X‐ray diffraction, a close agreement between values from both techniques is observed. However, due to a change in the bowing parameter, some deviation is observed for layers with compositions near 75%. The method is then applied to cleaved cross‐sections of an AlGaN buffer whose group III precursor flow molar ratio is varied linearly throughout the growth. Herein, the hyperspectral nature of the CL datasets is exploited such as to produce composition maps by converting the relevant AlGaN‐NBE emission energy at each pixel of the CL data to a composition.

DOI: 10.1002/pssa.202200830 Herein, the use of cathodoluminescence (CL) hyperspectral mapping in the quantification of the AlGaN alloy composition in graded buffer structures is explored. The quantification takes advantage of the known parabolic dependence of the AlGaN bandgap on the alloy composition allowing the AlGaN near-bandedge (NBE) emission energy recorded from CL to be converted to a composition. The proposed quantification method is first applied to cleaved cross-sections of two nominally step-graded AlGaN buffer structures each containing five AlGaN layers with different compositions. By comparing the compositions obtained from CL to those calculated using X-ray diffraction, a close agreement between values from both techniques is observed. However, due to a change in the bowing parameter, some deviation is observed for layers with compositions near 75%. The method is then applied to cleaved cross-sections of an AlGaN buffer whose group III precursor flow molar ratio is varied linearly throughout the growth. Herein, the hyperspectral nature of the CL datasets is exploited such as to produce composition maps by converting the relevant AlGaN-NBE emission energy at each pixel of the CL data to a composition.
compositions match that of the sample with standard-less approaches giving relative uncertainties that be as high as 90%. [17] In addition to the large errors involved, high acceleration voltages are required for the production of characteristic X-rays. This limits the minimum size of the primary electron interaction volume, especially in scanning electron microscopy-based EDS, and hence the lateral spatial resolution.
To overcome the limitations of both XRD and EDS, cathodoluminescence (CL) hyperspectral mapping can be utilized. CL is advantageous as it is a high-throughput technique that provides a nanometre-scale lateral spatial resolution. [18,19] During CL hyperspectral mapping, a focused electron beam with energy in the kV regime is rastered across the investigated sample surface exciting carriers within the material that can recombine radiatively emitting photons that are then detected. Compositional quantification using CL is not direct but relies on the established relationship between the optical bandgap, obtained as the near-band-edge (NBE) emission energy, and the alloy composition. [20] The alloy composition can be estimated from the AlGaN-NBE emission energy using the parabolic composition dependence highlighted by Equation (1). [13,21] In Equation (1), E g;AlGaN , E g;AlN , and E g;GaN represent the AlGaN, AlN, and GaN bandgaps, respectively, x is the AlN fraction and b is the bowing parameter representing the deviation from linearity.
The aim of this work is to explore the possibility of using CL hyperspectral mapping and Equation (1) to quantify the AlGaN composition in graded buffer structures.

Experimental Section
Three multilayered epitaxial AlGaN buffer structures were investigated and are shown in Figure 1. The structures were grown using metalorganic vapour-phase epitaxy (MOVPE) which employed trimethylgallium (TMGa), trimethylalluminium (TMAl), and ammonia (NH 3 ) as Ga, Al, and N precursors, respectively. All the samples investigated utilize a silicon (111) substrate and an AlN nucleation layer. The AlGaN composition in the buffer layers was varied by controlling the group-III precursor flow ratio. The group-III precursor flow molar ratio was abruptly changed to produce the step-graded buffers, as shown in Figure 1a,b but was varied linearly throughout for the graded buffer, as shown in Figure 1c. The thicknesses shown in Figure 1 are approximate thicknesses obtained from in situ reflectivity.
The nominally step-graded structures A and B were used to verify the CL-based compositional quantification proposed by comparing to XRD measurements. The AlGaN compositions for these samples are shown in Table 1. After the verification, CL hyperspectral mapping will then be used to quantify the  www.advancedsciencenews.com www.pss-a.com compositional depth profile of structure C. The start and end compositions for structure C are shown in Table 1.
The AlGaN compositions and associated in-plane strains in these samples were calculated using high-resolution XRD reciprocal space map measurements of the (1-104), (1-105), , and (2-205) AlGaN reflections. These measurements were performed with a PANalytical Empyrean diffractometer equipped with a two-bounce hybrid monochromator with 0.25 ∘ a primary beam slit, and a PIXcel solid-state area detector.
CL hyperspectral mapping was performed at 10 K and room temperature (RT), on cleaved cross-sections of structures A-C, in an Attolight Allalin 4027 Chronos scanning electron microscope cathodoluminescence system. CL measurements were taken using an iHR320 spectrometer with a grating density of 600 lines per mm. A scan dwell time of 100 ms was utilized for the RT measurements while 50 ms was employed at 10 K. The microscope was operated at an electron beam current of 5 nA and an acceleration voltage of 3 kV, which corresponds to 90% of the beam energy being deposited in a depth of %30 nm as determined by Monte-Carlo simulations. [22] The CL hyperspectral maps were then analyzed using HyperSpy. [23] 3. Results and Discussion

Test Samples
To study the depth variation of the AlGaN alloy composition for an AlGaN buffer, such as structure C, we first need to verify that indeed CL can be used to quantify the composition in unknown samples. For this, nominally step-graded structures A and B will be utilized. To achieve this verification, the optical bandgaps measured from the AlGaN NBE emission energy of the AlGaN layers in each sample will be calculated. The composition will then be estimated from the optical bandgaps using Equation (1) and the 10 K and RT literature values of E g;AlN and E g;GaN , which are shown in Table 4, along with the value for b. The compositions calculated from CL will then be compared to those from XRD.
Structure A, shown in Figure 1a, consists of five AlGaN layers whose composition changes from 78% nearest to the substrate (A1) to 25% furthest from the substrate (A5). In Table 1, there is a large separation in composition between neighboring layers with the minimum difference being 12% between layers A5 and A4.
Cleaved cross-sections of structure A were investigated using CL hyperspectral mapping at RT and 10 K. Secondary electron (SE) images of the cleaved surfaces and corresponding panchromatic CL maps are shown in Figure 2. It should be noted that the regions investigated at 10 K and RT are of different positions on the surface of the sample cross-section. From the SE images shown in Figure 2a,c, the five AlGaN layers of structure A, labeled A1-A5, can be observed. These layers are especially apparent in the SE image recorded at 10 K which shows a stronger contrast between the layers. Also highlighted in the SE images is the GaN epilayer which was grown on top of AlGaN layer A5. Figure 2b,d shows the corresponding panchromatic CL intensity maps recorded at 10 K and RT, respectively, for the surfaces in Figure 2a,c. Note that the panchromatic CL maps are not aligned with the SE images due to drift caused by charging of the sample surface during the acquisition of the CL maps. When compared to that at RT, the panchromatic CL intensity map recorded at 10 K shows a much higher emission intensity and higher signal-to-noise ratio. This is because at 10 K, there is less thermal energy available to activate nonradiative recombination centers. Hence, a larger proportion of recombination events are radiative. [24] From the panchromatic CL maps, it is clear that the layers furthest away from the substrate (A3, A4, and A5) show a higher emission intensity compared to those closer to the substrate (A1 and A2). The lower emission intensity of layers A1 and A2 can be rationalized by an increased density of nonradiative defects, especially threading dislocations, closer to the substrate which limits the optical emission efficiency. [25] Moreover, the efficiency of the detector decreases as the emission energy tends further into the ultraviolet contributing to the lower observed intensity.
To investigate the luminescence properties of structure A, mean CL spectra were extracted from the hyperspectral datasets corresponding to the fields of view in Figure 2b,d. The approximate regions from which these mean CL spectra were extracted are highlighted by the red boxes in Figure 2a,c. The mean CL spectra are shown in Figure 3a,b for the 10 K and RT data, respectively. The mean spectra show AlGaN-NBE luminescence bands which correspond to the optical bandgaps of the five layers. For layer A5 in Figure 3a,b, only one AlGaN-NBE emission band is observed which corresponds to band-to-band recombination within the layer. However, for layers A4 to A1, additional bands are observed because carriers can drift toward neighboring layers with a lower bandgap and recombine. For instance, in Figure 3a, the spectrum for layer A3 at 10 K shows three separate AlGaN-NBE bands centered at %4.03, %4.26, and %4.54 eV. The band at %4.54 eV is the expected emission from this layer whilst those at %4.03 and %4.26 eV appear due to carrier drift toward layers A4 and A5. A similar rationale applies to the other mean spectra. From this, assuming that no photons from directly excited carriers are recorded from the adjacent layers, it can be said that the AlGaN-NBE band representing luminescence from the composition of that layer is the one that appears at the highest emission energy in each spectrum. It should be noted that at RT, there is sufficient energy for carriers to escape from localization centers induced by alloy fluctuations. [26] Hence, diffusion will also contribute to this carrier transfer toward the lower bandgap layers at RT.
Re-examining the RT panchromatic map of structure A in Figure 2d, higher emission intensity regions can be observed for layers A3-A5 that are surrounded by lower emission intensity regions. To unravel the nature of these higher-intensity regions, mean CL spectra were extracted from the regions of lower (1 and 3) and higher (2 and 4) emission intensity highlighted in the RT panchromatic CL map in Figure 2d for layers A4 and A5, respectively. These mean CL spectra are shown in Figure 4a,b. The CL spectra recorded for the lower emission intensity regions (1 and 3) show that AlGaN-NBE band corresponding to the respective composition of the layers dominates the spectra. For region 3, additional emission bands can be observed at %4.1 eV, corresponding to a very localized AlGaN region of a slightly different composition in layer A4, and at %3.9 eV corresponding to drift of carriers toward layer A5. When considering the higher emission intensity regions (2 and 4), a broader and unexpected luminescence band appears at energies in the range %3.7-%4.0 eV and www.advancedsciencenews.com www.pss-a.com  www.advancedsciencenews.com www.pss-a.com dominates the luminescence intensity. This emission band only manifests when similar higher-intensity regions are probed at RT and always appears in the same emission energy range. In fact, this RT trend is consistent for all the samples investigated in this work. The luminescence from these regions is associated with AlGaN regions within the layers that likely expose different crystallographic facets with a lower incorporation rate of AlN and hence lower emission energy than the surrounding AlGaN matrix. [27] In the analysis that follow, these high-emission intensity regions will be disregarded and only mentioned briefly as they are beyond the scope of this work and do not affect the analysis. Structure B also consists of five AlGaN layers whose composition changes from 78% nearest to the substrate (B1) to 38% furthest from the substrate (B5). Compared to structure A, the minimum separation between compositions in neighboring layers is 5% between layers B3 and B4. Cleaved cross-sections of structure B were investigated using CL hyperspectral mapping at RT and 10 K. SE images of the cleaved surfaces are shown in Figure 5a,c for the 10 K and RT data, respectively. The corresponding panchromatic CL maps of this sample are shown in Figure 5b, d. Similarly to structure A, only the layers furthest from the substrate (B3-B5) can be observed from the panchromatic CL maps.
Mean CL spectra were extracted along the lengths of the AlGaN layers in the CL hyperspectral maps for the fields of view in Figure 5. The approximate regions from which these mean CL spectra were extracted are highlighted by the red boxes in Figure 5a,c. The mean spectra are shown in Figure 6 for the 10 K and RT datasets. As shown in Figure 6, the highest energy AlGaN-NBE bands for each spectrum can be observed which were established to correspond to the AlGaN composition of that layer. However, for layer B2 at 10 K, the highest energy band observed is that from layer B1 which can be observed at %5.3 eV. Even though it was ensured that the boundaries of the region in which the mean spectrum of layer B2 was collected did not encroach into layer B1, the finite size of the interaction volume, which was estimated to be %30 nm from Monte-Carlo simulations, [22] resulted in photons emitted from layer B1 being collected. With that being said, CL was able to distinguish between layers B1 and B2 which have measured thicknesses of %190 nm highlighting the few 10 nm scale spatial resolutions of this technique. This is especially apparent at RT where no emission from layer B1 can be observed in the mean spectrum extracted from B2. Similar to structure A, luminescence peaks associated with the higher emission intensity regions observed in Figure 5b can be seen in Figure 6b. These appear in the range %3.7-%4.0 eV for layers B2-B5 in the RT spectra. An observation to note in Figure 6a is the closeness of emission energies between the compositions of layers B3 and B4. This is exemplified by the spectrum extracted for layer B3 where the emission from the composition of this layer appears as a shoulder on the emission associated with diffusion toward layer B4. The closeness of the emission energies of these layers suggests a closeness in the AlGaN alloy compositions that can nonetheless be resolved using CL.
To quantify the AlGaN alloy compositions for the layers in structures A and B, Gaussian curves were fitted to the AlGaN-NBE bands for the spectra in Figure 3 and 6. The center emission energy was then extracted from the fit for the band that is associated with emission from the alloy composition of that layer. These center emission energies were then converted to a composition using Equation (1) by employing the materials parameters, as shown in Table 4. The calculated AlGaN compositions for each layer in structures A and B are shown in Table 3 along with the corresponding compositions calculated from XRD. The error in the AlGaN composition calculated from CL represents the uncertainty in the CL center emission energy obtained from the fit and the uncertainty in the CL emission energy as induced by changes the in-plane strain within the layers. To calculate the error associated with changes the in-plane strain, layers A1 and A5 were considered. These have the largest measured difference in in-plane strain being a tensile strain of 0.0001 and a compressive strain of 0.0021, respectively, giving an in-plane strain difference (Δε) of 0.0022. Equation (2), derived by Lee et al., [28] shows the relationship between the bandgap emission energy and in-plane stress in GaN. This was used to estimate the maximum change in the bandgap energy (ΔE CL ) produced by the www.advancedsciencenews.com www.pss-a.com stress difference (Δσ) by assuming that the stress in the AlGaN layers is comparable to that in the GaN layer similar to. [20] The stress difference was calculated from the strain difference using Equation (3). The elastic constants C11, C12, C13, and C33 for the A1 and A5 AlGaN layers were calculated as a weighted average from those of GaN and AlN, as shown in Table 2.
There is a close agreement between the CL and XRD compositions, especially for the last four layers grown (A2-A5 and B2-B5) with no discernible difference between the RT and 10 K data. For the first AlGaN layers grown (A1 and B1), the method shows a larger deviation between the compositions determined from CL with those from XRD. In fact, this deviation is observed to increase from minimum in the last layers grown (A5 and B5) to maximum for the first layers grown (A1-B1). Rationale for this deviation can be attributed to the calculation of the composition using Equation (1). First, the calculation relies on using the literature values of the bowing parameter. In this case, it was assumed to be 0.9 eV [29] and consistent between the different AlGaN layers of structures A and B. However, in the literature, there are disagreements in the value of the bowing parameter with a range of values being reported. [30,31] Berrah et al. [32] have reported a dependence of the bowing parameter Figure 5. a,c) are secondary electron images recorded at 10 K and RT, respectively, for cleaved cross-sections of structure B. The AlGaN layers B1-B5 are highlighted in the images. The red boxes in (a,c) represent approximate regions from which mean CL spectra were extracted. b,d) are panchromatic CL images recorded at 10 K and RT, respectively, from cleaved cross-sections of structure B. The red boxes in (b,d) represent regions of lower (1) and higher (2) emission intensity.
www.advancedsciencenews.com www.pss-a.com on the AlGaN alloy composition determining values similar to the 0.9 eV used earlier for compositions in the 25%-50% range but %1.3 eV for compositions close to 75%. As an illustration, applying this larger bowing parameter to the RT data for layers A1 and B1 produces the values 73% and 74%, respectively, which are much closer to the 78% calculated from XRD. Furthermore, the bowing parameter will depend on the in-plane strain state [33] which was observed to vary across the layers, as seen in Table 3.
Second, in the calculation for the composition performed, there is an assumption that the AlGaN-NBE emission energy calculated corresponds to the bandgap of the AlGaN. However, effects like localized heating by the electron beam and Stokes's shift will lead to a deviation between the these two quantities. [33,34] With that said, in general, there is a close agreement between the AlGaN compositions calculated from CL with those from XRD. Deviations observed at higher AlGaN alloy compositions can be corrected by considering changes in the bowing parameter. As such, this method can be used to quantify AlGaN alloy compositions in graded buffers.

Depth-Resolved Analysis of Structure C
The above analysis has verified that CL can be applied in the quantification of alloy compositions in unknown step-graded AlGaN buffer structures. The next step will be to apply this method to structure C. Figure 7a,b are panchromatic CL maps recorded for cross-sections of structure C at 10 K and RT, respectively. The majority of the fields of view is occupied by the graded AlGaN layer with the regions occupied by the AlN and GaN layers being labeled in the figures. Similar to the previous samples, higher emission intensity regions can be observed in the RT panchromatic map, as shown in Figure 7b.
From the CL hyperspectral maps of which the panchromatic images were extracted, Gaussian curves were fitted to the spectrum in each pixel. At 10 K only one Gaussian curve was utilized to fit the single AlGaN-NBE emission peak observed at each pixel. This peak shifted according to the AlGaN composition at that pixel from %4.0 to %5.4 eV. At RT, an additional Gaussian was added to account for the higher emission intensity regions which emit in the range %3.7 to %4.0 eV. The center emission energy was extracted from the Gaussian associated with the AlGaN composition at each pixel and converted to a composition using Equation (1) and the materials parameters in Table 4. This allowed the AlGaN composition to be mapped across crosssections of structure C. These composition maps are shown in Figure 7c,d for the 10 K and RT datasets. It is noted here that carriers will drift toward the lower bandgap AlGaN as discussed   The strain values determined from XRD are also shown.
www.advancedsciencenews.com www.pss-a.com earlier in the text. Hence, there will be emissions from these lower bandgap regions being detected along with that from the AlGaN region being probed directly by the electron beam.
To investigate the change in the AlGaN composition across structure C, linescans were extracted as an average over the regions highlighted in Figure 7c,d. These regions approximately cover the full extent of the depth of the AlGaN buffer. Figure 8 shows these linescans along with a linear trend-line suggested by the group-III precursor flow ratio. The start and end gas-phase AlGaN compositions of the linear trend were determined to be %7.5% and %25% from the precursor flow rates in the growth recipes. Compared to the gas-phase composition in the reactor during growth, the start and end compositions obtained from the CL linescans show good agreement being 69% AE 3% and 25% AE 3%, respectively, and at both measurement temperatures. As detailed above, the deviation observed at high compositions is related to a change in the bowing parameter.
Compared to the linear trend-line, the depth variation of the composition obtained from CL is sublinear at both measurement temperatures. This behavior is expected since the species obtained from pyrolysis of TMAl are reactive and undergo parasitic prereactions slowing down the effective growth rate of the AlGaN layer and reducing the incorporation efficiency of AlN Figure 7. a,b) show the panchromatic CL maps recorded from cross-sections of structure C at 10 K and RT, respectively. Highlighted in the figures are the AlGaN and AlN regions. c,d) show the compositional variation of the AlGaN alloy composition at 10 K and RT. Line scans were extracted from the marked rectangular regions. Table 4. Values of E g;AlN and E g;GaN at 10 K and RT and the bowing parameter, b, used to calculate the AlGaN compositions from the CL optical bandgap.

Quantity
Value at 10 K Value at RT E g;AlN 6.28 eV [38] 6.20 eV [39] E g;GaN 3.47 eV [40] 3.39 eV [41] b 0.9 eV [29] www.advancedsciencenews.com www.pss-a.com leading to a lower AlGaN composition when compared to the composition that would be suggested by the input group III precursor flow ratio into the reactor. [35,36]

Conclusion
CL hyperspectral mapping was used to quantify the AlGaN alloy composition in graded buffer structures at 10 K and RT. This was done by converting the AlGaN-NBE center emission energy from CL to a composition using the parabolic relationship relating the two quantities. First, cleaved cross-sections of two AlGaN buffer structures, each with five AlGaN layers of different compositions, were considered. From CL panchromatic maps, higher intensity regions were observed at RT which emitted in the %3.7-%4.0 eV regime. These local variations in the AlGaN composition within the layers could be observed due to the high spatial resolution of CL. Similarly, other local variations such as those relating to defects, surface morphology changes, and other deviations from the intended growth process can also potentially be resolved using CL. Utilizing the hyperspectral datasets, mean spectra were extracted along the lengths of the AlGaN layers within the buffer structures and by extracting the center emission energy from the relevant AlGaN-NBE bands, estimates of the compositions of the layers could be calculated. Comparisons of the compositions from the CL analysis with those determined from XRD showed a close match. However, a deviation was observed for the first layer grown in each sample corresponding to the layer with the highest composition. A change in the bowing parameter at such compositions was used to rationalize this deviation. The quantification was then applied to cleaved crosssections of an AlGaN buffer whose group-III precursor flow molar ratio was varied linearly throughout the growth. From the CL hyperspectral datasets, the center emission energy at each pixel was converted to a composition producing compositional maps such that the change in composition with depth could be extracted. The depth-variation in AlGaN alloy composition obtained from CL was sublinear when compared to the linear trend expected from the group-III precursor flow ratio in the MOVPE reactor during the growth process. This was rationalized by parasitic prereactions of the TMAl precursor species which reduced the incorporation rate of AlN. The close agreement between CL and XRD and the application of this technique to buffers whose group-III precursor flow molar ratio were varied linearly during growth demonstrates its potential as a quality control tool for industrial semiconductor fabrication processes. www.advancedsciencenews.com www.pss-a.com