Nucleation control of high crystal quality heteroepitaxial Sc_0.4Al_0.6N grown by molecular beam epitaxy

Thin film pseudo-binary alloys between rock-salt ScN and wurtzite AlN with compositions of Sc_xAl_1−xN (ScAlN) having x < 0.43 have received significant attention in recent years due to their fivefold increase in the piezoelectric polarization relative to AlN^1–5 and the demonstration of ferroelectric switching.^6–9 The high piezoresponse makes wurtzite-phase ScAlN well-suited to wide-bandwidth and high frequency acoustic resonator-based filters.^10,11 The demonstration of a CMOS-compatible nitride ferroelectric has led to interest in ScAlN-based ferroelectric non-volatile memory, such as ferroelectric diode memristors^9,12 and ferroelectric field effect transistors.¹³ Both acoustoelectric and ferroelectric applications can benefit from increased ScN fraction. For instance, the piezoresponse has a super-linear dependence on ScN fraction,¹ and an increased piezoresponse gives a higher electromechanical coupling coefficient (k₂) and wider filter bandwidth.¹⁰ Ultimately, resonator performance will depend on the product of k² and the quality factor (Q). The definition of k₂ will depend on the specific device in question but generally scales with the square of the piezoelectric coefficient, and inversely with the stiffness and dielectric constant. Thus, the optimal resonator performance may not occur at the highest ScN fraction, and maintaining high Q at high ScN fraction is critically important. For ferroelectric devices, the critical field for ferroelectric switching decreases faster than the breakdown field with increasing ScN fraction,^6–8 reducing the voltage required to switch films with higher ScN fraction. Maintaining low electrical leakage and charge trapping, and, thus, high structural quality in the ScAlN is required to take advantage of the reduced coercive fields in high ScN fraction ferroelectric devices.

ScAlN is also well-suited to electronic and optoelectronic applications. The high spontaneous polarization of Sc_xAl_1−xN enables very high channel charge densities for Sc_xAl_1−xN/GaN heterostructures from 2.5 to 7 × 10¹³ cm⁻² due to the polarization difference between Sc_xAl_1−xN and GaN, although compressive strain leads to lower charge densities with increasing x.^2,14–19 High channel charge, in turn, enables channel current densities in excess of 2.5–3 A/mm for Sc_0.18Al_0.82N-barrier layers and a high-electron-mobility transistor RF output power of 11 W/mm at the Ka-band.²⁰ Additionally, novel etch-stop behavior of ScAlN under chlorine-based plasmas enables improved control and manufacturability of recessed cap processes in these types of devices.^20,21 The combination of both the ferroelectric and electronic properties of ScAlN has led to the demonstration of novel ScAlN-barrier ferroelectric HEMTs, opening up applications for logic devices with integrated non-volatile memory.^12,13 There are also potential applications in non-linear optics, motivated by the recent demonstration of Sc_0.36Al_0.66N second order non-linear susceptibility of 62 pm/V, 12 times higher than AlN, and twice as high as lithium niobate.²² 

Sc_xAl_1−xN alloys are predicted to be thermodynamically stable in the wurtzite phase for x < 0.55–0.57;^23,24 however, experimentally realized majority-wurtzite films have been limited to x ≤ 0.43.^1,5,25 While increasing ScN fraction is desirable for both acoustoelectric and ferroelectric applications as described above, the formation of anomalously oriented grains (AOGs) limits the maximum achievable piezoresponse and may lead to increased electrical leakage and charge trapping at grain boundaries. Both rock-salt and zincblende phases have inversion symmetry and are, thus, non-polar, effectively acting as the dead material, reducing piezoresponse, and increasing critical field. Wurtzite domains that are not c-plane oriented will have a reduced thickness-mode piezoresponse, as the piezoelectric polarization is reduced for all non-c-plane orientations.²⁶ X-ray diffraction (XRD) rocking curve full width at half maximum (FWHM) about the 0002 reflection is commonly used to quantify the general crystal quality,^10,27 as the 0002 reflection is sensitive to defects in the c-plane related to the thickness-mode piezoresponse. However, XRD is not always very sensitive to AOGs, as their crystal quality may be too poor to lead to measurable diffraction and they may not be oriented such that the Bragg criterion is met during a simple line scan. Thus, alternate characterization techniques such as reflection high-energy electron diffraction (RHEED), atomic force microscopy (AFM), scanning electron microscopy, and/or transmission electron microscopy (TEM) may be needed to assess AOG formation and density.²⁸ 

Historically, the majority of ScAlN thin film deposition has been done by sputtering, often on metal electrode layers on Si substrates. XRD 0002 reflection rocking curve FWHM values from 1° to 2° (3600–7200 arcsec) have been reported for the Sc_xAl_1−xN of varying compositions, with higher FWHM at higher x. Generally, these reports are for films of greater than 500 nm thickness (typically ≥ 1 μm), with increasing FWHM in thinner films.^29,30 In one report, the FWHM increases from 1.3° at 1150 nm to 2.1° at 350 nm, and 3.1° at 115 nm.³⁰ For reference, a FWHM of 2° has been used as a baseline value in which the measured piezoresponse matches closely with the theoretically predicted values.¹⁰ More recently, high quality epitaxial layers of Sc_xAl_1−xN with x ≤ 0.4 have been grown on GaN templates,^8,16,19,31 and those with x ≤ 0.32 have been grown on SiC using molecular beam epitaxy, and those with x ≤ 0.30 have been grown on GaN/sapphire templates by metalorganic chemical vapor deposition (MOCVD).³² Epitaxial growth methods are potentially advantageous when high quality is required in relatively thin (100–300 nm) ScAlN films for high frequency filter applications.

Growth of epitaxial Sc_xAl_1−xN on SiC substrates allows the direct integration of ScAlN-based filters and/or ferroelectric memory with industry-standard GaN/SiC RF electronics. Growth on SiC also enables the active use of low acoustic loss SiC substrates as part of the acoustic device, such as in all-epitaxial ScAlN/NbN_x/SiC high overtone bulk acoustic resonators.^33,34 Other types of resonators, such as surface acoustic wave resonators, can directly be integrated on SiC,³⁵ while thickness-mode resonators such as film bulk acoustic resonators and ferroelectric devices typically require a lower electrode and either release from the substrate or a method to confine the mode within ScAlN. The lower electrode and/or release process could be integrated using an epitaxial NbN layer as mentioned above,³⁴ combined with a heated XeF₂ release process.³⁶ Alternately, the release and metallization could be accomplished using a through-wafer via etch and metallization, as is common in RF monolithic microwave integrated circuit backend processing, utilizing the excellent etch-stop properties of ScAlN.²¹ 

AlN nucleation layers (NLs) are commonly used in III-N heteroepitaxy as well as in sputtered ScAlN to improve the structural quality over the overlying film.^{24,28,37–40} In addition, growth conditions, particularly growth temperature, have previously been shown to have a strong impact on the ScAlN microstructure.^1,28 In this work, we investigate the impact of an AlN nucleation layer, ScAlN growth temperature, and ScAlN epitaxial layer structure on the crystal quality and phase purity of heteroepitaxial Sc_0.40Al_0.60N thin films grown on SiC substrates.

Sc_xAl_1−xN samples were grown on 4H-SiC substrates using plasma-assisted molecular beam epitaxy. A high temperature effusion cell and a standard cold-lip dual zone effusion cell were used to provide Sc and Al flux, respectively. An RF nitrogen plasma was used to provide active nitrogen flux sufficient for a growth rate of 0.72 Å/s in an N-limited GaN calibration sample. The substrates were first heated to 1020 °C for 2 min to outgas and thermally clean the SiC wafer, and then ramped to 835 °C for the growth of a 5 nm AlN NL, unless otherwise stated. Growth was then interrupted and the substrate was ramped down to the ScAlN growth temperature of interest for the growth of the nominally 150 nm-thick Sc_xAl_1−xN layer. Sc_xAl_1−xN composition was varied by simultaneously changing both the Sc and Al flux to provide constant total metal flux at a growth rate of 0.56 Å/s and a nominal III/V ratio of 0.77.²⁸ Sc and Al fluxes were calibrated using separately grown calibration samples where the composition was measured by x-ray photoelectron spectroscopy (XPS)²⁸ and the metal-flux-limited growth rate was measured by x-ray reflectivity (XRR).

Several series of Sc_xAl_1−xN samples were grown to study the change in the ScAlN crystal quality with composition and growth temperature. In the first series, the Sc_xAl_1−xN composition x was varied from 0.20 to 0.40 by changing both the Sc and Al fluxes, as described above, at a constant growth temperature of 490 °C. Next, x = 0.36 and 0.40 samples were grown at growth temperatures of 300, 430, and 490 °C.

Two additional series were grown to study nucleation effects in Sc_xAl_1−xN films. In the first, the thickness of the AlN NL was varied among 0, 5, and 10 nm. Two additional samples with different ScAlN initiation procedures were grown to compare with the single composition Sc_0.40Al_0.60N sample: a two-step sample, which started with 50 nm Sc_0.32Al_0.68N, followed by 100 nm Sc_0.40Al_0.60N, and a graded ScAlN nucleation sample, which started with a 100 nm grade from Sc_0.32Al_0.68N to Sc_0.40Al_0.60N (Sc_0.32→0.40AlN), followed by 50 nm Sc_0.40Al_0.60N. The two-step and graded samples were designed to have the same average ScN fraction, x = 0.37. To examine defect evolution in thicker films, two additional samples were grown with 100 nm Sc_0.32→0.40AlN graded initiation layers. The first sample had an additional 400 nm Sc_0.40Al_0.60N for a total of 500 nm and average x = 0.393, and the second had an additional 900 nm Sc_0.40Al_0.60N for a total of 1 μm with an average x = 0.396. Samples were characterized using in situ RHEED, and XRD rocking curve measurements about the 0002 reflection. The selected samples were also characterized by AFM and TEM.

As shown in Fig. 1, the crystal quality of ScAlN grown on SiC degrades as the ScN fraction increases. The XRD 0002 FWHM of the 150 nm-thick films increases from 1440 arcsec for Sc_0.20Al_0.80N to 3500 arcsec for Sc_0.32Al_0.68N, and then rapidly increases to over 7000 arcsec for the Sc_0.36Al_0.66N and Sc_0.40Al_0.60N samples, as shown in Fig. 1(a). A similar trend can be observed when measuring the FWHM of the center spot of the zeroth order RHEED streak [Fig. 1(b)]; the FWHM increases slowly with increasing ScN fraction up to Sc_0.32Al_0.68N and then quickly for Sc_0.36Al_0.66N and Sc_0.40Al_0.60N.

Varying the growth temperature over a relatively wide range, from 300 to 490 °C, had a significant impact on the quality of 150 nm-thick Sc_0.36Al_0.66N and Sc_0.40Al_0.60N samples. The initial samples grown at 490 °C show broadened spots and partial rings in the RHEED pattern, as shown in Fig. 1(c) for the Sc_0.40Al_0.60N sample. The rings suggest the presence of polycrystalline grains in the film. The sample grown at 300 °C, shown in Fig. 1(a), has a RHEED pattern with a pair of offset spots on the first order streak, consistent with in-plane-rotated or twinned cubic grains.⁴¹ The absence of the center spot on the first order streak is consistent with an FCC-type lattice (e.g., rock salt or zinc blende), while the doubled spot suggests in-plane twinning. The spots themselves are broadened and show a ring-like character, suggesting some angular distribution in the grain alignment. Finally, the sample grown at 430 °C shows a RHEED pattern in Fig. 1(b) having only spots suggesting wurtzite ScAlN with some degree of surface roughness. The XRD and RHEED FWHM are also shown in Figs. 1(d) and 1(e) for Sc_0.36Al_0.66N and Sc_0.40Al_0.60N samples grown at 430 °C and are much lower than samples grown at 490 °C, consistent with the improvements in the RHEED pattern. XRD FWHM measurements of the samples grown at 300 °C were difficult to measure due to very broad and low intensity peaks indicative of poor crystalline quality, as well as the presence of a second ScAlN-related peak, and were not included in Fig. 1.

The XRD FWHM and RHEED images of a Sc_0.32Al_0.68N sample grown with no AlN NL, a 5 nm NL, and a 10 nm NL are shown in Fig. 2. The presence of the AlN NL strongly affected the crystal quality of the film, reducing the FWHM from over 7200 to 4100 and 4500 arcsec for the 5 and 10 nm NL, respectively. The RHEED pattern was also improved (narrower spots, less ring character) for samples with an AlN NL as shown in Fig. 2(c), with respect to the sample with no AlN NL, shown in Fig. 2(d), after 30 nm of Sc_0.32Al_0.68N growth. Generally, it is desirable to minimize the thickness of an NL, as the AlN would lower the average piezoresponse or increase ferroelectric switching voltage. The thinnest NL examined here was 5 nm-thick, which was the limit at which a streaky AlN RHEED pattern could be achieved, as shown in Fig. 2(b). The Sc_0.32Al_0.68N sample with a 5 nm AlN NL also had the lowest XRD FWHM and was used for subsequent studies.

RHEED patterns for one-step, two-step, and two-step graded Sc_0.40Al_0.60N samples grown on 5 nm AlN NLs are given in Fig. 3. Shortly after starting growth directly on the AlN NL (one-step), a double-spot RHEED pattern is clearly visible, as shown in Fig. 3(d), and the zero order spot on the first order streak is absent, consistent with the presence of rotated/twinned face-centered cubic grains.⁴¹ By the end of the full 150 nm growth, the RHEED pattern had significantly improved, showing only a typical wurtzite spot pattern, though with faint ring segments visible at the top of the image and in the background. A second sample used a two-step approach, where the initiation of the ScAlN layer is done using a 50 nm Sc_0.32Al_0.68N layer to suppress the clear double spot RHEED pattern at the beginning of the ScAlN layer, shown in Fig. 3(f). At this point, the spots are still very broad and diffuse suggesting relatively poor crystalline ordering on the surface similar to the one-step sample, but a stronger wurtzite character. A wider region on the first-order spot hints at an unresolved second spot indicating some remaining degree of cubic grain formation. After the additional 100 nm of Sc_0.40Al_0.60N growth, the RHEED pattern improves, showing only wurtzite spots, with no ring segments visible in Fig. 3(g). Initiating the ScAlN layer with a 100 nm grade from Sc_0.32Al_0.68N to Sc_0.40Al_0.60N shows further improvements in RHEED early in the growth. The spots, while still broad, are narrower than in the two-step sample with no indication of double-spots on the first-order reflection. The final RHEED spot pattern after the final 50 nm Sc_0.40Al_0.60N layer is sharp and relatively narrow, indicating improved surface crystallinity relative to the two-step and one-step samples. Note that the two-step and graded ScAlN samples both have an average nominal ScN fraction of 0.373 and all three samples have a total thickness of 150 nm.

High-angle annular dark-field (HAADF) scanning TEM (STEM) micrographs shown in Fig. 4 show a microstructural evolution similar to the surface evolution observed by RHEED. Bragg-filtered HAADF images, shown in Figs. 4(d)–4(f), using (200) reflections indexed to rock-salt ScN, highlight the presence of rock-salt grains in the otherwise wurtzite ScAlN films. These images were formed by using an aperture mask across reflections that were indexed to rock-salt ScN in the fast Fourier transform (FFT), and then taking the inverse-FFT image and overlaying it on the parent image for visualization.⁴² For the one-step Sc_0.40Al_0.60N sample, rock-salt grains can be observed at the Sc_0.40Al_0.60N/AlN interface, decreasing density closer to the surface, with few beyond the first 10 nm of growth. For two-step samples, very few rock-salt grains are observed in the Sc_0.32Al_0.68N layer and rock-salt grains of lower density are seen in the Sc_0.40Al_0.60N compared to the one-step growth. The graded-initiation sample shows only a few, small rock-salt grains right at the AlN interface and very few later in the grade or in the overlying Sc_0.40Al_0.60N layer. The smaller white dots seen in Figs. 4(e)–4(f) are the artifacts of the filtering process and not rock-salt grains (as they can also be seen in the AlN layer and SiC substrate). Energy dispersive x-ray spectroscopy (EDS) line scans did not show evidence of compositional variation in the wurtzite and rock-salt grains within the ∼2 at. % resolution limit of EDS, in agreement with Ref. 43 and in contrast to Ref. 44.

XRD and AFM measurements of the one-step Sc_0.40Al_0.60N sample and 150 nm, 500 nm, and 1 μm-total-thickness graded-initiation Sc_0.40Al_0.60N samples are given in Fig. 5. The 0002 reflection XRD FWHM narrows significantly from 4280 to 3190 arcsec for the thicker film, indicating the annihilation of extended defects as the film grows thicker. The FWHM increases to 3558 arcsec for the 1-μm film, presumably due to the growth of AOGs. This is the first reported FWHM under 1° for a heteroepitaxial Sc_xAl_1−xN layer with a weighted average ScN fraction in a 500 nm film with x = 0.393.

The AFM scans in Fig. 6 show small island features in the height images that correlate with phase contrast in the phase image and can be attributed to AOGs. The 150 nm one-step and graded initiation samples have areal AOG densities of 6.3 × 10⁸ and 1.6 × 10⁷ cm⁻², respectively, as extracted from the phase images. The AOG density stays relatively constant with increasing thickness, but the average AOG diameter increases from 46 nm at 150 nm to 319 nm at 1 μm. The rms roughness increases from 0.69 to 1.57 to 4.00 nm with increasing thickness and is dominated by the AOGs. The regions between the AOGs are relatively smooth, with an rms roughness of 0.6 nm taken from a 2 × 2 μm² region positioned between AOGs on the 500 nm sample. The areal AOG fill factor is defined as the percentage of the wafer area consisting of an AOG (summed AOG area/total area). For the one-step and graded initiation 150 nm samples, the fill factor was 0.1% and 0.03%, respectively. The fill factor increases to 0.5% for the 500 nm sample and 4.2% for the 1 μm sample. AOGs are expected to have a lower or zero piezoresponse, and one would expect the electromechanical coupling coefficient to, at a minimum, decrease in proportion to the AOG volumetric fill factor. The areal fill factor can be used as an approximation for the volumetric fill factor and suggests that the AOGs in the 150 and 500 nm films may only have a minimal impact on their mechanical properties.

A reduction in the crystal quality, as shown by an increasing XRD FWHM, for samples with higher ScN fraction is consistent with results for sputtered ScAlN films.^24,45 Several factors make high ScN fraction ScAlN more difficult to grow. Misfit strain for (Sc)AlN grown on SiC increases from −0.99% for AlN to −6.7% for Sc_0.40Al_0.60N.⁴⁶ Even though Sc_xAl_1−xN is predicted to be wurtzite for x < 0.57, the formation energy difference between the wurtzite and metastable hexagonal/rock-salt phase decreases as the ScN fraction increases, thus reducing the energy penalty for non-wurtzite grains. In addition, even in a random alloy, the local composition is expected to follow a binominal distribution, meaning that even without Sc clustering, one would statistically expect some regions with higher Sc content. For high ScN fraction layers, it is plausible that there may be regions that could be near or beyond compositions required for thermodynamically stable rock-salt domains. A recent study suggested a higher ScN fraction at grain boundaries, leading to the formation of rock-salt domains,⁴⁴ although we did not observe compositional inhomogeneity on a size scale visible using STEM EDS in this work.

It is clear from Fig. 1 that the optimal growth temperature also decreases with increasing ScN fraction, as has been seen previously.^1,28,45 Good quality Sc_0.18Al_0.82N films have been grown at temperatures ranging from 520 to 1200 °C,^14,31,47 but higher ScN fraction films grown on SiC appear to require lower growth temperatures, typically less than 500 °C.^1,28 The dual-spot RHEED pattern in Fig. 1 suggests the presence of a twinned cubic crystal structure and the ring-like character suggests the presence of polycrystalline grains at the surface at 300 °C. It appears that a substrate temperature of 300 °C is too cold under these growth conditions, considering the absence of the additional ad-atom kinetic energy that would be provided by energetic ions present in sputtering processes or surface migration enhancement from pulsed growth processes.^15,16 At 490 °C, the faint rings in RHEED suggest a higher density of polycrystalline grains, and the RHEED pattern is much broader, indicating higher disorder and obscuring the presence of an incipient rotated cubic doubled spot. To get sufficient ad-atom mobility for epitaxial growth, conventional III-V MBE growth temperatures for films grown in the group-V-rich regime are often half of the material melting temperature.⁴⁸ It is, thus, surprising that we are able to see relatively high quality materials at a growth temperature of 430 °C, given that AlN and ScN both have expected melting temperatures well above 2000 °C.⁴⁸ 

While rock-salt gains have been identified here in Sc_0.40Al_0.60N/SiC films, previous reports of Sc_0.40Al_0.60N/GaN have also observed stacking faults and zincblende grains,³¹ pointing to the complex nature of defects in Sc_0.40Al_0.60N. The high density rock-salt grains observed by STEM in Fig. 4 that form at the nucleation of the one-step Sc_0.40Al_0.60N film appear to largely self-terminate after the first 30–40 nm of growth. In contrast, the low density of surface AOGs increases in diameter with increasing film thickness, as seen in Fig. 5. Expansion of the AOG diameter with increasing thickness was also observed in Sc_0.40Al_0.60N films deposited by sputtering.⁴⁹ It appears that the crystal quality is improving, suggested via the narrowing of the XRD FWHM, with increasing thickness up to 500 nm due to defect annihilation, as is commonly seen for both epitaxial and sputtered films. In general, XRD is most sensitive to defects when the defect separation distance is similar to or less than the film thickness. As the film thickness increases to 1 μm, the AOG diameter continues to increase and the separation between AOGs decreases, approaching 1 μm. Thus, the AOG size growth likely causes the broadening of the 1-μm ScAlN film, even though the AOG density does not appear to be significantly increasing.

It is not clear at this stage if the AOGs are related to the rock-salt material observed by TEM, although there are reports that rock-salt ScAlN grains can act as nucleation sites for semipolar-oriented wurtzite ScAlN AOGs.⁴⁴ The correlation of AOG density with rock-salt inclusions in the early stages of the film growth observed here is consistent with this model of rock-salt grains acting as potential AOG nucleation sites. A graded ScAlN initiation layer has also been used in sputtered ScAlN films deposited on Si to suppress AOG formation.⁵⁰ More work is required to fully understand AOG nucleation and growth in high ScN fraction ScAlN films.

Both the two-step and graded ScAlN structures limit rock-salt grain formation in Sc_0.40Al_0.60N by starting with Sc_0.32Al_0.68N, which does not show a measurable rock-salt grain content under our growth conditions. While the compressive strain in Sc_0.32Al_0.68N (−5.5%) is lower than Sc_0.40Al_0.60N (−6.7%),⁴⁶ it is likely that Sc_0.32Al_0.68N still relaxes very quickly during the nucleation of the ScAlN layer. Relaxation rarely occurs in planar c-plane wurtzite materials by dislocation glide due to the absence of resolved shear stress on an easy slip system in wurtzite materials.^51,52 Thus, relaxation presumably occurs in this case by an alternate mechanism such as plastic relaxation and coalescence of islands, or dislocation inclination.⁵³ If there was little relaxation occurring in the initiation layer, one would expect the two-step and graded samples to have similar ending in-plane lattice constants and, thus, similar strain in the overlying Sc_0.40Al_0.60N layer. The reduction of rock-salt grains in the Sc_0.40Al_0.60N region of the two-step sample, and near absence in the graded sample, supports the model of rapid relaxation in the initial layer. Fast relaxation in the graded layer would, thus, allow Sc_0.40Al_0.60N to grow with reduced strain. This suggests that strain may be a significant driving force for rock-salt grain formation, particularly in high ScN fraction films that are already approaching the phase boundary.

In conclusion, we have demonstrated MBE grown Sc_0.40Al_0.60N under N-rich growth conditions at a substrate temperature of 430 °C and a 5 nm AlN nucleation layer on a 4H-SiC substrate, having a 0002 XRD rocking curve FWHM of 4100 arcsec (1.1°) in a 150 nm-total-thickness film. We observed the presence of rock-salt grains at the nucleation of the Sc_0.40Al_0.60N layer by both RHEED and TEM, and were able to suppress these rock-salt grains by introducing an x = 0.32 → 0.40 Sc_xAl_1−xN graded initial layer in ScAlN, leading to a reduction in the AOG density by over an order of magnitude. Using this graded initial layer, we have demonstrated a 150 nm Sc_xAl_1−xN sample with average x = 0.37, having an AOG areal fill factor of 0.07% as well as a 500 nm sample with average x = 0.39, an XRD FWHM of 3190 arcsec (0.89°), and an AOG areal fill factor of 1.0%.

This work was supported by the Office of Naval Research (NRL Base Program; N0001419WX01704, Dr. Dan Greene). The authors thank Marty Chumbes, Jeff LaRoche, Jay Logan, Adam Peczalski, Clay Long, and David Storm for their helpful discussions.

The authors have no conflicts to disclose.

Matthew T. Hardy: Conceptualization (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (equal). Andrew C. Lang: Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). Eric N. Jin: Investigation (supporting); Writing – review & editing (supporting). Neeraj Nepal: Investigation (supporting). Brian P. Downey: Conceptualization (supporting); Writing – review & editing (equal). Vikrant J. Gokhale: Conceptualization (supporting); Writing – review & editing (equal). D. Scott Katzer: Writing – review & editing (supporting). Virginia D. Wheeler: Supervision (equal); Writing – review & editing (equal).

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