We report the use of suboxide molecular-beam epitaxy (S-MBE) to grow β-Ga2O3 at a growth rate of ∼1 µm/h with control of the silicon doping concentration from 5 × 1016 to 1019 cm−3. In S-MBE, pre-oxidized gallium in the form of a molecular beam that is 99.98% Ga2O, i.e., gallium suboxide, is supplied. Directly supplying Ga2O to the growth surface bypasses the rate-limiting first step of the two-step reaction mechanism involved in the growth of β-Ga2O3 by conventional MBE. As a result, a growth rate of ∼1 µm/h is readily achieved at a relatively low growth temperature (Tsub ≈ 525 °C), resulting in films with high structural perfection and smooth surfaces (rms roughness of <2 nm on ∼1 µm thick films). Silicon-containing oxide sources (SiO and SiO2) producing an SiO suboxide molecular beam are used to dope the β-Ga2O3 layers. Temperature-dependent Hall effect measurements on a 1 µm thick film with a mobile carrier concentration of 2.7 × 1017 cm−3 reveal a room-temperature mobility of 124 cm2 V−1 s−1 that increases to 627 cm2 V−1 s−1 at 76 K; the silicon dopants are found to exhibit an activation energy of 27 meV. We also demonstrate working metal–semiconductor field-effect transistors made from these silicon-doped β-Ga2O3 films grown by S-MBE at growth rates of ∼1 µm/h.

With its very high bandgap, dopability, good mobility for electrons, and the availability of a large-diameter native substrate, β-Ga2O3 has emerged as a promising material for high-power electronics.1,2 Although molecular-beam epitaxy (MBE) is the leading technique for the growth of most compound semiconductors, for the growth of β-Ga2O3, it has serious limitations, and metalorganic chemical vapor deposition (MOCVD) is currently the method of choice.3,4 A direct comparison of the best electrical properties reported for the growth of β-Ga2O3 films by MBE5,6 and MOCVD3 at growth rates near current limits for each is shown in Table I, revealing the shortcomings of MBE.

TABLE I.

Comparison of the highest reported electrical mobilities of β-Ga2O3 films grown at a relatively high rate by MBE vs MOCVD.

Mobility at room Peak Temperature Growth Range of
temperature mobility of peakrate controlled doping
(cm2 V−1 s−1) (cm2 V−1 s−1) mobility(K) (μm/h) (cm−3)References
MBEa 129 390 97 0.09 1017–1020 5  
MBEb 136 168 165 0.3 4 × 1016–2 × 1019 6  
MOCVD 190 3425 53 2.9 2 × 1016–4 × 1019 3  
Mobility at room Peak Temperature Growth Range of
temperature mobility of peakrate controlled doping
(cm2 V−1 s−1) (cm2 V−1 s−1) mobility(K) (μm/h) (cm−3)References
MBEa 129 390 97 0.09 1017–1020 5  
MBEb 136 168 165 0.3 4 × 1016–2 × 1019 6  
MOCVD 190 3425 53 2.9 2 × 1016–4 × 1019 3  
a

Conventional plasma-assisted MBE.

b

Metal-oxide catalyzed epitaxy (MOCATAXY).

The conventional MBE growth of β-Ga2O3 starts with metallic gallium, which undergoes a two-step reaction to form solid Ga2O3,7–9,
2Ga+oxidantGa2O+additionaloxidantGa2O3,
(1)
where the oxidant is either oxygen plasma or ozone. The suboxide produced in the first step, Ga2O, is volatile at typical growth temperatures, and if there is insufficient oxidant present to oxidize it, it will desorb from the substrate surface diminishing the throughput of the second step. The first step is rate-limiting and even operating at the oxidant pressure limit that hot filaments in an MBE can withstand, i.e., ∼10−5 Torr, the growth rate of β-Ga2O3 is relatively slow, in the ∼0.1 µm/h range.2,5,6 It is possible to enhance this meager growth rate by catalytic means10 using a process referred to as metal-oxide catalyzed epitaxy (MOCATAXY)11 or metal-exchange catalyzed molecular beam epitaxy (MEXCAT-MBE).12 The metallic catalyst can be added indium, which can be incorporated into β-(AlxGa1−x)2O3 films at the ∼1% level11 or through the addition of a dopant, e.g., tin.13 Another way to increase the growth rate is to bypass the first step of the two-step reaction mechanism and directly supply an incident molecular beam of Ga2O, i.e., suboxide MBE (S-MBE),14 rather than by supplying a molecular beam of gallium.

Using S-MBE increases the growth rate by overcoming the kinetic limits imposed by the first reaction shown in Eq. (1), leading to an order of magnitude higher growth rate in the ∼1 µm/h range.14 There are a couple of options to produce a molecular beam of Ga2O suboxide. One is to use solid Ga2O3 itself,15,16 and the other is to use a mixture of solid Ga2O3 and liquid gallium.17 Vapor pressure calculations show that the dominant species in the molecular beam for both methods is the suboxide Ga2O.18,19 An advantage, however, of using the Ga2O3 + gallium mixture is the far lower temperature needed to produce the Ga2O molecular beam.18,19 This allows more types of crucibles to be used to contain the mixture (e.g., Al2O3 and BeO crucibles), increases the Ga2O flux that can be achieved (and with it the growth rate of the β-Ga2O3 film), and decreases contaminants coming from the hot crucible and effusion cell. For example, when solid Ga2O3 has been used as a source, even at source temperatures in the 1700 °C range, the maximum growth rate that has been achieved is 0.14 µm/h and the films have been contaminated with ∼5 × 1018 iridium atoms cm−3 coming from the iridium crucible used to contain the very hot Ga2O3 source.20–22 In contrast, films of β-Ga2O3 produced using S-MBE using a Ga2O3 + gallium mixture result in growth rates exceeding 1 µm/h, excellent crystallinity, and smooth surfaces all at a relatively low growth temperature, Tsub.14 The disadvantage of S-MBE is that generating a Ga2O molecular beam at low temperatures utilizes a source containing a mixture of Ga2O3 powder plus gallium metal.14,17 Unfortunately, the highest purity of Ga2O3 powder that we are able to obtain commercially is only 99.999% (5N), whereas 99.99999% (7N) pure gallium is the norm for conventional MBE. This lower purity raises questions about whether S-MBE can grow device-quality films. The direct way to answer this question is to make devices on β-Ga2O3 layers grown by S-MBE and see how they perform.

Studying the mobility of β-Ga2O3 films and fabricating β-Ga2O3-based devices necessitate controlled doping. Silicon is the preferred dopant for β-Ga2O3 films as it not only yields films with highest mobility2,3,23–25 but has been demonstrated to provide abrupt and controlled doping over the 1016–1020 cm−3 range in β-Ga2O3 films grown by MOCVD.2,3,24–27 Silicon segregates less to the surface during the MBE growth than does tin,6 making it a superior dopant, and it has the advantage over germanium of a far lower diffusion coefficient in β-Ga2O3 at temperatures required for device processing.28 The traditional MBE approach to dope with silicon is to create a silicon molecular beam by heating silicon to high temperatures in an MBE source. Unfortunately, in the high oxidant pressure (∼10−5 Torr) used for the growth of β-Ga2O3 by MBE, the surface of the silicon doping source may also oxidize.29 Whether the silicon surface gets covered over by a layer of SiO2 or is able to desorb gaseous SiO at the same rate that the silicon source is oxidized and, thus, remain uncoated depends on the temperature of the silicon and the oxidant pressure. For the case that the oxidant pressure is fixed at 1 × 10−5 Torr, at high temperatures TSi830°C), the silicon surface is able to desorb all of the oxide that forms and remains clean, whereas at low temperature, TSi830°C), the silicon surface gets coated by solid SiO2.30–32 These changes with the oxidation of the silicon source result in huge changes in the flux of silicon or SiO emanating from the silicon source, thwarting controlled and reproducible doping at device-relevant concentrations.4,5,29

This paper tackles the challenges of growing silicon-doped β-Ga2O3 thin films by taking advantage of the suboxide forms of both silicon and gallium. In this work, we demonstrate both controllable and reproducible silicon doping of β-Ga2O3 at device-relevant concentrations, i.e., the 5 × 1016–1019 cm−3 range, with a growth rate of ∼1 µm/h by S-MBE. Having overcome the doping challenge, we then evaluate the mobility of the silicon-doped β-Ga2O3 layers and demonstrate working devices made by S-MBE at a growth rate of ∼1 µm/h.

All films were grown using a Veeco GEN10 MBE system equipped with retractable and differentially pumped effusion cells that can be exchanged without venting the entire MBE system. This facilitates refilling the Ga2O3 + gallium source. The film growth took place on (0001)-oriented sapphire substrates (Kyocera) or (010)-oriented iron-doped β-Ga2O3 single-crystal substrates (Novel Crystal Technology) with 10 × 10 × 0.5 mm3 dimensions held in substrate holders made of Haynes® 214® alloy. The backside of each substrate was coated with a ∼200 nm thick platinum layer (on top of a ∼20 nm thick titanium adhesion layer) to enable it to be radiatively heated by an SiC heating element to Tsub = 525 or 550 °C as measured by an optical pyrometer operating at a wavelength of 980 nm.

A detailed description of the thermodynamics and kinetics of the growth of Ga2O3 by suboxide MBE is given in prior publications.14,33 Thermodynamic calculations in the present work were performed using the Scientific Group Thermodata Europe (SGTE) Substance Database (SSUB5)34 within the Thermo-Calc software.35 

To obtain a molecular beam of gallium suboxide, we shake the combination of Ga2O3 powder (Alfa Aesar, 99.999% purity) and molten metallic gallium (Alfa Aesar, 99.99999% purity) to produce a mixture with a molar fraction of oxygen of x(O) = 0.4. The Ga2O3 + gallium charge is contained within a beryllium oxide (BeO) crucible (Materion, 99.7% purity) in the MBE effusion cell. Our thermodynamic calculations estimate that such a mixture heated to the 750–1000 °C range of temperatures used in this study will produce a molecular beam that is 99.98% Ga2O.14 Films were grown at a background pressure of distilled ozone (∼80% ozone with the balance being O2) of PO3 = (1–5) × 10−6 Torr. The growth rate of films grown on c-axis sapphire substrates was determined by measuring the thicknesses of the β-Ga2O3 films by x-ray reflectivity (XRR). For films grown on (010)-oriented iron-doped β-Ga2O3 single-crystal substrates, the growth rate was estimated by growing calibration films on c-axis sapphire substrates and assuming that the growth rate was the same on the (010)-oriented β-Ga2O3 substrates. The thickness of one sample (sample a) was measured by scanning transmission electron microscopy (STEM) and found to be ∼40% thicker than this simple estimation. For two of the homoepitaxial β-Ga2O3 films (samples k and l), the growth rate was established by depth measurements made using a stylus profilometer on secondary-ion mass spectrometry (SIMS) craters.

To dope silicon into β-Ga2O3 films, we tried two silicon-containing oxide sources: SiO (Alfa Aesar, 99.99% purity) and SiO2 (Kurt J. Lesker, 99.99% purity) contained within Al2O3 crucibles (McDanel, 99.8% purity). From vapor pressure calculations, both sources are expected to produce a molecular beam of suboxide SiO.19 This approach is an attempt to circumvent the challenges associated with going back and forth between the active and passive oxidation regimes of elemental silicon as the silicon source temperature is changed, as unfortunately occurs in the growth of β-Ga2O3 by conventional MBE using a silicon source.5,29 Both SiO and SiO2 have previously been used as doping sources for silicon in oxide MBE: SiO to dope β-Ga2O3 films36,37 and SiO2 to dope α-Al2O3 films.38 

The SiOx flux emanating from the SiO and SiO2 doping sources was measured in two ways. At high SiO and SiO2 source temperatures, where the SiOx flux was sufficient to build up a multi-nanometer thick film in a reasonable time, its thickness was determined by XRR. XRR measurements were made on amorphous SiOx films deposited on unheated (0001) Al2O3 or (100) MgO substrates using the calibration scheme described by Ref. 37. The silicon fluxes calculated from these XRR measurements were independent of the oxidant employed for background pressures of distilled ozone ranging from none (vacuum) up to at least 2.5 × 10−6 Torr. At lower SiO and SiO2 source temperatures, the SiOx flux was inferred from Hall effect measurements of silicon-doped β-Ga2O3 films. The Hall effect measurements were made using a van der Pauw geometry39 with four ohmic contacts on 1 µm thick silicon-doped β-Ga2O3 films grown by S-MBE at a growth rate of ∼1 µm/h on iron-doped β-Ga2O3 (010) substrates that were 10 × 10 × 0.5 mm3 in size. For highly silicon-doped samples (greater than 1 × 1019 cm−3), contacts to the films were made by soldering indium at the corners. In order to make ohmic contact to more lightly silicon-doped films, ∼90 nm of n+ epitaxial β-Ga2O3 was regrown on the four corners of the films using a shadow mask in an Agnitron Agilis 100 MOCVD system. The donor density (Nd) in these n+ layers was greater than 1 × 1019 cm−3 to ensure that the contacts are ohmic. The MOCVD reactor pressure was 50 Torr, and the substrate temperature was 630 °C. Triethylgallium (TEGa), oxygen (99.999%), and silane (25 ppm SiH4 in argon) were used as precursors, with argon (99.999%) as the carrier gas. Then, indium was soldered on top of the regrown n+ β-Ga2O3 contacts. A Nanometrics HL5500 Hall system was used on these samples to determine the sheet carrier concentration of mobile charges at room temperature. The silicon flux was estimated under the assumption that all silicon is activated at room temperature in the β-Ga2O3 film. The temperature-dependent transport properties of select samples (samples a, b, and d) were measured as a function of temperature using a vacuum cryostat with a closed-cycle helium compressor and an electromagnet with an applied magnetic field of 0.5 T for Hall-effect measurements.

X-ray diffraction (XRD) and x-ray reflectivity (XRR) measurements were performed in a coplanar symmetric geometry using a PANalytical Empyrean system equipped with a copper anode and a hybrid incident-beam monochromator to provide Cu Kα1 radiation. Rocking curves were collected in a triple-axis configuration using a 220 Ge analyzer crystal. An Asylum Research Cypher ES atomic force microscope (AFM) was used to measure the surface roughness.

SIMS measurements were made either using a Hiden Analytical SIMS Plus Workstation or by EAG Laboratories. The Hiden Analytical SIMS Plus Workstation used an O2+ ion source as the primary beam to profile the sample. The system features a MAXIM quadrupole mass analyzer to detect and analyze the emitted secondary ions at 30° to the probe axis. The O2+ primary ion beam was oriented at 45° relative to the sample surface. The primary beam voltage and current for the analysis were 2 kV and 140 nA, respectively. The crater area, scan density, electronic gate, and oxygen flooding pressure were 400 × 400 µm2, 100 × 100 pixels2, 5% of the raster area, and 4.0 × 10−6 Torr, respectively. The SIMS system base pressure was ∼5.0 × 10−10 Torr.

The microstructure of one epitaxial β-Ga2O3 film (sample a) was examined using STEM. The sample was prepared in the cross-sectional geometry perpendicular to the [201] direction and thinned to electron transparency using a Thermo Fisher Helios G4 UX focused ion beam with a final milling step of 5 keV to minimize the damage of the top layer. Carbon and platinum protective layers were deposited on the sample prior to milling to minimize the ion-beam damage. STEM measurements were taken with an aberration-corrected Thermo Fisher Spectra 300 CFEG operated at 300 keV with a high-angle annular dark-field (HAADF) detector.

Metal–semiconductor field-effect transistors (MESFETs) were fabricated using annealed Ti/Al/Ni/Au ohmic contacts, a Ni/Au gate, and mesa isolation via reactive-ion etching,40 with a channel length of 3 µm and a gate length of 1 µm.

Utilizing a Ga2O3 + gallium two-phase mixture to produce a molecular beam of the suboxide Ga2O, we first map out the growth rate of β-Ga2O3 on (0001) Al2O3 substrates as a function of suboxide flux under conditions yielding epitaxial films. In Fig. 1, we demonstrate that the growth rate of β-Ga2O3 is a function of substrate temperature, distilled ozone pressure, and Ga2O flux. For a constant substrate temperature and background pressure of distilled ozone, the growth rate, at first, increases linearly with the Ga2O flux and then plateaus. This behavior is seen in Fig. 1(a). For the growth conditions studied, the β-Ga2O3 films grown on (0001) Al2O3 were fully epitaxial by reflection high-energy electron diffraction and XRD with 2̄01 orientation in agreement with prior reports of the growth of β-Ga2O3 on (0001) Al2O3 by pulsed-laser deposition,41 MOCVD,42 conventional MBE,7,8,37,43,44 and S-MBE.14–16 The linear region corresponds to oxidant-rich conditions, where all of the Ga2O supplied in the incident flux is oxidized to Ga2O3 during its residence time on the substrate surface. When the Ga2O flux increases further—into the Ga2O-rich regime—the excess Ga2O, beyond what can be oxidized by the background pressure of the distilled ozone, is desorbed from the surface due to the volatility of Ga2O at the substrate temperatures employed. This results in a plateau in the growth rate with increasing gallium suboxide Ga2O flux. The growth rate in the plateau regime depends solely on the background pressure of the distilled ozone (and substrate temperature); it is an adsorption-controlled growth regime, where the insufficient ozone flux limits the adsorption of the excess Ga2O flux. As the background ozone pressure is increased, more Ga2O can be oxidized during its residence time and the growth rate is found to increase. This occurs by an extension of the oxidant-rich (linear) regime to a new plateau of the growth rate at a higher Ga2O flux, beyond which there is insufficient ozone present to oxidize all of the Ga2O to Ga2O3 during its residence time on the substrate surface. At a substrate temperature of 525 °C and a background distilled ozone pressure of PO3 = 5 × 10−6 Torr, we achieve growth rates as high as 2.5 µm/h on (0001) Al2O3. Similarly, when keeping the ozone pressure constant and varying the substrate temperature, the growth rate is seen [Fig. 1(b)] to decrease with increasing substrate temperature due to the decreased residence time of the Ga2O on the substrate surface as the substrate temperature is increased. The oxidant-rich and adsorption-controlled growth regimes are still observed, just shifted due to the change in the residence time. These results agree with a kinetic model developed for S-MBE.14,33

FIG. 1.

Growth rate of β-Ga2O3 on (0001) Al2O3 substrates as a function of Ga2O flux. (a) Growth rate at a constant substrate temperature (Tsub = 525 °C) at four different background pressures (in Torr) of distilled ozone showing the oxidant-rich (linear) regime and the Ga2O-rich (adsorption-controlled) regime. (b) The effect of substrate temperature on the growth rate. The smooth curves indicate a fit to the experimental growth rates by the kinetic model described in Ref. 33.

FIG. 1.

Growth rate of β-Ga2O3 on (0001) Al2O3 substrates as a function of Ga2O flux. (a) Growth rate at a constant substrate temperature (Tsub = 525 °C) at four different background pressures (in Torr) of distilled ozone showing the oxidant-rich (linear) regime and the Ga2O-rich (adsorption-controlled) regime. (b) The effect of substrate temperature on the growth rate. The smooth curves indicate a fit to the experimental growth rates by the kinetic model described in Ref. 33.

Close modal

Having established the conditions for the epitaxial growth of β-Ga2O3 films at a rate of ∼1 µm/h, we next consider doping them with silicon. For this purpose, we tried both of the oxides of silicon, first SiO and then SiO2, as source materials to dope β-Ga2O3. To calibrate the flux of the SiO molecular beam, XRR was used to determine the growth rate of amorphous SiOx films. As XRR provides a measure of both the film thickness and the film density,45 the XRR spectra of smooth SiOx films enable the silicon flux to be calculated as a function of temperature of the SiO source, TSiO. From the XRR spectra, the density of the amorphous SiOx films deposited by the SiO source was about 1.8 g/cm3, comparable to that reported in prior studies of vacuum-deposited SiOx films deposited under similar conditions.37,46 To evaluate the stability of the SiO source and the associated reproducibility of growing silicon-doped β-Ga2O3 films over a range of desired conditions, we grew amorphous SiOx calibration films at oxidant pressures ranging from vacuum to PO3 = 5 × 10−6 Torr. While the SiO source behaved well at the high values of TSiO used for the growth of the XRR samples, at the lower values of TSiO relevant to doping β-Ga2O3 films with silicon concentrations in the 1017–1019 cm−3 range, SIMS measurements revealed a major challenge with using SiO as a source. At a lower TSiO, the flux is not reproducible. Not only did doping at the same value of TSiO vary considerably from growth to growth (as seen in Hall measurements), but often, the doping concentrations measured in SIMS stacks would not follow an Arrhenius relationship as TSiO was varied. Presumably, this is due to the surface of the SiO forming an SiO2 crust in the presence of ozone, causing the flux to plummet. This is consistent with the results reported by Ardenghi et al.37 for SiO used in conjunction with an oxygen plasma in the growth of silicon-doped β-Ga2O3 by plasma-assisted MBE (PAMBE). For this reason, we found SiO to be unsuitable as a controlled and reproducible doping source and moved on to evaluating SiO2 for this purpose.

In calibrating the SiO2 source, XRR measurements of amorphous SiOx on (0001) Al2O3 substrates revealed that a well-behaved and reproducible silicon flux emanates from it, despite changing the oxidant pressure from vacuum to PO3 = 2.5 × 10−6 Torr. From the XRR spectra, the density of the amorphous SiOx films deposited by the SiO2 source was about 2.1 g/cm3 as tabulated for each sample in the supplementary material (Table S1). Having established that the SiO2 source performed well when its temperature, TSiO2, was high, we moved on to evaluating its stability at lower TSiO2 relevant to doping β-Ga2O3 films. For these lower fluxes of the silicon-containing dopant species (mainly SiO from vapor pressure calculations19), Hall measurements were performed on silicon-doped homoepitaxial β-Ga2O3 films in both the oxidant-rich and adsorption-controlled regimes. The silicon flux is determined from the Hall measurements assuming full activation at room temperature, an assumption that may underestimate the silicon flux. On the other hand, mobile carriers due to the unintentional silicon contamination that often occurs at the interface between the β-Ga2O3 film and the underlying substrate14,25,47–49 could lead to the Hall measurements overestimating the silicon flux. Tables II and S1 (supplementary material) list the growth conditions of the samples grown using an SiO2 source. Table II lists the samples investigated by Hall measurements (samples a–l), while Table S1 lists the samples measured by XRR (samples o–v).

TABLE II.

Growth parameters and electrical characteristics of the β-Ga2O3 films measured by the Hall effect and SIMS.a

NameMobility (cm2 V−1 s−1)Carrier density (cm−3)SiO2 source temperature (°C)Thickness (nm)Ga2O flux (molecules cm−2 s−1)
Sample a 124 2.7 × 1017 1286 1000 1 × 1015 
Sample b 119 2.9 × 1017 1134 1000 6 × 1014 
Sample c 111 3.5 × 1017 1115 1000 6 × 1014 
Sample d 129 3.5 × 1017 1119 1000 1 × 1015 
Sample e 104 9.8 × 1017 1187 1000 6 × 1014 
Sample f 86 1.3 × 1018 1225 1000 1 × 1015 
Sample g 98 1.5 × 1018 1171 1000 6 × 1014 
Sample h 91 2.4 × 1018 1176 1000 1 × 1015 
Sample i 75 5.5 × 1018 1262 1000 1 × 1015 
Sample j 79 1.1 × 1019 1286 1000 1 × 1015 
Sample k 62 3.0 × 1019 1319 1000 1 × 1015 
Sample l 68 4.4 × 1019 1350 1000 1 × 1015 
Sample m ⋯ ⋯ Figure 3(a)  6500 6 × 1014 
Sample n ⋯ ⋯ Figure 3(c)  9000 1 × 1015 
NameMobility (cm2 V−1 s−1)Carrier density (cm−3)SiO2 source temperature (°C)Thickness (nm)Ga2O flux (molecules cm−2 s−1)
Sample a 124 2.7 × 1017 1286 1000 1 × 1015 
Sample b 119 2.9 × 1017 1134 1000 6 × 1014 
Sample c 111 3.5 × 1017 1115 1000 6 × 1014 
Sample d 129 3.5 × 1017 1119 1000 1 × 1015 
Sample e 104 9.8 × 1017 1187 1000 6 × 1014 
Sample f 86 1.3 × 1018 1225 1000 1 × 1015 
Sample g 98 1.5 × 1018 1171 1000 6 × 1014 
Sample h 91 2.4 × 1018 1176 1000 1 × 1015 
Sample i 75 5.5 × 1018 1262 1000 1 × 1015 
Sample j 79 1.1 × 1019 1286 1000 1 × 1015 
Sample k 62 3.0 × 1019 1319 1000 1 × 1015 
Sample l 68 4.4 × 1019 1350 1000 1 × 1015 
Sample m ⋯ ⋯ Figure 3(a)  6500 6 × 1014 
Sample n ⋯ ⋯ Figure 3(c)  9000 1 × 1015 
a

All samples were grown at Tsub = 525 °C in PO3 = 2.5 × 10−6 Torr on iron-doped (010) β-Ga2O3 substrates and doped with an SiO2 source.

Figure 2 shows an Arrhenius plot of the silicon flux calculated from both the XRR and Hall data as a function of TSiO2. A clear Arrhenius behavior with an activation energy of about 5 eV is seen between the silicon flux and 1/TSiO2. To assess our ability to control silicon doping over the 1016–1019 cm−3 range using the SiO2 suboxide doping source, we attempted to grow two 7 µm thick films for SIMS analysis, one in the oxidant-rich regime and the other in the adsorption-controlled regime. Each film starts off with a 1 µm thick undoped β-Ga2O3 buffer layer followed by alternating 0.5 µm thick layers of silicon-doped and undoped β-Ga2O3 as shown by the schematics in Figs. 3(a) and 3(c) for the SIMS stacks grown in the oxidant-rich and adsorption-controlled regimes, respectively. To keep the growth conditions similar and yet explore the two growth regimes to see whether they affect the dopant incorporation or the doping profile in some way, both SIMS stacks were grown at the same Tsub = 525 °C and the same PO3 = 2.5 × 10−6 Torr. Accessing the oxidant-rich regime vs the adsorption-controlled regimes was achieved by using different Ga2O fluxes for these two SIMS stacks: 6 × 1014 molecules cm−2 s−1 for the oxidant-rich regime and 1 × 1015 molecules cm−2 s−1 for the adsorption-controlled regime [Fig. 1(a)]. The growth rates in these two regimes for the growth conditions used differ (0.86 vs 1.3 µm/h), requiring different TSiO2 values. During the growth of each undoped layer, the temperature of the SiO2 source is increased to provide the silicon flux targeted for the next silicon-doped layer.

FIG. 2.

Silicon flux incorporated into β-Ga2O3 films as measured by XRR (red squares), SIMS (triangles), and the Hall effect (stars) as a function of the temperature of the SiO2 doping source (TSiO2). The linear fit shown is calculated based on the XRR and SIMS data points, where TSiO2 is in kelvin. Two of the samples on which the Hall effect was measured were also measured by SIMS. For those two samples, the calculated silicon flux values are indicated by the vertical arrows, showing that the fraction of silicon that is electrically active is lower when the β-Ga2O3 is less highly doped. The vertical axis on the right side of the figure gives the silicon doping concentration that the silicon flux would produce in a film of β-Ga2O3 grown at 1 µm/h.

FIG. 2.

Silicon flux incorporated into β-Ga2O3 films as measured by XRR (red squares), SIMS (triangles), and the Hall effect (stars) as a function of the temperature of the SiO2 doping source (TSiO2). The linear fit shown is calculated based on the XRR and SIMS data points, where TSiO2 is in kelvin. Two of the samples on which the Hall effect was measured were also measured by SIMS. For those two samples, the calculated silicon flux values are indicated by the vertical arrows, showing that the fraction of silicon that is electrically active is lower when the β-Ga2O3 is less highly doped. The vertical axis on the right side of the figure gives the silicon doping concentration that the silicon flux would produce in a film of β-Ga2O3 grown at 1 µm/h.

Close modal
FIG. 3.

SIMS profiles showing the concentrations of silicon, iron, aluminum, and beryllium as a function of depth of silicon-doped β-Ga2O3 films grown at Tsub = 525 °C and a background oxidant pressure of 2.5 × 10−6 Torr of distilled ozone. (a) Schematic of the targeted doping profile, including TSiO2 for each layer, and (b) the measured SIMS profile of the silicon-doped β-Ga2O3 films grown in the oxidant-rich (linear) regime at a growth rate of 0.86 µm/h at a Ga2O flux of 6 × 1014 molecules cm−2 s−1. (c) Schematic of the targeted doping profile, including TSiO2 for each layer, and (d) the measured SIMS profile of the silicon-doped β-Ga2O3 films grown in the Ga2O-rich (adsorption-controlled) regime at a growth rate of 1.3 µm/h at a Ga2O flux of 1 × 1015 molecules cm−2 s−1.

FIG. 3.

SIMS profiles showing the concentrations of silicon, iron, aluminum, and beryllium as a function of depth of silicon-doped β-Ga2O3 films grown at Tsub = 525 °C and a background oxidant pressure of 2.5 × 10−6 Torr of distilled ozone. (a) Schematic of the targeted doping profile, including TSiO2 for each layer, and (b) the measured SIMS profile of the silicon-doped β-Ga2O3 films grown in the oxidant-rich (linear) regime at a growth rate of 0.86 µm/h at a Ga2O flux of 6 × 1014 molecules cm−2 s−1. (c) Schematic of the targeted doping profile, including TSiO2 for each layer, and (d) the measured SIMS profile of the silicon-doped β-Ga2O3 films grown in the Ga2O-rich (adsorption-controlled) regime at a growth rate of 1.3 µm/h at a Ga2O flux of 1 × 1015 molecules cm−2 s−1.

Close modal

Figures 3(b) and 3(d) are the resulting SIMS measurements depicting the concentration of elements of interest—silicon, iron, aluminum, and beryllium—with respect to the sputtered depth. The SIMS data show clear and well-defined steps, demonstrating controllable silicon-doping from 5 × 1016 atoms cm−3 to 1 × 1019 atoms cm−3. The steepness of the step edges of the silicon profile differs between the oxidant-rich and adsorption-controlled regimes, with the oxidant-rich regime consistently showing sharper steps. The underlying reason could be the increased rms roughness of the ∼9 µm thick SIMS stack grown in the adsorption-controlled regime (53 nm) in comparison with the ∼6.5 µm thick SIMS stack grown in the oxidant-rich regime (11 nm). We also note that when the silicon shutter is open, the silicon profile is also observed to be flatter for the oxidant-rich regime [Fig. 3(b)], whereas it has a slight upward slope (indicative of silicon riding the surface) for the adsorption-controlled regime [Fig. 3(d)].

Despite calibrating the silicon incorporation by XRR and Hall measurements, the silicon concentration measured by SIMS in Figs. 3(b) and 3(d) does not precisely match the incorporation targeted in our SIMS stack design in Figs. 3(a) and 3(c). At high silicon-doping (TSiO2 > 1187 °C), the match is good, but at lower TSiO2, the concentration observed by SIMS is lower than the predicted silicon incorporation by up to a factor of 5. One explanation of this discrepancy is that the Hall data overestimate the silicon concentration at low doping because of the unintentional silicon contamination at the substrate interface14,25,47–49 giving rise to a concentration of mobile carriers beyond that provided by the silicon flux during growth. To assess this hypothesis, additional SIMS measurements were conducted on two Hall samples (samples k and e), one in each growth regime. If this hypothesis were true, then the concentration of silicon measured by SIMS should be less than the mobile carrier concentration measured on the same samples by the Hall effect. The results are shown in Fig. 2, where the vertical arrows point to the silicon fluxes measured by SIMS and Hall effect on the same sample. The data do not support the hypothesis. Rather, the data show that the silicon concentration measured by SIMS is as large as or larger than the concentration measured by the Hall effect. The data show that at high doping, almost all of the silicon is electrically active, ∼90% at 3 × 1019 cm−3 doping. At lower doping, however, the fraction of silicon dopants that produce mobile carriers is far lower, with ∼40% activation of silicon at 2 × 1018 cm−3 doping. This could be from a background of compensating acceptor states in our films, but the concentration involving ∼1018 cm−3 of acceptors or traps is so high that it is inconsistent with the relatively high mobilities seen in other films as we describe below.

The concentration of silicon incorporated into the β-Ga2O3 films as a function of TSiO2 in the SIMS stacks shown in Figs. 3(b) and 3(d) was used to calculate the silicon flux at doping-relevant temperatures and is also plotted in Fig. 2. From these SIMS values and the XRR values, a more accurate fit to the Arrhenius behavior between the silicon flux and 1/TSiO2 can be obtained. Unlike the Hall measurement, which only probes mobile carriers, the SIMS and XRR data measure all of the silicon incorporated. The resulting best fit has an activation energy of 5.3 eV/molecule. Although some scatter exists, particularly between Hall and SIMS values, the results in Fig. 2 show a linear trend that extends over 5 orders of magnitude, establishing that SiO2 is a well-behaved doping source for the growth of β-Ga2O3 by suboxide MBE. We attribute the more stable behavior of the SiO2 doping source over an SiO or silicon doping source to the fact that SiO2 is fully oxidized and free of the active/passive oxidation issues30–32 that plague SiO37 and silicon5,29 sources when used at the high oxidant pressures involved in the growth of β-Ga2O3 by MBE.

In addition to measuring the concentration of silicon, the concentrations of iron, aluminum, and beryllium were also measured by SIMS. This is because these elements are the major impurities in our Ga2O3 powder or they are the major constituents of the BeO and Al2O3 crucibles used to contain the Ga2O3 + gallium mixture and SiO2 sources, respectively. A composition analysis on the 99.999% Ga2O3 powder reveals aluminum, boron, sodium, and iron to be the only elements present at above the ppm level. A broad screening of these elements and more by SIMS analysis (not shown) indicated that the major contaminants in our undoped β-Ga2O3 films grown by S-MBE are aluminum, silicon, and iron; all impurities that are not isoelectronic with gallium have concentrations below 1016 cm−3.14 The low concentration of beryllium in the SIMS in Figs. 3(b) and 3(d) demonstrate that BeO is a suitable crucible for the Ga2O3 + gallium mixture. Of concern, however, are the high iron levels seen in Figs. 3(b) and 3(d). The steps in iron contamination seen by SIMS track the temperature changes and the shutter opening of the SiO2 source. This indicates that the iron contamination is coming from either (1) the impurities in the SiO2 source material, with its 99.99% purity; (2) the 99.8% pure Al2O3 crucible used to contain the SiO2; or (3) the iron impurities from the iron-doped β-Ga2O3 substrate that ride the growth front50 and are preferentially incorporated in the presence of silicon dopants.

When SiO2 is heated to a temperature range of 1075–1490 °C, as is done in this work, the stable polymorph varies as is described in Fig. S1 of the supplementary material. Over this temperature range, the silicon-containing species with the highest vapor pressure is the suboxide SiO, followed by SiO2. According to our thermodynamic calculations (Fig. S1), the SiO makes up 61% of the silicon-containing species in the gas phase at 1075 °C and 99.3% at 1490 °C. Experimentally, the dominant silicon-containing species observed in the gas phase when SiO2 is evaporated is SiO.51–53 Furthermore, the activation of energy of the measured vapor pressure of SiO, averaged from three studies (all with f < 4 × 10−3, where f is a parameter characterizing the effusion cell and, at this small magnitude, is consistent with measurements of the equilibrium vapor pressure), is 5.29 ± 0.21 eV.51–53 This agrees well with the activation energy of 5.3 eV from the fit in Fig. 2.

Having established that SiO2 is a well-behaved doping source, 1 µm thick films of silicon-doped β-Ga2O3 are grown in both the oxidant-rich and adsorption-controlled regimes at ∼1 µm/h. Figure 4(a) shows the mobility deduced from the Hall measurements of silicon-doped β-Ga2O3 films grown by S-MBE (red stars) together with the best results from the literature of silicon-doped β-Ga2O3 films grown by other leading techniques.3,5,24,27,54,55 From the mobility comparison, it is evident that β-Ga2O3 grown by S-MBE with a β-SiO2 doping source is on a par with other leading techniques. Figure 4(b) clarifies which S-MBE films shown in Fig. 4(a) were grown in the oxidant-rich regime and which were grown in the adsorption-controlled regime by S-MBE. Interestingly, there is no clear difference between the mobility at room temperature of silicon-doped β-Ga2O3 grown by S-MBE in the oxidant-rich or adsorption-controlled regime.

FIG. 4.

(a) Comparison of the electron mobility as a function of electron density measured at room temperature by the Hall effect on the silicon-doped β-Ga2O3 films grown in this study at ∼1 µm/h by S-MBE to leading reports of silicon-doped β-Ga2O3 films by other techniques from the literature. The S-MBE results are indicated by the red stars. (b) A close-up of the S-MBE results [the results indicated by the red stars in (a)] showing which films were grown in the oxidant-rich regime (hollow stars) and which films were grown in the adsorption-controlled regime (solid stars).

FIG. 4.

(a) Comparison of the electron mobility as a function of electron density measured at room temperature by the Hall effect on the silicon-doped β-Ga2O3 films grown in this study at ∼1 µm/h by S-MBE to leading reports of silicon-doped β-Ga2O3 films by other techniques from the literature. The S-MBE results are indicated by the red stars. (b) A close-up of the S-MBE results [the results indicated by the red stars in (a)] showing which films were grown in the oxidant-rich regime (hollow stars) and which films were grown in the adsorption-controlled regime (solid stars).

Close modal

The sample with the highest mobility at room temperature is sample a, a 1 µm thick film grown by S-MBE with the SiO2 doping source in the adsorption-controlled regime. At room temperature, it has a mobility of 124 cm2 V−1 s−1. The temperature-dependence of this mobility measured by the Hall effect is shown in Fig. 5. The mobility peaks at 76 K at a mobility of 627 cm2 V−1 s−1. This value is significantly higher than all prior reports of β-Ga2O3 grown by MBE, i.e., higher than PAMBE5 and MOCATAXY.6 Using the temperature-dependent carrier density data for this sample as measured by the Hall effect, an activation energy of 27 meV and a compensating acceptor density (Na) of 4 × 1015 cm−3 were determined by fitting the temperature-dependent Hall carrier density using the charge neutrality equation.56,57 This activation energy for silicon from our SiO2 doping source is comparable to that of silicon in β-Ga2O3 grown by conventional MBE (with an elemental silicon doping source)5,57 and MOCVD.3,23,25

FIG. 5.

Temperature-dependent Hall effect measurements made on a 1 µm thick film (sample a) grown by S-MBE at a growth rate of ∼1 µm/h with a mobile carrier concentration of 2.7 × 1017 cm−3 and a room-temperature mobility of 124 cm2 V−1 s−1. The mobility of the charge carriers (electrons) (a) and their density (b) are shown as a function of temperature. The mobility peaks at 76 K at a mobility of 627 cm2 V−1 s−1.

FIG. 5.

Temperature-dependent Hall effect measurements made on a 1 µm thick film (sample a) grown by S-MBE at a growth rate of ∼1 µm/h with a mobile carrier concentration of 2.7 × 1017 cm−3 and a room-temperature mobility of 124 cm2 V−1 s−1. The mobility of the charge carriers (electrons) (a) and their density (b) are shown as a function of temperature. The mobility peaks at 76 K at a mobility of 627 cm2 V−1 s−1.

Close modal

The results of additional structural characterization measurements on this same high-mobility sample (Sample a) are shown in Fig. 6. The film is unremarkable when analyzed by XRD; single-phase epitaxial β-Ga2O3 is seen. Rocking curves of the 020 β-Ga2O3 peak reveal full widths at half maxima (FWHMs) of 43 and 122 arcsec along two perpendicular in-plane directions. These values are on a par with the rocking curves of the bare iron-doped β-Ga2O3 (010) substrates. AFM reveals an rms roughness of 1.8 nm for this 1 µm thick film grown at 0.86 µm/h. High-angle annular dark-field STEM (HAADF-STEM) imaging reveals a uniform, single-crystalline β-Ga2O3 film with high structural quality. The thickness of the epilayer was measured to be ∼1.4 µm, where the interface between the film and substrate is indicated by the black dashed line. The slight contrast at the interface likely originates from contamination at the surface of the air-exposed substrate or from point defects as has been observed in other homoepitaxial β-Ga2O3 films.58 Dislocations were not observed at the film/substrate interface or in the epilayer. The variation in contrast at the surface of the film is a result of the TEM sample being prepared as a wedge that is thinner at the surface. We thus demonstrate that using S-MBE for both the semiconductor and the dopant tackles some of the major challenges associated with the conventional MBE growth of β-Ga2O3.

FIG. 6.

Structural characterization of the same film shown in Fig. 5 by (a) θ–2θ XRD scan in the vicinity of the 020 β-Ga2O3 peak where the scans along ϕ = 0° and ϕ = 90° are offset for clarity. (b) Rocking curve of the 020 β-Ga2O3 peak showing a FWHM of 122 arcsec (blue) and 43 arcsec (gray) along ϕ = 0° and ϕ = 90°, respectively; the scans are offset for clarity. (c) AFM scan of the same film revealing an rms roughness of 1.9 nm. (d) HAADF-STEM images of the same film along the [201] zone axis, where the dashed line indicates the interface between the β-Ga2O3 (010) substrate and the grown β-Ga2O3 film.

FIG. 6.

Structural characterization of the same film shown in Fig. 5 by (a) θ–2θ XRD scan in the vicinity of the 020 β-Ga2O3 peak where the scans along ϕ = 0° and ϕ = 90° are offset for clarity. (b) Rocking curve of the 020 β-Ga2O3 peak showing a FWHM of 122 arcsec (blue) and 43 arcsec (gray) along ϕ = 0° and ϕ = 90°, respectively; the scans are offset for clarity. (c) AFM scan of the same film revealing an rms roughness of 1.9 nm. (d) HAADF-STEM images of the same film along the [201] zone axis, where the dashed line indicates the interface between the β-Ga2O3 (010) substrate and the grown β-Ga2O3 film.

Close modal

Having demonstrated that S-MBE appears to be a viable method for the growth of β-Ga2O3 with good structural and electrical properties at record growth rates (for MBE), we return to the question of whether it can produce device-quality materials. As an initial test, we prepared a simple MESFET on a 65 nm thick homoepitaxial β-Ga2O3 layer grown by S-MBE at a growth rate of ∼1 µm/h with the structure shown in Fig. 7(a). For this test device, the SiO doping source was used to dope the epilayer. The MESFET results are shown in Figs. 7(b) and 7(c); although these are initial results, the ability of S-MBE to produce device-quality materials is evident. Device contacts were ohmic, and the channel showed good modulation, with a peak transconductance (Gm) of 23.4 mS/mm, threshold voltage Vth ∼ −6 V, and Voff = −13 V. The relatively low on/off ratio can be attributed to the leakage through the parasitic channel formed by unintentional silicon contamination at the interface between the β-Ga2O3 film and the underlying substrate.14,25,47–49 These MESFETs perform comparably to devices with similar architectures,40,59 indicating that the channel material grown by S-MBE is, indeed, suitable for device fabrication.

FIG. 7.

(a) Schematic of the annealed-ohmic MESFET fabricated using a silicon-doped β-Ga2O3 film grown at ∼1 µm/h by S-MBE with Nd = 1018 cm−3. (b) Output curves at Vgs = 0, −2, −4, −6, −8, and −10 V and (c) transfer curve and transconductance of the MESFET.

FIG. 7.

(a) Schematic of the annealed-ohmic MESFET fabricated using a silicon-doped β-Ga2O3 film grown at ∼1 µm/h by S-MBE with Nd = 1018 cm−3. (b) Output curves at Vgs = 0, −2, −4, −6, −8, and −10 V and (c) transfer curve and transconductance of the MESFET.

Close modal

We have overcome the kinetic limitation to the slow growth rate of β-Ga2O3 by conventional MBE and demonstrate a growth rate of epitaxial β-Ga2O3 as high as 2.5 µm/h on (0001) Al2O3 substrates by S-MBE. By using a doping source in which silicon is in its most oxidized state, SiO2, we avoid the oxidation issues of previously used silicon4,5,29 and SiO dopant sources37 when used at high oxidant pressures. This enables controllable and reproducible silicon-doping of β-Ga2O3 in the 5 × 1016 cm−3–1019 cm−3 range for the high growth rates used. The doped films grown at ∼1 µm/h exhibit mobilities at room temperature rivaling leading techniques and mobilities, at low temperatures, that are the highest achieved to date by MBE, 627 cm2 V−1 s−1 at 76 K. While these characteristics are still inferior to the electrical properties of β-Ga2O3 grown by MOCVD,2–4,23–25 S-MBE is emerging as a viable technique for the growth of electronic-grade β-Ga2O3 at rates enabling the intensive investigation of thick vertical heterostructures.

See the supplementary material for calculated partial pressures and additional sample data.

K.A., C.A.G., N.A.P., J.S., J.P.M., D.J., H.G.X., D.A.M., M.O.T., H.P.N., and D.G.S. acknowledge the support from the AFOSR/AFRL ACCESS Center of Excellence under Award No. FA9550-18-1-0529. J.P.M. also acknowledges the support from the National Science Foundation within a Graduate Research Fellowship under Grant No. DGE-1650441. P.V. and Y.A.B. acknowledge the support from ASCENT, one of six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA. F.V.E.H. acknowledges the support from the Alexander von Humboldt Foundation in the form of a Feodor Lynen fellowship. F.V.E.H. also acknowledges the support from the National Science Foundation (NSF) [Platform for the Accelerated Realization, Analysis and Discovery of Interface Materials (PARADIM)] under Cooperative Agreement No. DMR-1539918. M.D.W., D.A.M., and D.G.S. acknowledge the support from the NSF under DMR-2122147. M.D.W. also acknowledges NSF Grant No. HRD-1924204 and ONR Award No. N00014-21-1-2823. This work made use of the Cornell Center for Materials Research (CCMR) Shared Facilities, which are supported through the NSF MRSEC Program (Grant No. DMR-1719875). The substrate preparation was performed, in part, at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NSF (Grant No. NNCI-2025233). This work also made use of the Cornell Energy Systems Institute Shared Facilities partly sponsored by the NSF (Grant No. MRI DMR-1338010).

The authors K.A., F.V.E.H., S.-L.S., P.V., Z.-K.L., and D.G.S. have been granted U.S. Patent No. 11,462,402 (4 October 2022) with the title “Suboxide Molecular-Beam Epitaxy and Related Structures.”

Kathy Azizie: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Validation (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Felix V. E. Hensling: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Supervision (supporting); Validation (supporting); Visualization (equal); Writing – review & editing (equal). Cameron A. Gorsak: Data curation (equal); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (supporting). Yunjo Kim: Formal analysis (supporting); Investigation (supporting); Visualization (supporting). Naomi A. Pieczulewski: Data curation (equal); Formal analysis (supporting); Investigation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Daniel M. Dryden: Formal analysis (supporting); Investigation (supporting); Visualization (equal). M. K. Indika Senevirathna: Formal analysis (supporting); Investigation (supporting); Visualization (equal). Selena Coye: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Visualization (equal). Shun-Li Shang: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Visualization (equal). Jacob Steele: Formal analysis (equal); Investigation (supporting); Methodology (equal); Visualization (equal). Patrick Vogt: Formal analysis (equal); Investigation (supporting); Methodology (equal); Visualization (supporting). Nicholas A. Parker: Formal analysis (supporting); Investigation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Yorick A. Birkhölzer: Investigation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Jonathan P. McCandless: Funding acquisition (equal); Investigation (supporting); Supervision (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Debdeep Jena: Funding acquisition (equal); Investigation (supporting); Supervision (supporting); Writing – review & editing (supporting). Huili G. Xing: Data curation (supporting); Funding acquisition (equal); Supervision (supporting); Writing – review & editing (supporting). Zi-Kui Liu: Data curation (supporting); Investigation (supporting); Supervision (supporting). Michael D. Williams: Investigation (supporting); Supervision (supporting). Andrew J. Green: Funding acquisition (equal); Investigation (supporting); Supervision (supporting). Kelson Chabak: Data curation (equal); Funding acquisition (equal); Investigation (supporting); Supervision (supporting); Visualization (equal); Writing – review & editing (equal). David A. Muller: Funding acquisition (equal); Resources (supporting); Supervision (supporting); Visualization (supporting); Writing – review & editing (supporting). Adam T. Neal: Data curation (equal); Funding acquisition (equal); Investigation (supporting); Supervision (supporting); Visualization (equal); Writing – review & editing (equal). Shin Mou: Funding acquisition (equal); Supervision (supporting); Writing – review & editing (equal). Michael O. Thompson: Conceptualization (lead); Funding acquisition (equal); Investigation (equal); Project administration (lead); Resources (lead); Supervision (supporting); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Hari P. Nair: Data curation (equal); Funding acquisition (equal); Investigation (equal); Supervision (supporting); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (equal). Darrell G. Schlom: Conceptualization (lead); Funding acquisition (lead); Investigation (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (equal); Visualization (supporting); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available within the article and are openly available at https://doi.org/10.34863/zsda-pa72.

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Supplementary Material