Atomic-scale investigation of γ-Ga₂O₃ deposited on MgAl₂O₄ and its relationship with β-Ga₂O₃ Open Access

Beta-gallium oxide (β-Ga₂O₃) is an emerging ultra-wide-bandgap semiconductor material for application in high-power electronic devices. Its higher theoretical breakdown electric field strength (∼8 MV/cm)¹ surpasses that of SiC and GaN due to its larger bandgap of ∼4.8 eV.^2–4 It also has significant advantages in bulk material production that uses cost-efficient melt growth techniques and in the growth of homoepitaxial thin films with controllable n-type doping using Si, Ge, and Sn.^5–10 The successful incorporation of deep acceptors such as Fe and Mg^11–13 into β-Ga₂O₃ has facilitated the creation of semi-insulating regions that effectively reduce the leakage current of the device. Aluminum alloyed β-Ga₂O₃ has also been explored for two purposes: (i) bandgap engineering to further extend the breakdown electric field strength for high-power electronic devices^14,15 and (ii) the formation of a two-dimensional electron gas at the (Al_xGa_1−x)₂O₃/Ga₂O₃ interface^16–19 for high electron mobility transistors. In addition, the bandgap energy of β-Ga₂O₃ falls in the deep ultraviolet range, so it is also a candidate material for solar-blind UV photodetectors.^20–22 

Ga₂O₃ exhibits five polymorphs, which are α (trigonal), β (monoclinic), γ (cubic-defective spinel), δ (cubic-bixbyite), and κ(ε) (orthorhombic). It was earlier suggested that the δ-phase was a nanocrystalline form of the κ(ε)-phase.²³ However, recently reported research²⁴ has demonstrated the epitaxial growth of δ-Ga₂O₃ on a cubic bixbyite-structured Fe₂O₃ buffer layer deposited on an yttrium-stabilized zirconia substrate. The exact crystal structure of δ-Ga₂O₃ remains a subject of ongoing debate; the structures of the other four phases are universally accepted. The β-phase is the thermodynamically stable polymorph from room temperature to its melting point. However, two or more polymorphs have been determined to occur in selective Ga₂O₃ thin films.^25–29 For example, γ-phase inclusions have been observed in Si, Ge, and Sn doped and Al and Sc alloyed β-Ga₂O₃ films as well as bulk β-Ga₂O₃ crystals.^30–37 A highly defective Ga₂O₃ intermediate layer with a close structural arrangement to γ-Ga₂O₃ was determined to have formed between a Au contact and a (100) β-Ga₂O₃ film,³⁸ affecting the electrical characteristics of the film. An understanding of the impact of “γ-phase” inclusions on the electronic and thermal properties of β-Ga₂O₃ and their elimination are crucial for the repeated fabrication of devices with replicable properties.

γ-Ga₂O₃, an analog of γ-Al₂O₃ (space group: Fd$3̄$m), has been surmised to have a cation defective spinel structure.^39,40 As such, 8/3 vacancies must be introduced into the cation sites of each unit cell to maintain the stoichiometric ratio between Ga and O at 2:3. However, the uncertainty of the preferred sites for the vacancies^41–44 in addition to the deviation from the ideal spinel structure associated with the partial filling of non-spinel positions (e.g., the 16c and 48f Wykoff positions^23,42) by Ga atoms makes this polymorph even more complicated. In terms of first-principles calculations, the Helmholtz free energies per formula unit for Ga₂O₃ polymorphs are in the sequence of β < κ(ε) < α < γ,⁴⁴ indicating that γ-Ga₂O₃ is the least stable polymorph. Most of the γ-Ga₂O₃ materials synthesized by solution-based methods^39,45–47 suffer from poor crystallinity, small particle size, and the unavoidable contamination of β-Ga₂O₃, which adds to the difficulty of characterizing this polymorph. Some progress on epitaxial stabilization of γ-Ga₂O₃ thin films grown via mist-CVD, pulsed laser deposition (PLD), and metal-organic chemical vapor deposition (MOCVD)^43,48–52 on substrates such as Al₂O₃, MgO, and MgAl₂O₄ has been reported, but detailed atomic-scale investigations of defects within the film and their relationships with β-Ga₂O₃ have rarely been investigated.^31,35,43

In this paper, the parameters employed and the results for the repeated growth of nominally phase pure γ-Ga₂O₃ films on (100) MgAl₂O₄ via MOCVD at 470 °C are presented. The temperature range for the deposition of γ-Ga₂O₃ was between 440 and 500 °C. Films grown at 530 °C were nominally phase pure β-Ga₂O₃. Previously, we reported the results and conclusions of our investigations of film growth and annealing within the higher temperature range of 550–1000 °C. In these studies, significant Mg and Al diffused from the MgAl₂O₄ substrates into the β-Ga₂O₃ layer. This resulted in the formation of γ-Ga₂O₃ solid solutions with a spinel structure, which were referred to as the “γ-phase.”⁵³ To avoid ambiguity, in this paper, we specifically use the term “γ-Ga₂O₃” to distinguish it from the “γ-phase,” as no measurable diffusion of Mg and Al was determined via energy dispersive x-ray spectroscopy (EDX) to occur during the film growth. In-depth atomic-scale investigations of select γ-Ga₂O₃ films using scanning transmission electron microscopy (STEM) revealed the presence of significant antiphase boundaries. An analysis of the epitaxial relationship in this study between γ-Ga₂O₃ and β-Ga₂O₃ is discussed.

Single-side, chemo-mechanically polished, epi-ready (100) MgAl₂O₄ substrates were used for film growth in a vertical, low-pressure, cold-wall MOCVD reactor. The parameters employed for these films are detailed in Table I. Triethylgallium (TEGa) stored in a stainless-steel bubbler from Sigma-Aldrich and ultra-high purity O₂ (5N) were used as the reactants. The carrier gas for TEGa was ultra-high purity N₂ (5N), which also served as a diluent gas to prevent any pre-reaction of the precursors. For all the growths, the bath temperature and the bubbler pressure were kept at 20 °C and 150 Torr, respectively; thus, the TEGa flow rate was solely determined by the carrier gas flow rate. To maintain a constant O/Ga (VI/III) ratio of 635, the molar flow rates of O₂ and TEGa were kept at 0.0223 and 7.02 × 10⁻⁵ mol/min, respectively. The reactor pressure was controlled using a butterfly valve and held at 20 Torr for all growths. The rotational speed of the Hastelloy susceptor was selected to be 120 revolutions per minute (rpm) to achieve a uniform flow over the substrates. The period for all growths was set to one hour. High-resolution x-ray diffraction (HRXRD) patterns were acquired using a PANalytical X’Pert Pro MPD x-ray diffractometer [four-crystal Ge(220) monochromator] equipped with a Cu K_α1 (1.5406 Å) x-ray source. The film thickness measurements were conducted using a Filmetrics F50-200 spectrometer. Transmission electron microscopy (TEM) and STEM investigations, including selected area electron diffraction (SAED), high-angle annular dark field (HAADF)-STEM imaging, and STEM-EDX spectroscopy, were performed using a Thermo Fisher Themis 200 G3 aberration-corrected TEM/STEM equipped with a Super-X EDX system. The TEM lamella for the γ-Ga₂O₃ films was prepared using an FEI Helios Xenon Plasma Dual Beam Focused Ion Beam (FIB).

Here, a comprehensive suite of XRD scanning techniques, including out-of-plane 2θ–ω scans, ϕ-scans, ω-scans, pole figure, and reciprocal spacing mapping (RSM), were used to investigate (i) the growth window for γ-Ga₂O₃ grown on MgAl₂O₄, (ii) the film/substrate epitaxial relationship, and (iii) the lattice distortion/relaxation of the film. The TEM-SAED patterns were acquired to further confirm the phase and crystal orientation of the deposited film. Figure 1(a) shows the out-of-plane 2θ–ω scans of the films grown using the parameters shown in Table I. The strongest peak at 44.79° indicated by the black star corresponds to the (400) planes of the MgAl₂O₄ substrate. The other peaks at 30.05°, 43.17°, and 44.14° are attributed to the (400) and (⁠$1̄$12) planes of β-Ga₂O₃⁵³ and the (400) plane of γ-Ga₂O₃,⁵⁰ respectively. For the film grown at 440 °C, only the substrate peak was detected, indicating that it was either poorly crystallized or amorphous. For the film grown at 470 °C, the (400) peak of γ-Ga₂O₃ was observed with no other film peaks, indicating an epitaxial relationship between the film and the substrate. The lattice mismatch between (400) γ-Ga₂O₃ and (400) MgAl₂O₄ is ∼+1.9%; thus, these major peaks occur near each other. Further increases in the growth temperature to 500 and 530 °C resulted in the formation of (i) a mixture of β-Ga₂O₃ and γ-Ga₂O₃ and (ii) nominally phase pure β-Ga₂O₃, respectively. The analytical results for films grown at higher temperatures (550–850 °C) under similar growth conditions have been presented and discussed in a separate paper.⁵³ As revealed in Fig. 1(a), the growth window of nominally phase pure γ-Ga₂O₃ was narrow and centered around 470 °C. Oshima et al. also reported a narrow growth window from 390 to 400 °C for pure γ-Ga₂O₃ deposited on (100) MgAl₂O₄ via mist-CVD.⁵⁰ 

Figure 1(b) shows the ϕ-scan of the {440} γ-Ga₂O₃ grown at 470 °C acquired simultaneously with that of the MgAl₂O₄ substrate. The resulting four peaks evenly spaced at 90° intervals illustrate the fourfold symmetry of γ-Ga₂O₃ when rotated along the [100] direction. The absence of additional peaks indicates the absence of in-plane rotational domains of γ-Ga₂O₃. A comparison of the peak locations between the film and the substrate reveals that the in-plane epitaxial relationship is [011] γ-Ga₂O₃ || [011] MgAl₂O₄, corresponding to the cube-on-cube growth. The absence of out-of-plane rotational domains was verified through the pole figure measurement of {444} γ-Ga₂O₃, as only four spots were detected at χ = 54.7°, as shown in Fig. 1(c). Both out-of-plane and in-plane epitaxial relationships between the film and the substrate match the published results.^50,51,54 Distortion within the as-grown γ-Ga₂O₃ at 470 °C was quantified by measuring the full-width-at-half-maximum (FWHM) of the x-ray rocking curve (XRC) or ω-scan of both the (800) symmetric peak and the (440) asymmetric peak of γ-Ga₂O₃ shown in Fig. 1(d). The FWHM values of these two peaks were 0.718° and 0.720°, respectively, indicating that the mosaicity within the γ-Ga₂O₃ lattice is equally distributed both out-of-plane and in-plane. Figure 1(e) shows the RSM around the 804 diffraction spots of the film and substrate. The observation of horizontal separation between the film spot and the substrate spot in reciprocal space confirms that the volume of the film wherein diffraction occurred is in a relaxed state.

For TEM/STEM analysis, a thicker film of ∼700 nm was grown for 2 h at 470 °C using the same parameters applied for the one-hour depositions. The peak positions in the XRD 2θ–ω pattern (not shown) for this film were the same as the ones shown in Fig. 1(a); the intensity of the γ-Ga₂O₃ peak for the 2 h film increased due to its greater thickness. Figure 2 shows the cross-sectional STEM and SAED patterns for the γ-Ga₂O₃ film grown at 470 °C acquired along the [010] and [011] zone axes, respectively. The film/substrate contrast was sharp, as can be observed in Figs. 2(a) and 2(d), and clearly differentiates the film from the substrate. The SAED patterns of the film along both [010] [Fig. 2(b)] and [011] [Fig. 2(e)] zone axes matched well with the simulated SAED patterns of γ-Ga₂O₃ shown in Figs. 2(c) and 2(f). The crystal model for γ-Ga₂O₃ was built assuming Fd$3̄$m symmetry with fully occupied and well-ordered cubic close packing in the O sublattice lattice. The Ga sublattice was partially occupied on 8a and 16d Wyckoff sites to balance the stoichiometry.³⁹ In addition, some elongated diffraction spots, such as 02$2̄$⁠, $4̄$2$2̄$⁠, and $11̄1$⁠, indexed in blue can be seen in Fig. 2(e). Other spots, such as 400, $2̄22̄$⁠, and $04̄4$⁠, indexed in red on the same figure possess a rounded shape without observable elongation. From structure factor calculations, the rounded diffraction spots are dominated by the well-ordered O sublattice, while the elongated spots are dominated by the Ga sublattice. The degree of elongation is affected by the formation of planar defects within the Ga sublattice. Similar spot broadening has been reported in γ-Al₂O₃,⁵⁵ which is thought to have the same crystal structure as γ-Ga₂O₃. As will be seen in Sec. III B, antiphase boundaries, a specific type of planar defect, were widely observed inside the γ-Ga₂O₃ film via atomic-scale STEM investigations.

Figure 3 presents the representative HAADF-EDX composition profile of the γ-Ga₂O₃ film grown at 470 °C. Five distinct areas (not shown) were selected and showed the same composition profile as shown in Fig. 3. Notably, a sharp contrast at the interface was observed and primarily attributed to an abrupt change in composition at the interface. The deviation in the Ga/O stoichiometry (∼43%/∼57%) can be attributed to the high uncertainty associated with the quantitative analysis for light elements such as O because of low x-ray fluorescence yields and self-absorption. Negligible Mg and Al were detected within the γ-Ga₂O₃ film. Our previously published results on (i) high-temperature growth between 550 and 850 °C⁵³ and (ii) high-temperature post-growth annealing between 800 and 1000 °C⁵⁶ showed that Mg and Al interatomic diffusion began to occur at ∼650 °C. This resulted in a gradual variation in the atomic concentration of all the elements at the interface and into the films. Thus, as noted earlier, the term “γ-Ga₂O₃” is used throughout this paper to specifically refer to the film grown at 470 °C to differentiate it from the terms “γ-phase” and “γ-Ga₂O₃ solid solutions” used in our previous publications.

Figure 4 shows the HAADF-STEM results of the γ-Ga₂O₃ film grown for 2 h at 470 °C, acquired along the [011] zone. Three distinct features indicated by red arrows, yellow parallelograms, and blue parallelograms were observed throughout the entire film as shown in Figs. 4(a)–4(c). To gain a more detailed view, Figs. 4(d)–4(f) display the zoomed-in atomic-scale HAADF-STEM images of each feature. In HAADF-STEM, the contrast of the image is directly related to the column density and atomic number (Z) of the atoms and scales roughly as Z².^29,57,58 Consequently, columns of Ga atoms (Z = 31) are visible in the γ-Ga₂O₃ film, while the O atoms (Z = 8) are only visible if the column density for this element is sufficiently high. When viewed along the [011] zone axis, columns of Ga atoms do not overlap columns of O atoms; thus, the contrast difference for the Ga sublattice observed in the atomic-resolution STEM images is purely due to the change in the column density of Ga atoms. Figure 4(d), from the regions marked by red arrows in Figs. 4(a)–4(c), shows a hexagonal atomic arrangement of ten columns of Ga atoms with an additional high-intensity single column of Ga atoms at the center of each hexagon. This arrangement aligns well with the ideal γ-Ga₂O₃ structure (the crystal model used here was the same as the one used in Sec. III A) viewed along the [011] zone, as depicted in Fig. 4(i). As can be seen in Fig. 4(i), each hexagon comprises six tetrahedrally occupied Ga atoms and five octahedrally occupied Ga atoms (four on the edge and one at the center). The column density of the Ga atoms at the center of each hexagon is twice compared to all the Ga atoms on the edge, resulting in a significantly higher contrast at the center in Fig. 4(d). Figures 4(e) and 4(f), corresponding to the regions marked by yellow parallelograms and blue parallelograms in Figs. 4(a)–4(c), reveal high-intensity diagonal stripes of Ga atoms and three atomic columns of Ga atoms with lower intensity between these high-intensity stripes. These types of Ga atomic arrangements are caused by a shift of the Ga sublattice in γ-Ga₂O₃ and the formation of planar defects.³⁴  Figures 4(j) and 4(k) show the overlaid structure of γ-Ga₂O₃ with a proper lattice shift, aligning well with the observed features shown in Figs. 4(e) and 4(f). Further details regarding the lattice shift will be discussed in conjunction with Fig. 5. An approximate 3 nm thick transition layer was observed between the film and the substrate shown in Fig. 4(c). Figure 4(g) shows a zoomed-in version of the pink area within the transition layer, presenting a regular hexagonal shape without any lattice shift. This type of feature matches well with the ideal γ-Ga₂O₃ structure shown in either Fig. 4(l) or Fig. 4(i). Figures 4(h) and 4(m) show the atomic-scale HAADF-STEM image of the MgAl₂O₄ substrate and its corresponding crystal structure viewed along the [011] zone, respectively. The transition layer was fully strained to match the underlying substrate, i.e., no lattice relaxation occurred. The lattice shift observed above the transition layer originated from the formation of antiphase boundaries due to the film relaxation.

Since its discovery in 1952, γ-Ga₂O₃ has been recognized as a cubic defective spinel structure.^23,39,47 However, due to its inherent disorder, the actual structure and the distribution of vacancies on the cation sites have been described in different ways in the literature. Ga atoms closely resemble Al atoms, which leads to similarities between Ga₂O₃ and Al₂O₃ polymorphs. α-, β-, and κ-Al₂O₃ have been identified as prototypes of α-, β-, and κ-Ga₂O₃, respectively. Similarly, γ-Ga₂O₃ is believed to have the same crystal structure as γ-Al₂O₃. Investigations of γ-Al₂O₃ have revealed the presence of planar defects, leading to broadening of specific diffraction peaks observed through XRD or SAED,^55,59 similar to the results presented in Fig. 2(e). Here, we apply the planar defects model, derived from lattice shifts observed within γ-Al₂O₃,^55,60,61 to describe the features observed in Fig. 4(e) and 4(f). The underlying assumption for the lattice shift model in generating planar defects is the preservation of atomic ordering within the cubic close-packed O sublattice while inducing a lattice shift within the cation sublattice (Al or Ga). Figure 5 illustrates the four types of planar defects produced by lattice shifts, which have been both experimentally and theoretically determined in γ-Al₂O₃. The glide plane is denoted by “(hkl),” and the corresponding shift vector is denoted by “[uvw].” Figures 5(a)–5(d) show the Ga sublattice for ideal γ-Ga₂O₃ before a lattice shift, as viewed along the [010] zone. The overlaid structures resulting from the indicated lattice shifts are shown in Figs. 5(a1)–5(d1) viewed along the [010] zone and in Figs. 5(a2)–5(d2) viewed along the [011] zone. When viewing along the [011] zone, the overlaid structures in Figs. 5(a2) and 5(b2) match well with the actual HAADF-STEM image presented in Fig. 4(e) and the overlaid structures in Fig. 5(c2) and 5(d2) match well with the actual HAADF-STEM image presented in Fig. 4(f). Further discussion of the HAADF-STEM images along the [010] zone and their comparison with Figs. 5(a1)–5(d1) will be covered in reference to Fig. 6.

Figure 6 shows the HAADF-STEM results of the γ-Ga₂O₃ film grown at 470 °C, acquired along the [010] zone. Two distinct features indicated by red arrows and blue arrows were consistently observed throughout the film, as shown in Figs. 6(a)–6(c). To gain a more detailed view, Figs. 6(d) and 6(e) display the zoomed-in atomic-scale HAADF-STEM images of each feature. Although columns of Ga atoms partially overlap columns of O atoms when viewed along the [010] zone axis, the column density of the O atoms is the same before and after the lattice shift, indicating that the variation in the contrast for the Ga sublattice observed in the atomic-resolution STEM images is also purely due to the change in the column density of Ga atoms. Figure 6(d), corresponding to the regions marked by red arrows in Figs. 6(a)–6(c), reveals an ideal γ-Ga₂O₃ structure without any lattice shift or the overlaid structure produced by a proper lattice shift, as presented in Figs. 5(b1) and 5(d1). Figure 6(e), acquired from the regions marked by blue arrows in Figs. 6(a)–6(c), shows a cubic atomic arrangement of Ga with high-intensity and low-intensity columns of Ga atoms occupying octahedral sites and tetrahedral sites, respectively. This arrangement aligns well with the overlaid γ-Ga₂O₃ structure interpreted by the lattice shift model presented in Figs. 5(a1) and 5(c1). Similar to the observation from the [011] zone, an approximate 3 nm thick transition layer was observed between the film and the substrate shown in Fig. 6(c). Figure 6(f) shows a magnified version of the region inside the transition layer, which reveals an ideal γ-Ga₂O₃ structure without lattice shift, as achieved by combining the knowledge acquired along the [011] zone at the interface. Figure 6(g) shows an atomic-scale HAADF-STEM image of the MgAl₂O₄ substrate. By comparing the in-plane lattice constant between the transition layer and the MgAl₂O₄ substrate, it was determined that the transition layer was fully strained to match the substrate. The same behavior of ∼3 nm thick fully strained transition layer was also reported by the MBE growth of γ-Ga₂O₃ films⁶² and γ-Al₂O₃/Ga₂O₃⁶³ superlattices on (100) MgAl₂O₄ substrates.

The presence of “γ-phase” inclusions within β-Ga₂O₃ epitaxial layers and bulk materials has garnered significant attention, particularly in materials where various dopants such as Si, Ge, Sn, Mg, Al, or Sc have been introduced. The reported observations of the co-existence of two or more polymorphs require in-depth investigations of the possible epitaxial relationships among these polymorphs. For example, do the “γ-phase” inclusions within β-Ga₂O₃ exhibit a discernible preferential orientation with the surrounding matrix phase or are they randomly oriented? Two in-plane epitaxial relationships have been identified, namely, [010] β-Ga₂O₃ || [011] γ-Ga₂O₃ and [001] β-Ga₂O₃ || [011] γ-Ga₂O₃. It is worth noting that even though the TEM samples were prepared along the [001] zone of β-Ga₂O₃, observations revealed the presence of both [001] and [010] β-Ga₂O₃ domains in the context of Al-alloyed β-Ga₂O₃.^31,33,37 The change in the domain orientation emanates from a transition in the growth plane from (010) to (⁠$1̄$02). The underlying mechanism for this 90° rotation (specifically from [001] β-Ga₂O₃ to [010] β-Ga₂O₃) has been experimentally and theoretically investigated.^31,33,37,64 Bhuiyan et al. concluded that this 90° rotation of β-Ga₂O₃ is due to the strain induced by a high Al concentration, which also promoted the growth of [011] γ-Ga₂O₃.³⁷ Chang et al. showed that the 90° rotation of Al alloyed β-Ga₂O₃ along (310) β-Ga₂O₃ [∼36° with respect to the (010) growth plane] demonstrated that within these (310) planes, [001] β-Ga₂O₃ is either rotated to [010] β-Ga₂O₃ or converted to [011] γ-Ga₂O₃.³¹ From the results of their DFT calculations, Wang et al. postulated that the 90° rotation is formed by the emergence of (010) β-Ga₂O₃ stacking faults at the interface that connects the [001] β-Ga₂O₃ and [010] β-Ga₂O₃ domains.⁶⁴ This connection subsequently gives rise to the (010)/(⁠$1̄$02) interface. In the following paragraphs, the results and conclusions concerning (i) the epitaxial relationship between β-Ga₂O₃ domains and (ii) the epitaxial correlation that bridges β-Ga₂O₃ and γ-Ga₂O₃ determined in the present study are discussed.

Figure 7(a) presents a HAADF-STEM micrograph showing a β-Ga₂O₃ inclusion (red box) within the γ-Ga₂O₃ film (blue box and beyond) grown at 470 °C. The image was acquired along the [011] zone of γ-Ga₂O₃. The areas within the boxes are magnified as shown in Figs. 7(b) and 7(c). Figure 7(b) shows the superimposed structure of [011] γ-Ga₂O₃ on the projected STEM image, which confirms the structure of γ-Ga₂O₃ in this area. Figure 7(c) shows the superimposed structure of [010] β-Ga₂O₃ on the projected STEM image, confirming the structure of highly defective β-Ga₂O₃ in this area. The term “highly defective” is used to describe the observation of excessive interstitial Ga columns marked by the red dotted circles in Fig. 7(c). These additional interstitial Ga columns have been consistently noted in Si, Ge, Sn, and Al-doped β-Ga₂O₃.^32,33,35 The formation of these interstitial Ga columns has received experimental and theoretical validation,^32,33,35,65 substantiated using a model of interstitial–divacancy complexes. In addition, the majority of these interstitial Ga columns marked, as indicated by the red dotted circles, exhibit a similar arrangement to the octahedrally positioned Ga atoms [purple atoms in Fig. 7(b)]. This suggests that these additional Ga columns may have formed due to the overlap of the [010] β-Ga₂O₃ domain and the [011] γ-Ga₂O₃ domain. Given that β-Ga₂O₃ is embedded within the γ-Ga₂O₃ matrix, the possibility of an overlap between these two phases is quite significant. The presence of a β-Ga₂O₃ inclusion within the γ-Ga₂O₃ film is evident as revealed in Fig. 7(c). However, the extent of this inclusion and the limited presence of β-Ga₂O₃ in more than 30 regions within additional STEM images were insufficient for comprehensive STEM and XRD characterization. As such, an ex situ post-annealing treatment at 600 °C in ambient air was conducted to promote the formation of a greater concentration of β-Ga₂O₃. A post-annealing treatment was used instead of growing films at higher temperatures. In the latter case (⁠$1̄$12) oriented β-Ga₂O₃ also occurs in addition to the formation of (400) oriented β-Ga₂O₃. In β-Ga₂O₃, the (⁠$1̄$12) plane has been determined to possess a higher surface energy than the (400) plane.⁶⁶ Due to the intrinsic similarities between the (⁠$1̄$12) and the (400) planes of β-Ga₂O₃, the co-existence of both orientations is favorable during growth, whereas this is less likely during post-annealing.

Figure 8 shows the rotational domains of β-Ga₂O₃ within the γ-Ga₂O₃ film as well as the corresponding epitaxial relationship between β-Ga₂O₃ and γ-Ga₂O₃ as derived from XRD ϕ-scans. Figure 8(a) reveals the recrystallization of β-Ga₂O₃ within the γ-Ga₂O₃ film annealed at 600 °C in ambient air for 1 h. The peak for (400) β-Ga₂O₃ is barely detectable before annealing; a broader (400) β-Ga₂O₃ peak is visible after heat treatment. The (400) γ-Ga₂O₃ peak has slightly shifted to a higher 2θ value, indicative of ongoing film relaxation. Figure 8(b) shows the XRD ϕ-scan of {40$1̄$} β-Ga₂O₃ and {440} γ-Ga₂O₃ for the post-annealed film. Four peaks with a 90° separation for each indicate the presence of four in-plane rotational domains in β-Ga₂O₃. The [010] β-Ga₂O₃ inclusion shown in Fig. 7 contains one of these domains. The epitaxial relationship between β-Ga₂O₃ and γ-Ga₂O₃ is presented in Fig. 8(c). The presence of the in-plane rotational domains of β-Ga₂O₃ can be attributed to the fourfold symmetry of the (400) plane of γ-Ga₂O₃. Moreover, the domain boundaries between the 180° rotated domains of either 1 and 3 or 2 and 4 stem from twin boundaries formed on the (100) plane of β-Ga₂O₃. These twin domains, achieved via a boundary plane mirror operation followed by a 0.5c displacement in the [001] direction, are a common occurrence in β-Ga₂O₃ homoepitaxial films. The DFT calculations validate the lower formation energy of twin boundaries on the (100) plane of β-Ga₂O₃ relative to other grain boundaries, thereby providing insights into the origin of these 180° in-plane rotational domains.⁶⁴ 

The initiation of the 90° rotation from [001] β-Ga₂O₃ to [010] β-Ga₂O₃, observed alongside the [011] γ-Ga₂O₃ inclusions when Al is introduced, was also considered. Using the evidence presented earlier, for the epitaxial relationship between β-Ga₂O₃ and γ-Ga₂O₃ (i.e., <010> β-Ga₂O₃ || <011> γ-Ga₂O₃), we postulate that the formation of the 90° rotation of β-Ga₂O₃ may be enhanced by the presence of γ-Ga₂O₃. As γ-Ga₂O₃ possesses a higher symmetry than β-Ga₂O₃, the presence of rotational domains becomes virtually inevitable. As illustrated in Fig. 8(c), visualizing γ-Ga₂O₃ along the [011] zone axis reveals that two domains of β-Ga₂O₃ are well aligned with respect to the [011] γ-Ga₂O₃ and constitute ± [010] domains (domains 1 and 3) and ± [001] domains (domains 2 and 4) of β-Ga₂O₃. Considering the role of Al in stabilizing the formation of the γ-phase,^67,68 we further postulate that the Al-induced emergence of the γ-phase ultimately triggers the 90° rotation in the β-phase.

This research revealed (i) a narrow window for the successful growth via MOCVD of thin films of γ-Ga₂O₃ on (100) MgAl₂O₄ substrates, (ii) the formation of a significant density of antiphase boundaries within γ-Ga₂O₃, and (iii) the nature of the epitaxial relationship between γ-Ga₂O₃ and β-Ga₂O₃. Specifically, nominally phase pure γ-Ga₂O₃ was grown at 470 °C, whereas either a mixture of γ-Ga₂O₃ and β-Ga₂O₃ or only β-Ga₂O₃ was grown at higher temperatures ranging from 500 to 530 °C. Integration of the diffusion profiles for Mg and Al acquired using EDX showed the absence of interatomic diffusion of these elements into the film grown at 470 °C. The atomic resolution STEM results showed that the antiphase boundaries produced lattice shifts in the Ga sublattice within the entire γ-Ga₂O₃ film grown at 470 °C. Twin boundaries (180° rotational domains) as well as 90° rotational domains were observed in the β-Ga₂O₃ inclusions that formed within the γ-Ga₂O₃ matrix. The results of a comprehensive investigation of the epitaxial relationship between these two phases were presented and reconciled with the existing reports concerning γ-phase inclusions containing various dopants. It was hypothesized that the introduction of dopants such as Si, Ge, Sn, Mg, Al, and Sc into β-Ga₂O₃ locally stabilizes the “γ-phase” based on their preferred site occupancy. This effectively favors the formation of “γ-phase” or γ-Ga₂O₃ solid solutions over β-Ga₂O₃. In contrast, in the absence of such dopants, pure γ-Ga₂O₃ remains the least stable phase, as indicated by its narrower growth window and lower growth temperatures, when using MOCVD growth techniques, than other Ga₂O₃ polymorphs. Further in situ TEM/STEM investigations on the phase transition from γ-Ga₂O₃ to β-Ga₂O₃ are ongoing and will be fully discussed in a separate paper.

This material was based upon work supported by the Air Force Office of Scientific Research (Program Manager, Dr. Ali Sayir) under Award No. FA9550-21-1-0360 and by the II-VI Foundation. The use of the Materials Characterization Facility at Carnegie Mellon University was supported by Grant No. MCF-677785. J. T. and K. J. would also like to acknowledge the Neil and Jo Bushnell Fellowship in Engineering for additional support.

The authors have no conflicts to disclose.

Jingyu Tang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead). Kunyao Jiang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (equal). Chengchao Xu: Data curation (equal); Writing – review & editing (equal). Matthew J. Cabral: Data curation (equal); Writing – review & editing (equal). Kelly Xiao: Writing – review & editing (equal). Lisa M. Porter: Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (lead). Robert F. Davis: Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (lead).

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