The development of novel ultra-wide bandgap (UWBG) materials requires precise understanding of the atomic level structural origins that give rise to their important properties. We study the aluminum atom incorporation, defect formation, and their relationships with phase stability in β-(AlxGa1−x)2O3 films, a promising candidate for UWBG applications, to explain atomic scale structural characteristics and properties using a combination of quantitative scanning transmission electron microscopy (STEM) and density functional theory (DFT). Our STEM analysis indicates that ∼54% of the incorporated Al substitutes on the octahedrally coordinated Ga2 site in a series of films grown with different techniques and alloy concentrations. DFT calculations show that, while Al energetically prefers the octahedral site, surface reconstructions and kinetic limitations during the epitaxial growth are responsible for Al occupying both octahedral and tetrahedral sites in (AlxGa1−x)2O3, ultimately limiting the stability of the β-phase at x < ∼50%. Local heterogeneity of composition results in the formation of a planar defect, affecting the stability of the β-phase. The similarity of such inclusions to the metastable γ-phase is discussed.

Fundamental to bandgap control in semiconductor materials is the precise understanding of the atomic scale structure and properties. Decades of progress have proven the viability of alloying to achieve semiconductor materials with desired bandgaps for various electronic and photonic applications. Still, exact control of the atomic scale structure and defects in these materials, such as alloy atom distribution and segregation1–3 and alloying-induced point-defect creation,4,5 remains pivotal to their advancement. Extended defects also critically influence the transport and optical properties of semiconductors, and their distribution is particularly vital to control tunable bandgaps when alloying. A detailed characterization of the structure and defects in alloyed semiconductors requires direct experimental information, particularly at the atomic scale, which can be directly correlated with measured or theoretically predicted properties. Obtaining this information will provide crucial guidance for the synthesis of novel bandgap-engineered semiconductor materials with desired properties.

Emerging as the next semiconductor material for electronic, optical, and power device applications,6–16 the transparent conductive oxide β-Ga2O3 exhibits tremendous potential because of its unique properties and opportunities for alloying with Al2O3. Due to its wide bandgap of 4.8 eV,17β-Ga2O3 shows optical transparency into the ultraviolet region18 and a high breakdown field.19 Combined with the ability to achieve controlled n-type doping,20 these unique properties make β-Ga2O3 a candidate material for high power electronics10,21 and deep ultraviolet photodetectors.22 Realizing its full potential as a semiconductor material involves the manipulation and control of the bandgap, which will enable heterostructure designs for carrier confinement and field effect transistors or deep UV optoelectronic devices.

To widen its bandgap, β-Ga2O3 can be alloyed with Al2O3.23,24 While exhibiting a bandgap of 8.8 eV, the ground state crystal structure of Al2O3 is the corundum phase,25 much different than the monoclinic (β) phase of ground state Ga2O3.26 Density functional theory (DFT) calculations have predicted that, despite their difference in the crystal structure, (AlxGa1−x)2O3 is expected to prefer the monoclinic phase for up to 71% Al incorporation.24 However, recent efforts to grow β-(AlxGa1−x)2O3 with a high Al composition have resulted in non-ideal film quality or phase transformations,13,27–34 demonstrating the difficulty in controlling point and extended defects and incorporating the theoretical maximum Al content while maintaining the β phase. These limitations have evidenced the need for a direct characterization of Al incorporation and defects in β-(AlxGa1−x)2O3 thin films.

In this paper, we report scanning transmission electron microscopy (STEM) and DFT investigation of the atomic structure and defects in β-(AlxGa1−x)2O3 thin films to explain the important characteristics of the alloy atom incorporation, defect formation, and phase stability. A quantitative STEM analysis of β-(AlxGa1−x)2O3 films grown by molecular beam epitaxy (MBE) and metal organic chemic vapor deposition (MOCVD) revealed two important atomic-scale origins of growth characteristics and properties of the films: (i) ∼54% of the incorporated Al occupied the octahedrally coordinated Ga2 site, despite that DFT calculations for bulk alloys show that Al energetically prefers the octahedral site by 0.1 eV in the dilute limit, highlighting that non-equilibrium growth conditions force a deviation from the theoretically predicted site occupancy. DFT calculations of surface reconstructions, on the other hand, show that Al can easily be incorporated on the tetrahedrally coordinated Ga1 site and that kinetic limitations will prevent it from moving to the energetically preferred Ga2 site. (ii) A planar defect forms perpendicular to the growth direction when the local Al concentration reaches a critical value of about 50%, which may further destabilize the β phase. DFT calculations demonstrate that the planar defect becomes more favorable at higher Al concentrations, and its formation reduces the stress in the tensile strained film. We also compare the local structure of the defect to the metastable γ-phase.

(010) grown β-(AlxGa1−x)2O3 thin films with x = 0.22 and x = 0.16, 0.27, and 0.40 were produced by MBE12 and MOCVD,13,34 respectively, on Fe-doped (010) β-Ga2O3 substrates. MOCVD films with different Al compositions were grown by tuning the Triethylgallium (TEGa)/Trimethylaluminum (TMAl) molar ratio at 880 °C. Pure O2 was used as the O precursor. The growth chamber pressure was varied between 20 and 80 Torr, and the VI/III ratio was tuned from 880 to 1760. MBE films were produced utilizing slightly oxygen rich conditions involving a Ga beam equivalent pressure (BEP) of 8 × 10−8 Torr, an Al BEP of 1 × 10−8 Torr, an oxygen pressure of 1.5 × 10−5 Torr, and a substrate temperature of 610 °C. The compositions of the films were determined by X-ray diffraction.13 

STEM was performed using a probe corrected FEI Titan STEM (Cs3 = 0.002 mm and Cs5 = 1.0 mm) with probe convergence half angles of 20.0 and 28.9 mrad and detector semi-angles of 78–400 and 51–300 mrad, respectively, at an accelerating voltage of 300 kV. A quantitative analysis of the acquired STEM images35,36 was performed to determine the exact location of individual atoms and to detect the exact Al composition in each atomic column. These results were compared to STEM images obtained using multislice simulation.37 More details of the quantitative STEM analysis are provided in the supplementary material.

We performed DFT calculations using the projector-augmented wave method (PAW)38 implemented in the Vienna ab initio Simulation Package (VASP),39 with a 500-eV cutoff energy for the plane wave expansion. Exchange and correlation were treated using the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Ernzerhof.40 The Ga 3d orbitals are included in the valence, which is essential for phase-stability calculations24 and correct site occupation of Al.24,41 The equilibrium primitive cell of Ga2O3 is fully optimized using a Γ-centered 8 × 8 × 8 k-point mesh, and internal degrees of freedom are relaxed until the Hellmann–Feynman force on each atom is lower than 10 meV/Å. We also constrained the lattice parameters a and c of the conventional cell of ordered Al0.5Ga1.5O3 and Al1Ga1O3 alloys to those of Ga2O3 and relaxed the lattice parameter b and all internal degrees of freedom. This was done using a 3 × 12 × 6 k-point mesh. The Ga2O3(010) surface is modeled using a slab consisting of a 1 × 5 × 1 multiple of the conventional unit cell of β-Ga2O3. We used a vacuum thickness of ∼19 Å to avoid interactions between the slab surfaces. Migration pathways and energy barriers are calculated using the climbing-image nudged elastic band method.42 More details of DFT calculations are explained in the supplementary material.

High angle annular dark field (HAADF) STEM images in Fig. 1 show the epitaxial growth of the films. The film layer, which exhibits the same orientation as the substrate, displays lower contrast, confirming Al incorporation. However, while the β-(Al0.16Ga0.84)2O3 and β-(Al0.22Ga0.78)2O3 films displayed complete epitaxial growth [Figs. 1(a) and 1(b)], the β-(Al0.27Ga0.73)2O3 and β-(Al0.40Ga0.60)2O3 films showed an average thickness of 200 and 10 nm, respectively, before undergoing a crystallographic rotation,34 as shown in Figs. 1(c) and 1(d). This demonstrates that the films with 27% and 40% Al are only partially stable and do not grow epitaxially beyond a critical thickness.

FIG. 1.

HAADF STEM images of [001]m (a) β-(Al0.16Ga0.84)2O3, (b) β-(Al0.22Ga0.78)2O3, (c) β-(Al0.27Ga0.73)2O3, and (d) β-(Al0.40Ga0.60)2O3 films with the β-(AlxGa1−x)2O3//β-Ga2O3 interface marked with a dashed yellow line. Bright contrast above upper dashed lines in (c) and (d) indicates a crystallographic rotation of the film. Films were grown by (a), (c) and (d) MOCVD and (b) MBE.

FIG. 1.

HAADF STEM images of [001]m (a) β-(Al0.16Ga0.84)2O3, (b) β-(Al0.22Ga0.78)2O3, (c) β-(Al0.27Ga0.73)2O3, and (d) β-(Al0.40Ga0.60)2O3 films with the β-(AlxGa1−x)2O3//β-Ga2O3 interface marked with a dashed yellow line. Bright contrast above upper dashed lines in (c) and (d) indicates a crystallographic rotation of the film. Films were grown by (a), (c) and (d) MOCVD and (b) MBE.

Close modal

We aim to provide an explanation for the abrupt discontinuation of the (010) β-(Al0.27Ga0.73)2O3 and β-(Al0.40Ga0.60)2O3 film growth and the general challenges in growing epitaxial β-(AlxGa1−x)2O3 thin films at high Al concentrations. First, we studied the site occupancy for substitutional Al atoms. The monoclinic crystal structure of β-Ga2O3 consists of two inequivalent cation environments: a tetrahedrally coordinated (Ga1) and an octahedrally coordinated (Ga2) site. In Fig. 2(a), a modeled β-Ga2O3 cell oriented along the [001]m(monoclinic) direction displays its positions. Recent DFT calculations have shown that Al energetically prefers the Ga2 site and is expected to completely inhabit this position in bulk β-(AlGa)2O3 alloys and is forced to occupy the Ga1 site when x > 0.50.24,41 This arrangement of Ga and Al in alloyed films was predicted to produce stable β-(AlxGa1−x)2O3 for up to x = 0.71. To compare this calculation to the case of our thin films, we quantitatively assessed the site distribution for Al from the atomic resolution HAADF STEM images of our β-(AlxGa1−x)2O3 films shown in Figs. 2(b)2(e). These images reveal Ga1 and Ga2 atomic columns, which display high intensity as compared to O columns due to the atomic number dependence of the HAADF scattered signal. The decrease in column intensity from the lighter substitutional Al in the β-(AlxGa1−x)2O3 films is clearly noticeable in the images. The quantitative comparisons between experimental and multislice simulated column intensities35,36 are displayed in Figs. 2(f) and 2(g) for the β-(Al0.16Ga0.84)2O3 and β-(Al0.27Ga0.73)2O3 films and the β-(Al0.22Ga0.78)2O3 and β-(Al0.40Ga0.60)2O3 films, respectively. The column intensity is the fraction of the scattered intensity to the incident beam intensity, and therefore, it has no unit. Datasets plotted together indicate that common microscopic parameters were used during collection and simulation {e.g., α = 20.0 mrad [Fig. 2(f)] and α = 28.9 mrad [Fig. 2(g)]}. As shown in Figs. 2(f) and 2(g), experimental Ga1 and Ga2 site intensities projected onto simulated column intensity vs Al composition trend data indicated that the compositions of the films, ordered corresponding to Figs. 2(b)2(e), are 18.8% ± 1.7%, 29.4% ± 1.3%, 22.2% ± 2.1%, and 41.2% ± 1.7% Al, verifying the compositions estimated by XRD (16%, 27%, 22%, and 40%, respectively). More specifically, the Ga2 sites contained 20.1% ± 1.8%, 31.2% ± 1.5%, 23.7% ± 1.8%, and 44.34% ± 1.6% Al, while the Ga1 site contained 17.4% ± 1.6%, 27.5% ± 1.1%, 20.7% ± 2.3%, and 38.0% ± 1.8% Al in the respective films [Figs. 2(f) and 2(g)]. The Al occupancy results are summarized in Fig. 2(h). Most importantly, the quantitative STEM comparison indicates that Al only slightly prefers the octahedrally coordinated Ga2 site, at an occupancy of nearly 54%, regardless of the overall Al composition.

FIG. 2.

Quantitative STEM analysis of β-(AlxGa1−x)2O3 films. (a) Crystal structure of β-Ga2O3 along the [001]m direction. (b)–(e) Atomic resolution HAADF STEM images of [001]m (b) β-(Al0.16Ga0.84)2O3, (c) β-(Al0.27Ga0.73)2O3, (d) β-(Al0.22Ga0.78)2O3, and (e) β-(Al0.40Ga0.60)2O3 grown on Fe-doped (010) β-Ga2O3 substrates. Films were grown by (b), (c), and (e) MOCVD and (d) MBE. Insets are the experimental PACBED patterns acquired from the β-Ga2O3 substrates and the corresponding multislice simulated patterns, indicating the TEM sample thicknesses of (b) 13.9 nm, (c) 27.8 nm, (d) 16.8 nm, and (e) 18.5 nm. (f) Quantitative comparison of (b) and (c) experimental and multislice simulated column intensities with varying Al compositions for microscopic parameters: V = 300 kV, α = 20.0 mrad, and HAADF collection angle range =78–400 mrad. (g) Quantitative comparison of (d) and (e) experimental and multislice simulated column intensities with varying Al compositions for microscopic parameters: V = 300 kV, α = 28.9 mrad, and HAADF collection angle range =51–300 mrad. (h) Plot showing the Al site occupancy (%) for the Ga1 (green x) and Ga2 (blue x) sites vs the determined Al composition of the films.

FIG. 2.

Quantitative STEM analysis of β-(AlxGa1−x)2O3 films. (a) Crystal structure of β-Ga2O3 along the [001]m direction. (b)–(e) Atomic resolution HAADF STEM images of [001]m (b) β-(Al0.16Ga0.84)2O3, (c) β-(Al0.27Ga0.73)2O3, (d) β-(Al0.22Ga0.78)2O3, and (e) β-(Al0.40Ga0.60)2O3 grown on Fe-doped (010) β-Ga2O3 substrates. Films were grown by (b), (c), and (e) MOCVD and (d) MBE. Insets are the experimental PACBED patterns acquired from the β-Ga2O3 substrates and the corresponding multislice simulated patterns, indicating the TEM sample thicknesses of (b) 13.9 nm, (c) 27.8 nm, (d) 16.8 nm, and (e) 18.5 nm. (f) Quantitative comparison of (b) and (c) experimental and multislice simulated column intensities with varying Al compositions for microscopic parameters: V = 300 kV, α = 20.0 mrad, and HAADF collection angle range =78–400 mrad. (g) Quantitative comparison of (d) and (e) experimental and multislice simulated column intensities with varying Al compositions for microscopic parameters: V = 300 kV, α = 28.9 mrad, and HAADF collection angle range =51–300 mrad. (h) Plot showing the Al site occupancy (%) for the Ga1 (green x) and Ga2 (blue x) sites vs the determined Al composition of the films.

Close modal

Differing from the Al occupation predicted for bulk β-(AlxGa1−x)2O3, our STEM results for the β-(AlxGa1−x)2O3 films show that Al only slightly favors the Ga2 site in all the β-(AlxGa1−x)2O3 films, with about 46% of Al occupying the energetically unfavorable Ga1 site [Fig. 2(h)]. This is likely because the DFT prediction would apply to bulk alloys in thermodynamic equilibrium, but the observed incorporation of a large fraction of Al on Ga1 sites indicates that non-equilibrium conditions govern the incorporation of Al in films. We confirmed this hypothesis using detailed DFT calculations of surface reconstructions and Al incorporation on the (010) surface during growth. Simulating conditions representative of epitaxial growth, we explored the co-adsorption of Al, Ga, and O adatoms on the surface with various coverages. As each layer of the Ga2O3 (010) slab has four Ga atoms and six O atoms, we examined various coverages of adatoms, which include 1–3 Al adatoms, 0–3 Ga adatoms, and up to six O adatoms. For each coverage, we also explored various possible adsorption sites for Al, Ga, and O to obtain the most stable configuration. Surfaces with relatively low formation energies are included in the formation energy diagram [Fig. 3(a)]. It covers the Al concentrations of 25% and 50%, which reflects the growth conditions. When the Al chemical potential is relatively low, the surface with one Al, three Ga, and three O adatoms is most stable [Alh + 3Ga + 3O in Fig. 3(b)]. Here, the Al adatom is adsorbed on a hollow site (Alh), midway between two tetrahedral (Ga1) sites; atoms adsorbed on this site will incorporate on tetrahedral (Ga1) sites in the growing layer. Higher Al chemical potentials lead to the Alh + 3Ga + 2O and Alh + Alatop + 2Ga + O surface reconstructions; the latter, depicted in Fig. 3(c), incorporates Al on an “atop” site, which is equivalent to the octahedral (Ga2) site in the bulk. To explore the surface with a higher O coverage, we also show the formation energy of the Alh + Alatop + 2Ga + 3O surface, which also incorporates an Al atom on an “atop” site. While we cannot assign a precise value to the Al chemical potential, it is clear from the stable surface reconstructions over a wide range of chemical potentials that Al is likely to get incorporated on a tetrahedral site. To assess the likelihood of staying on this site, despite its higher energy in the bulk, we also need to examine the barriers for Al to migrate to an octahedral site. Figure 3(d) shows one example of such a study, showing a barrier of 1.72 eV. Migration studies on other reconstructed surfaces show similar or higher barriers. We have also considered the possibility of Al migrating from tetrahedral (Ga1) to octahedral (Ga2) sites in the bulk and found even higher activation barriers. All this indicates that once Al is incorporated on the tetrahedral (Ga1) site, it will be constrained from moving to the lower-energy octahedral (Ga2) site.

FIG. 3.

(a) Formation energies Ef (in eV/1 × 1 unit cell) for the lowest energy surface reconstructions under Ga-rich conditions, as a function of the Al chemical potential. Top and side views of the Ga2O3 (010) surfaces with (b) Alh + 3Ga + 3O and (c) Alh + Alatop + 2Ga + O. (d) Potential energy diagram for an Al adatom migration from an Alh hollow site to a nearby Alatop octahedral site on the bare Ga2O3 (010) surface. Color code: Ga1 (green), Ga2 (blue), O (red), adsorbed Ga (highlighted green), adsorbed O (highlighted red), and adsorbed Al (highlighted cyan with purple circles).

FIG. 3.

(a) Formation energies Ef (in eV/1 × 1 unit cell) for the lowest energy surface reconstructions under Ga-rich conditions, as a function of the Al chemical potential. Top and side views of the Ga2O3 (010) surfaces with (b) Alh + 3Ga + 3O and (c) Alh + Alatop + 2Ga + O. (d) Potential energy diagram for an Al adatom migration from an Alh hollow site to a nearby Alatop octahedral site on the bare Ga2O3 (010) surface. Color code: Ga1 (green), Ga2 (blue), O (red), adsorbed Ga (highlighted green), adsorbed O (highlighted red), and adsorbed Al (highlighted cyan with purple circles).

Close modal

As a consequence, with the increasing Al concentration or film thickness, the total number of Al atoms substituting on the Ga1 site increases, leading to a structure with higher energy. Thus, we conclude that the lack of control over Al site incorporation leads to eventual phase transformations or rotations of the films34 and the formation of defects, which has limited the growth of epitaxial β-(AlxGa1−x)2O3 films with Al concentrations higher than ∼50%. It is also worth noting that the finding here applies to both MBE- and MOCVD-grown films.

We also show the formation of extended (planar) defects within the films. The defect, forming perpendicular to the growth direction, observed in the β-(Al0.40Ga0.60)2O3 film as an example is shown in Fig. 4(a). This defect contains a string of atomic columns located directly between neighboring Ga1 sites. The projection of this site is in an identical location as the most probable position for the migration of a Ga1 atom in the formation of the DFT predicted43 and recently directly observed36 divacancy–interstitial complex or “split vacancy.” These atomic columns, which we mark with a dashed circle and label ic in Fig. 4(b), comprise the planar defect and display intensities comparable to unperturbed Ga site columns in the film. Related to this is the observed distinct loss of adjacent Ga1 sites, labeled V. The signal located in the ic position coupled with the complete loss of neighboring Ga1 column intensity reveals an entire defective line throughout the 18.5 nm thickness of the TEM foil (i.e., along the “depth direction”). Additionally, the signal is detected at the original Ga2 sites (dashed blue circle) and at typically vacant positions directly next to the original Ga2 sites between neighboring ic atomic columns (solid blue circle). The intensities of both columns are notably lower than those of typical Ga2 site columns in the β-(Al0.40Ga0.60)2O3 film. This local atomic structure within the defect in fact resembles a [110]-view γ-phase (AlxGa1−x)2O3 material as demonstrated in Figs. 4(c)4(e). As shown in Fig. 4(c), the defect in Fig. 4(b) is visualized within the β-phase structure. A [110]-view γ-Al2O3 unit cell is displayed in Fig. 4(d). To compare the γ-phase structure to the experimentally observed structure in Fig. 4(c), we displaced the γ-Al2O3 model in Fig. 4(d) from its origin at 0,0,0 to the 12, 12,0 point of the [001]-view β-(AlxGa1−x)2O3 cell, which is shown in Fig. 4(e). At the projected ic position shown in [110] γ-(AlxGa1−x)2O3 [Fig. 4(d)], the atomic column contains twice the number of atoms along the depth direction as compared to a β-phase Ga1 column, and atoms in this site are octahedrally coordinated, surrounded by six oxygen positions (red atoms) nearby. When coupled with the observed vacant Ga1 sites, the stoichiometry is maintained. In addition, the oxygen lattice is nearly identical for [001] β-(AlxGa1−x)2O3 and [110] γ-(AlxGa1−x)2O3. However, while the local structure of the defect has some similarity to the γ-phase, we note that the structure does not entirely complete the γ-phase lattice, and therefore, the defect cannot be viewed as a phase transformation.

FIG. 4.

Planar defect found in the MOCVD grown β-(Al0.40Ga0.60)2O3 film running perpendicular to the (010) growth direction. (a) [001]m HAADF STEM image of the 6 nm planar defect. (b) Defect region in (a) showing adjacent ic site intensities (green dashed circle), completely vacant Ga1 site columns (V), and Ga2 intensities (blue circles) that have relaxed to form the stable structure. (c) Modeled defect structure visualized from the β-phase, indicating the complete loss of the Ga1 site intensity (V), ic atomic position (green dashed circles), original Ga2 site (blue dashed circles), and their relaxation (orange arrows) to a new location (blue solid circles). (d) γ-phase Al2O3 structure oriented along the [110] direction. (e) [110] γ-phase cells from (d) positioned with the octahedrally coordinated atomic column located at ic, overlaid on the β-phase visualized defect model from (c), producing the observed planar defect. (f) Quantitative STEM analysis of the Ga sites above and below the defect interface as a function of distance in unit cells [1–3 labeled in (a)]. Experimental intensities are directly compared to the 18.5 nm thick β-(AlxGa1−x)2O3 simulation. The average film site concentrations from the β-(Al0.40Ga0.60)2O3 film are marked on the plot.

FIG. 4.

Planar defect found in the MOCVD grown β-(Al0.40Ga0.60)2O3 film running perpendicular to the (010) growth direction. (a) [001]m HAADF STEM image of the 6 nm planar defect. (b) Defect region in (a) showing adjacent ic site intensities (green dashed circle), completely vacant Ga1 site columns (V), and Ga2 intensities (blue circles) that have relaxed to form the stable structure. (c) Modeled defect structure visualized from the β-phase, indicating the complete loss of the Ga1 site intensity (V), ic atomic position (green dashed circles), original Ga2 site (blue dashed circles), and their relaxation (orange arrows) to a new location (blue solid circles). (d) γ-phase Al2O3 structure oriented along the [110] direction. (e) [110] γ-phase cells from (d) positioned with the octahedrally coordinated atomic column located at ic, overlaid on the β-phase visualized defect model from (c), producing the observed planar defect. (f) Quantitative STEM analysis of the Ga sites above and below the defect interface as a function of distance in unit cells [1–3 labeled in (a)]. Experimental intensities are directly compared to the 18.5 nm thick β-(AlxGa1−x)2O3 simulation. The average film site concentrations from the β-(Al0.40Ga0.60)2O3 film are marked on the plot.

Close modal

The planar defect can, therefore, be regarded as a combination of motifs, each of which consists of a column of split vacancies and a column of displaced Ga2 atoms. In fact, the structural motif presented in Fig. 4(e) is also consistent with our DFT calculations of surface reconstructions shown in Fig. 3. At higher Al coverage, the Alh + Alatop + 2Ga + O reconstruction is favored [Fig. 3(c)]. Alh sits midway between two tetrahedral sites, which coincides with the column of split vacancies. The Al adatom on the octahedral site (Alatop) is relaxed toward Alh, mainly due to the shorter Al–O bond length compared to Ga–O. The position of the relaxed Alatop adatom coincides with the displaced Ga2 atoms (solid blue circle) in Figs. 4(b) and 4(c). Since the planar defect has a higher Al concentration than the surrounding material (see below), we suggest that “freezing in” the surface reconstruction with Alh + Alatop + 2Ga + O may explain the occurrence of the planar defect.

Utilizing quantitative STEM, we identify the origin of the planar defect through the analysis of the defect structure and local change in the Al concentration. To determine any local variation in the composition, Ga1 and Ga2 site intensities were averaged as a function of distance (unit cell) above and below the defect interface. The first three layers considered are marked in Fig. 4(a). These experimental intensities were directly compared to the simulated 18.5 nm thick β-(AlxGa1−x)2O3 data and are plotted in Fig. 4(f). Over eight unit cells, nearing the planar defect along the direction perpendicular to the defect, the local Al concentration significantly increases from the average film concentration of 38.0% and 44.3% for Ga1 and Ga2 sites to 45.8% and 54.9%, respectively. This trend signifies that the formation of the planar defect is driven by the local increase in Al, reaching a critical concentration of nearly 50%. Additionally, ic columns within the defect, composed of double the number of atoms as Ga1 and Ga2 columns, which are accompanied by a complete loss in the Ga1 site signal, displayed intensity, confirming that a high concentration of Al inhabits the position. This again illustrates the likelihood of the suggested “freezing in” of the surface reconstruction that occurs with the increased Al concentration mentioned above. Furthermore, the new arrangement of atoms between adjacent ic columns is likely formed by the relaxation of some of the Ga2 site atoms, as shown with the orange arrows in Figs. 4(b) and 4(c), arranging in positions similar to [110] γ-(AlxGa1−x)2O3 [Figs. 4(d) and 4(e)] and acting to stabilize the structure.

Identical planar defects found in a β-(Al0.56Ga0.44)2O3 superlattice structure confirm its formational dependence on Al incorporation exceeding the critical limit of about 50%. A HAADF STEM image of the β-(Al0.56Ga0.44)2O3 superlattice structure grown by MOCVD is shown in Fig. 5. The immediate formation of planar defects observed in each β-(Al0.56Ga0.44)2O3 layer demonstrates the inability to grow epitaxial β-(Al0.56Ga0.44)2O3 for any thickness using the given growth parameters.

FIG. 5.

[001]m oriented HAADF STEM image of planar defects in the MOCVD grown β-(Al0.56Ga0.44)2O3//β-Ga2O3 superlattice structure.

FIG. 5.

[001]m oriented HAADF STEM image of planar defects in the MOCVD grown β-(Al0.56Ga0.44)2O3//β-Ga2O3 superlattice structure.

Close modal

To gain insight into the stability and possible formation mechanisms of the observed planar defect, we explicitly modeled the planar defect [assuming that it is infinitely extended in the (010) plane] in a supercell in which defects are separated by regions of the β-phase material (Fig. 6). We performed these calculations for both pure Ga2O3 and (Al0.40Ga0.60)2O3 alloys. Al occupations in the planar defect were assigned in accordance with the STEM analysis reported above, while in the undefective β-phase regions, Al atoms were allowed to randomly occupy both tetrahedral and octahedral sites. The in-plane lattice parameters of the heterostructure were constrained to those of the β-Ga2O3 substrate, reflecting pseudomorphic growth. We started from the simulated structure in Fig. 4(c) and allowed out-of-plane lattice parameters and atomic positions to relax, finding that the proposed structure is, indeed, locally stable, allowing us to calculate the formation energy of the planar defect Eplanar (see the supplementary material for details) as follows:

Eplanar=[EtotheterostructureEtotbulk]/A,
(1)

where Etotheterostructure is the total energy of the heterostructure containing the planar defect and Etotbulk is the reference energy for the corresponding bulk material. We obtain an energy per unit area by dividing by A, the in-plane area of the supercell. For x = 0, the bulk reference is pure Ga2O3, while for x = 0.4, we model the bulk (Al0.40Ga0.60)2O3 alloy by averaging over calculations for random placements of Al atoms in a supercell of the same dimensions, i.e., the supercells for modeling both the planar defect and the bulk alloy contain 40 formula units (200 atoms). The total energies of the bulk-alloy supercells are very similar; for the purposes of Eq. (1), Etotbulk is an arithmetic average.

FIG. 6.

Model of a heterostructure incorporating a planar defect (red highlighted region) and a β-phase bulk-like region (blue highlighted region). Colors of atoms are consistent with Fig. 2(a).

FIG. 6.

Model of a heterostructure incorporating a planar defect (red highlighted region) and a β-phase bulk-like region (blue highlighted region). Colors of atoms are consistent with Fig. 2(a).

Close modal

Table I lists the formation energies of the planar defect at x = 0 and 0.4. At x = 0, the planar-defect structure has a formation energy Eplanar = 1.57 eV/uc [uc is the area of the (010)-plane bulk unit cell, which is 71.1 Å2]. For x = 0.4, the distribution of Al atoms in the region of the planar defect (red-shaded region in Fig. 6) is always the same, but the distribution of Al atoms in the undefective (bulk) portion of the supercell (blue-shaded region) is varied, resulting in six values of formation energies. At x = 0.4, the formation energy of the planar defect is always lower than at x = 0, which indicates that the planar defect becomes significantly easier to form at higher Al concentrations. Among the six heterostructure supercells, the lower-energy structures contain a higher concentration of Al in the layers adjacent to the planar defect. This agrees with the experimental observation [Fig. 4(d)] of the increasing Al concentration as one approaches the planar defect.

TABLE I.

Formation energies of the planar defect Eplanar [eV/uc, where uc is the area of the (010)-plane bulk unit cell] [Eq. (1)] for the heterostructure with the planar defect at x = 0 and 0.4 in (AlxGa1−x)2O3. The difference between the six supercells for x = 0.4 is described in the text.

x = 0x = 0.4
Supercell 
Eplanar 1.57 1.49 0.93 0.71 0.43 0.29 0.21 
x = 0x = 0.4
Supercell 
Eplanar 1.57 1.49 0.93 0.71 0.43 0.29 0.21 

All the modeled structures at x = 0.4 (alloys and defect-containing heterostructures) are under tensile strain to reflect the pseudomorphic lattice matching to β-Ga2O3. The presence of tensile strain (and stress) leads to a buildup of elastic energy as the layer grows thicker. Such strain is known to be relieved, beyond a critical layer thickness, by formation of cracks,44 dislocations, V-defects, etc. We found that here the formation of the planer defect at x = 0.4 effectively reduces the in-plane stress and thereby lowers the elastic energy. For example, the in-plane stress averaged over four random β-phase (Al0.40Ga0.60)2O3 materials is −54.4 kbar, while that averaged over the six heterostructures is only −31.2 kbar. This indicates that the planar defect provides a stress-release mechanism and is favorable at higher Al concentrations.

In conclusion, the STEM investigation of point and extended defects in β-(AlxGa1−x)2O3 films at the atomic scale revealed two important results: (i) an almost equal distribution of Al between the Ga1 and Ga2 sites and (ii) the formation of a planar defect perpendicular to the growth direction accompanied by an increase in the local Al concentration resembling a γ-phase inclusion at the local level. The quantitative STEM Al-site occupancy analysis indicated that 54% of the incorporated Al occupied the octahedrally coordinated Ga2 site, leading to a higher energy structure. DFT calculations show that Al can occupy the thermodynamically less favorable tetrahedral site due to its incorporation in particular configurations on the surface and kinetic limitations. A planar defect forms when the local Al concentration reaches a critical value of about 50%. DFT calculations demonstrate that these planar defects are locally stable, and their formation enthalpy relative to the β-phase is reduced at high Al concentrations. We also found that the presence of the planar defect reduces the in-plane stress of the tensile-strained film, thus releasing the stored elastic energy. This type of STEM study provides critical atomic scale information on defect incorporation in bandgap-engineered semiconductors that can ultimately be used to guide the synthesis of the materials with desired properties.

See the supplementary material for the details of the STEM experiment and DFT calculation.

This work was supported by the Department of Defense, Air Force Office of Scientific Research GAME MURI Program (Grant No. FA9550-18-1-0479). Electron microscopy was performed, in part, at the Center for Electron Microscopy and Analysis (CEMAS) at The Ohio State University and at the Penn State University Materials Characterization Laboratory. Computational facilities purchased with funds from the National Science Foundation (NSF) (Grant No. CNS-1725797) was used and administered by the Center for Scientific Computing (CSC). The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center (MRSEC; Grant No. NSF DMR 1720256) at UC Santa Barbara. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE), which was supported by the National Science Foundation under Grant No. ACI-1548562. This work was also partially performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. DOE, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office.

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

1.
K.
Watanabe
,
N.
Nakanishi
,
T.
Yamazaki
,
J. R.
Yang
,
S. Y.
Huang
,
K.
Inoke
,
J. T.
Hsu
,
R. C.
Tu
, and
M.
Shiojiri
, “
Atomic-scale strain field and in atom distribution in multiple quantum wells InGaN/GaN
,”
Appl. Phys. Lett.
82
,
715
(
2003
).
2.
B.
Mazumder
,
S. W.
Kaun
,
J.
Lu
,
S.
Keller
,
U. K.
Mishra
, and
J. S.
Speck
, “
Atom probe analysis of AlN interlayers in AlGaN/AlN/GaN heterostructures
,”
Appl. Phys. Lett.
102
,
111603
(
2013
).
3.
S. E.
Bennett
,
R. M.
Ulfig
,
P. H.
Clifton
,
M. J.
Kappers
,
J. S.
Barnard
,
C. J.
Humphreys
, and
R. A.
Oliver
, “
Atom probe tomography and transmission electron microscopy of a Mg-doped AlGaN/GaN superlattice
,”
Ultramicroscopy
111
,
207
(
2011
).
4.
A. R.
Arehart
,
A. A.
Allerman
, and
S. A.
Ringel
, “
Electrical characterization of n-type Al0.30Ga0.70N Schottky diodes
,”
J. Appl. Phys.
109
,
114506
(
2011
).
5.
T. A.
Henry
,
A.
Armstrong
,
A. A.
Allerman
, and
M. H.
Crawford
, “
The influence of Al composition on point defect incorporation in AlGaN
,”
Appl. Phys. Lett.
100
,
043509
(
2012
).
6.
S. I.
Stepanov
,
V. I.
Nikolaev
,
V. E.
Bougrov
, and
A. E.
Romanov
, “
Gallium oxide: Properties and applications—A review
,”
Rev. Adv. Mater. Sci.
44
,
63
(
2016
).
7.
M.
Orita
,
H.
Ohta
,
M.
Hirano
, and
H.
Hosono
, “
Deep-ultraviolet transparent conductive β-Ga2O3 thin films
,”
Appl. Phys. Lett.
77
,
4166
(
2000
).
8.
M. A.
Mastro
,
A.
Kuramata
,
J.
Calkins
,
J.
Kim
,
F.
Ren
, and
S. J.
Pearton
, “
Perspective—Opportunities and future directions for Ga2O3
,”
ECS J. Solid State Sci. Technol.
6
,
P356
(
2017
).
9.
M.
Higashiwaki
,
H.
Murakami
,
Y.
Kumagai
, and
A.
Kuramata
, “
Current status of Ga2O3 power devices
,”
Jpn. J. Appl. Phys., Part 1
55
,
1202A1
(
2016
).
10.
M.
Higashiwaki
,
A.
Kuramata
,
H.
Murakami
, and
Y.
Kumagai
, “
State-of-the-art technologies of gallium oxide power devices current status of Ga2O3 power devices
,”
J. Phys. D: Appl. Phys.
50
,
333002
(
2017
).
11.
S.
Fujita
, “
Wide-bandgap semiconductor materials: For their full bloom
,”
Jpn. J. Appl. Phys., Part 1
54
,
030101
(
2015
).
12.
S.
Krishnamoorthy
,
Z.
Xia
,
C.
Joishi
,
Y.
Zhang
,
J.
McGlone
,
J.
Johnson
,
M.
Brenner
,
A. R.
Arehart
,
J.
Hwang
,
S.
Lodha
, and
S.
Rajan
, “
Modulation-doped β-(Al0.2Ga0.8)2O3/Ga2O3 field-effect transistor
,”
Appl. Phys. Lett.
111
,
023502
(
2017
).
13.
A. F. M.
Anhar Uddin Bhuiyan
,
Z.
Feng
,
J. M.
Johnson
,
Z.
Chen
,
H.-L.
Huang
,
J.
Hwang
, and
H.
Zhao
, “
MOCVD epitaxy of β-(AlxGa1-x)2O3 thin films on (010) Ga2O3 substrates and N-type doping
,”
Appl. Phys. Lett.
115
,
120602
(
2019
).
14.
Z.
Feng
,
A. F. M.
Anhar Uddin Bhuiyan
,
M. R.
Karim
, and
H.
Zhao
, “
MOCVD homoepitaxy of Si-doped (010) β-Ga2O3 thin films with superior transport properties
,”
Appl. Phys. Lett.
114
,
250601
(
2019
).
15.
F.
Alema
,
Y.
Zhang
,
A.
Osinsky
,
N.
Valente
,
A.
Mauze
,
T.
Itoh
, and
J. S.
Speck
, “
Low temperature electron mobility exceeding 104 cm2/V s in MOCVD grown β-Ga2O3
,”
APL Mater.
7
,
121110
(
2019
).
16.
M.
Baldini
,
Z.
Galazka
, and
G.
Wagner
, “
Recent progress in the growth of β-Ga2O3 for power electronics applications
,”
Mater. Sci. Semicond. Process.
78
,
132
(
2018
).
17.
H. H.
Tippins
, “
Optical absorption and photoconductivity in the band edge of β-Ga2O3
,”
Phys. Rev.
140
,
A316
(
1965
).
18.
N.
Ueda
,
H.
Hosono
,
R.
Waseda
, and
H.
Kawazoe
, “
Synthesis and control of conductivity of ultraviolet transmitting β-Ga2O3 single crystals
,”
Appl. Phys. Lett.
70
,
3561
(
1997
).
19.
M.
Higashiwaki
,
K.
Sasaki
,
A.
Kuramata
,
T.
Masui
, and
S.
Yamakoshi
, “
Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates
,”
Appl. Phys. Lett.
100
,
013504
(
2012
).
20.
S.
Rafique
,
L.
Han
,
M. J.
Tadjer
,
J. A.
Freitas
,
N. A.
Mahadik
, and
H.
Zhao
, “
Homoepitaxial growth of β-Ga2O3 thin films by low pressure chemical vapor deposition
,”
Appl. Phys. Lett.
108
,
182105
(
2016
).
21.
M.
Higashiwaki
,
K.
Sasaki
,
H.
Murakami
,
Y.
Kumagai
,
A.
Koukitu
,
A.
Kuramata
,
T.
Masui
, and
S.
Yamakoshi
, “
Recent progress in Ga2O3 power devices
,”
Semicond. Sci. Technol.
31
,
034001
(
2016
).
22.
T.
Oshima
,
T.
Okuno
,
N.
Arai
,
N.
Suzuki
,
S.
Ohira
, and
S.
Fujita
, “
Vertical solar-blind deep-ultraviolet Schottky photodetectors based on β-Ga2O3 substrates
,”
Appl. Phys. Express
1
,
011202
(
2008
).
23.
F.
Zhang
,
K.
Saito
,
T.
Tanaka
,
M.
Nishio
,
M.
Arita
, and
Q.
Guo
, “
Wide bandgap engineering of (AlGa)2O3 films
,”
Appl. Phys. Lett.
105
,
162107
(
2014
).
24.
H.
Peelaers
,
J. B.
Varley
,
J. S.
Speck
, and
C. G.
Van de Walle
, “
Structural and electronic properties of Ga2O3-Al2O3 alloys
,”
Appl. Phys. Lett.
112
,
242101
(
2018
).
25.
R. H.
French
, “
Electronic band structure of Al2O3, with comparison to AlON and AIN
,”
J. Am. Ceram. Soc.
73
,
477
(
1990
).
26.
J.
Åhman
,
G.
Svensson
, and
J.
Albertsson
, “
A reinvestigation of β-gallium oxide
,”
Acta Crystallogr., Sect. C
52
,
1336
(
1996
).
27.
S. W.
Kaun
,
F.
Wu
, and
J. S.
Speck
, “
β-(AlxGa1−x)2O3/Ga2O3 (010) heterostructures grown on β-Ga2O3 (010) substrates by plasma-assisted molecular beam epitaxy
,”
J. Vac. Sci. Technol. A
33
,
041508
(
2015
).
28.
C.
Kranert
,
M.
Jenderka
,
J.
Lenzner
,
M.
Lorenz
,
H.
Von Wenckstern
,
R.
Schmidt-Grund
, and
M.
Grundmann
, “
Lattice parameters and Raman-active phonon modes of β-(AlxGa1−x)2O3
,”
J. Appl. Phys.
117
,
125703
(
2015
).
29.
J.
Li
,
X.
Chen
,
T.
Ma
,
X.
Cui
,
F.-F.
Ren
,
S.
Gu
,
R.
Zhang
,
Y.
Zheng
,
S. P.
Ringer
,
L.
Fu
,
H. H.
Tan
,
C.
Jagadish
, and
J.
Ye
, “
Identification and modulation of electronic band structures of single-phase β-(AlxGa1-x)2O3 alloys grown by laser molecular beam epitaxy
,”
Appl. Phys. Lett.
113
,
041901
(
2018
).
30.
Q.
Feng
,
X.
Li
,
G.
Han
,
L.
Huang
,
F.
Li
,
W.
Tang
,
J.
Zhang
, and
Y.
Hao
, “
(AlGa)2O3 solar-blind photodetectors on sapphire with wider bandgap and improved responsivity
,”
Opt. Mater. Express
7
,
1240
(
2017
).
31.
B.
Mazumder
,
J.
Sarker
,
Y.
Zhang
,
J. M.
Johnson
,
M.
Zhu
,
S.
Rajan
, and
J.
Hwang
, “
Atomic scale investigation of chemical heterogeneity in β-(AlxGa1−x)2O3 films using atom probe tomography
,”
Appl. Phys. Lett.
115
,
132105
(
2019
).
32.
T.
Oshima
,
T.
Okuno
,
N.
Arai
,
Y.
Kobayashi
, and
S.
Fujita
, “
β-Al2xGa2-2xO3 thin film growth by molecular beam epitaxy
,”
Jpn. J. Appl. Phys., Part 1
48
,
070202
(
2009
).
33.
P.
Vogt
,
A.
Mauze
,
F.
Wu
,
B.
Bonef
, and
J. S.
Speck
, “
Metal-oxide-catalyzed epitaxy: Example of O plasma-assisted molecular beam epitaxy of β-(AlxGa1−x)2O3/β-Ga2O3 heterostructures
,”
Appl. Phys. Express
11
,
115503
(
2018
).
34.
A. F. M.
Anhar Uddin Bhuiyan
,
Z.
Feng
,
J. M.
Johnson
,
H.-L.
Huang
,
J.
Sarker
,
M.
Zhu
,
M. R.
Karim
,
B.
Mazumder
,
J.
Hwang
, and
H.
Zhao
, “
Phase transformation in MOCVD growth of (AlxGa1−x)2O3 thin films
,”
APL Mater.
8
,
031104
(
2020
).
35.
J.
Hwang
,
J. Y.
Zhang
,
A. J.
D’Alfonso
,
L. J.
Allen
,
S.
Stemmer
,
A. J. D.
Alfonso
,
L. J.
Allen
, and
S.
Stemmer
, “
Three-dimensional imaging of individual dopant atoms in SrTiO3
,”
Phys. Rev. Lett.
111
,
266101
(
2013
).
36.
J. M.
Johnson
,
Z.
Chen
,
J. B.
Varley
,
C. M.
Jackson
,
E.
Farzana
,
A. R.
Arehart
,
H.
Huang
,
A.
Genc
,
S. A.
Ringel
,
C. G.
Van de Walle
,
D. A.
Muller
, and
J.
Hwang
, “
Unusual formation of point defect complexes in the ultra-wide band gap semiconductor β-Ga2O3
,”
Phys. Rev. X
9
,
041027
(
2019
).
37.
E. J.
Kirkland
,
R. F.
Loane
, and
J.
Silcox
, “
Simulation of annular dark field stem images using a modified multislice method
,”
Ultramicroscopy
23
,
77
(
1987
).
38.
P. E.
Blöchl
, “
Projector augmented-wave method
,”
Phys. Rev. B
50
,
17953
(
1994
).
39.
G.
Kresse
and
J.
Furthmüller
, “
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
,”
Phys. Rev. B
54
,
11169
(
1996
).
40.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
(
1996
).
41.
S.
Mu
,
H.
Peelaers
, and
C. G.
Van de Walle
, “
Ab initio study of enhanced thermal conductivity in ordered AlGaO3 alloys
,”
Appl. Phys. Lett.
115
,
242103
(
2019
).
42.
G.
Henkelman
,
B. P.
Uberuaga
, and
H.
Jónsson
, “
Climbing image nudged elastic band method for finding saddle points and minimum energy paths
,”
J. Chem. Phys.
113
,
9901
(
2000
).
43.
J. B.
Varley
,
H.
Peelaers
,
A.
Janotti
, and
C. G.
Van de Walle
, “
Hydrogenated cation vacancies in semiconducting oxides
,”
J. Phys.: Condens. Matter
23
,
334212
(
2011
).
44.
S.
Mu
,
M.
Wang
,
H.
Peelaers
, and
C. G.
Van de Walle
, “
First-principles surface energies for monoclinic Ga2O3 and Al2O3 and consequences for cracking of (AlxGa1−x)2O3
,”
APL Mater.
8
,
091105
(
2020
).

Supplementary Material