1. Introduction

In parallel with the surge in interest in electronics based on group III–nitride compound semiconductors [1,2] and silicon [3,4], structural and optical properties of advanced materials based on gallium oxide (Ga$_2$O$_3$) have recently received considerable attention because of their potential in developing reliable power electronic devices [5–11] by virtue of their large bandgaps and high chemical stability [12–16]. In particular, the energy band alignment at the interfaces of ([Al][In]Ga)$_2$O$_3$ and native and foreign materials has become the central theme of numerous studies [17–24]. The employment of amorphous Al$_2$O$_3$ as a gate dielectric in thin-film transistors [25], wide-bandgap-semiconductor metal–oxide–semiconductor field-effect transistors (MOSFETs) [26] and metal–oxide–semiconductor high-electron-mobility transistors (MOS-HEMTs) [27] can potentially exhibit low leakage-current densities and high breakdown voltages and gate capacitances while demonstrating Fowler–Nordheim quantum mechanical tunneling, which reduces stress-induced gate-leakage currents and negative fixed charge density in wide-bandgap-semiconductors, and improves threshold voltage hysteresis and gate leakage characteristics, respectively. As reported by Carey IV et al., the band alignment of Al$_2$O$_3$ with ($\bar {2}01$) $\beta$-Ga$_2$O$_3$ revealed a straddling heterojunction (type I) with a valence band offset (VBO) of 0.07 eV for an Al$_2$O$_3$ film deposited using atomic layer deposition (ALD), whereas a staggered type II heterojunction with a VBO of $-0.86$ eV was discovered for Al$_2$O$_3$ prepared using radio frequency (RF) magnetron sputtering [28]. This highlights the empirically proven fact that similar films prepared using different film preparation techniques give different band offset characteristics. Despite the fact that the physical processes of thin film growth and laser–target interaction are rather complex, pulsed laser deposition (PLD) has emerged as a primary physical vapor deposition tool by virtue of its relatively simple setup and the high-quality films it is capable of producing. Power devices perform optimally when fabricated using high-quality single-crystalline materials, given the necessity of higher breakdown voltages [29]. Single-crystalline $\alpha$-Al$_2$O$_3$ is widely used as a substrate for the growth of epitaxial Ga$_2$O$_3$ films [30–32]. This is because of its excellent quality, high thermal conductivity, availability, cost-effectiveness, and compatibility. However, band offset characteristics at heterostructure interfaces involving PLD-grown group III–oxide materials on foreign substrates have not been adequately addressed in the literature. Sun et al. investigated the energy band offset properties at ALD-deposited amorphous and polycrystalline ($\bar {2}01$) $\beta$-Ga$_2$O$_3$/In$_2$O$_3$ interfaces [19], while Wakabayashi et al. studied the band alignment at $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$/$\beta$-Ga$_2$O$_3$ (100) interfaces grown by PLD [18]. Furthermore, Zhang et al. fabricated photodetectors on sapphire that employed (In$_x$Ga$_{1-x}$)$_2$O$_3$ grown by PLD [33].

In this article, we determine the energy band alignment characteristics at an $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterojunction grown using PLD [34,35]. High-resolution X-ray photoelectron spectroscopy (HRXPS) was employed to examine the band offset parameters, namely the VBO and conduction band offset (CBO), at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface. The VBO and CBO were determined to be $0 \pm 0.1$ and $4.87 \pm 0.1$ eV, respectively, with a type-I heterostructure. High-resolution transmission electron microscopy (HRTEM) was used to confirm the sharp interface characteristics at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface, and most importantly, analyze the interface dislocation characteristics. Our work will aid in the development of $\alpha$-Al$_2$O$_3$/$\beta$-(InGa)$_{2}$O$_{3}$ resonant-tunneling diodes (RTDs). It is paramount to note that RTDs need ultra-sharp interfaces and high-quality undoped or lightly doped materials with high band offsets for stable confinement of states. Relatively thick layers with sandwiched superlattices on foreign substrates and the ability to make doped layers for contacts on a $\beta$-Ga$_2$O$_3$ system have not been successfully achieved yet. Therefore, the fundamental limits of this material system with regards to resonant-tunneling structures still need to be studied.

Given that there is a scarcity of published (In$_{x}$Ga$_{1-x}$)$_2$O$_3$ studies in the literature, we believe reporting optical and interfacial characteristics of low-indium-fraction (In$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloy is of value to the optoelectronics research community. Based on our material target information (Section (2.1)) and the fact that indium is a low-vapor-pressure material [36], we expected the indium atomic fraction to be below 10% given the gallium and indium relative atomic masses of 69.72 and 114.82, respectively. This especially holds true for PLD deposition, whereby local heating of the material target caused by ultrafast laser pulses could have led to higher rates of indium evaporation. Another reason we chose to study a low-indium-fraction (In$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloy is because if we were to significantly increase the indium content, we anticipated observing more indium segregation effects [37], leading to poorer crystalline quality and therefore less applicability. Also given its low-vapor-pressure nature, indium contents lower than 7.2% in (In$_{x}$Ga$_{1-x}$)$_2$O$_3$ can be difficult to achieve and control with an acceptable level of repeatability and will most probably only affect the bandgap of the material, so the band alignment and contact type characteristics are not significantly affected.

2. Experimental methods

2.1 Thin film growth

Double-side polished c-plane sapphire substrates were cleaned using acetone and isopropyl alcohol, then blew dried using dry nitrogen gas and loaded into a Neocera Pioneer 180 PLD chamber [38] at a base pressure of $10^{-8}$ mTorr. Unintentionally doped $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin films were grown at an ambient thermocouple temperature of 850 $^{\circ}$C and an oxygen partial pressure of 50 mTorr. A 248 nm KrF excimer laser was used. The laser pulse frequency was set at 5 Hz, with an energy of 250 mJ per pulse, yielding a fluence of 2.12 J/cm$^{2}$. The PLD target used for (In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin film growth was a ceramic target pellet from a homogenized powder of pure (InGa)$_2$O$_3$ (99.999%, PLD Targets (https://www.pldtargets.com)) with about 14 w/w% In$_2$O$_3$ sintered at 1050 $^{\circ}$C for 12 hours in air. The films were deposited with a target-to-substrate distance of 80 mm. The growth rate under these conditions was determined to be 0.16 Å/pulse. Based on this calibration, films with thicknesses of 5 nm (thin) and 80 nm (thick) were deposited, as illustrated in Fig. 1. As the electron extraction depth in XPS is less than 10 nm, the 5 nm-thick sample allowed for probing both $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ and $\alpha$-Al$_2$O$_3$ at the interface, while the 80 nm-thick film along with the sapphire substrate provided XPS data solely from the $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film and $\alpha$-Al$_2$O$_3$, respectively. For the reference $\beta$-Ga$_2$O$_3$ sample used in the X-ray crystallography study in section (3.3), an unintentionally doped $\beta$-Ga$_2$O$_3$ film was grown on c-plane sapphire at an ambient thermocouple temperature of 800 $^{\circ}$C and an oxygen partial pressure of 5 mTorr.

 

Fig. 1. Schematic illustrations of the sample structures under study.

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2.2 X-ray crystallography

The crystal structure properties of the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ stack were examined by Bruker D8 Advance (out-of-plane incidence X-ray diffraction (XRD), without a monochromator given the high sensitivity of the set up) and Bruker D8 Discover ($\phi$-scan skewed asymmetric XRD, equipped with a monochromator) X-ray diffractometers using Cu $K\alpha$ ($\lambda _\textrm {X-ray} = 1.5406$ Å) radiation, where $\lambda _\textrm {X-ray}$ is the used X-ray beam wavelength. Loosely referred to as “in-plane” XRD measurements in literature, $\phi$-scan asymmetric XRD measurements, whereby parallel diffracting planes are detected with respect to their rotations, reveal how the crystal axes are aligned azimuthally with respect to each other. For the out-of-plane XRD scan, the measurements were performed with a scan speed of around 10 ms/step, a step size of 0.01$^{\circ}$, and a scan range of $15^{\circ}$–$65^{\circ}$. For the $\phi$-scan, the measurements were performed with a scan speed of around 1 second/step, a step size of $0.1^{\circ}$, and a scan range of $(-)20^{\circ}$–$340^{\circ}$. Multiple repeat scans were performed to reduce the measurement noise.

2.3 Ion beam analysis

For Rutherford backscattering spectrometry (RBS) measurements and analysis, a $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film sample with a total thickness of approximately 150 nm was prepared on a c-plane sapphire substrate. RBS experiments were carried out using a high-resolution RBS system (Kobe Steel, Ltd. HRBS-V500). A detection angle of 107.5$^{\circ}$ and a 400 keV beam of He$^{+}$ ions were used for the analysis. The 150 nm-thick sample was coated with iridium (Ir) and silver (Ag) to attain electrical conductivity.

2.4 High-resolution electron microscopy

HRTEM micrographs and fast Fourier transform (FFT) patterns were acquired using an FEI Titan ST microscope operating at 300 keV. A crystal model of each material was created by a computer software, VESTA, and the corresponding FFT pattern was simulated based on the created crystal model and matched to the FFT pattern extracted from HRTEM micrographs. The TEM lamella of an $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterojunction sample was prepared through focused ion beam milling using an FEI Helios G4 FIB-SEM.

2.5 High-resolution X-ray photoelectron spectroscopy

The HRXPS measurements were carried out using a Kratos Axis Supra DLD spectrometer equipped with a monochromatic Al K$\alpha$ X-ray source ($h\nu$ = 1486.6 eV) operating at 150 W, a multi-channel plate, and a delay line detector under a vacuum of approximately 10$^{-9}$ mbar. High-resolution spectra were collected at fixed analyzer pass energy of 20 eV. The samples were mounted in floating mode to avoid differential charging. Charge neutralization was required for all samples. All binding energies were referenced to the C 1s binding energy of adventitious carbon contamination, which was taken to be 284.8 eV.

3. Results and discussion

3.1 Rutherford backscattering spectrometry

Fig. 2(a) shows the measured and simulated RBS measurement curves for a 150 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film on sapphire (RBS sample), confirming the stoichiometry of each layer and the well-defined interfaces. The inset in Fig. 2(a) shows the simulated RBS spectrum superimposed on the measured output spectrum. It can be seen that the Ga and indium (In) signals overlap with each other; the Ir and Ag signals originate from the metallic layer sputtered onto the sample before the RBS experiment in order to avoid electrostatic charging. Fig. 2(b) confirms the presence of an intermixed layer at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface, most likely caused by interdiffusion during the film’s growth, with a thickness of less than 5 nm. In our RBS model, the stoichiometry of the $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film, except within the intermixed layer, was confirmed to be In:Ga = 1:12.889, Ga:O = 1:1.616, and In:O = 1:20.833.

 

Fig. 2. (a) RBS measurements for a PLD-grown $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin film on sapphire; the inset shows the simulated spectrum, which fits with the measured spectrum. (b) Simulation-extracted atomic concentration depth profile.

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3.2 Ultraviolet–visible spectra

Fig. 3(a) shows the measured transmittance (T) and reflectance (R) spectra for the grown $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin film on sapphire, while the calculated absorbance (A) spectrum is shown in Fig. 3(b). Fig. 3(c) depicts the calculated absorption coefficient ($\alpha _\textrm {abs}$) and the $(\alpha _\textrm {abs} h \nu )^{1/r}$–$h \nu$ Tauc plot ($r = 2$ for indirect allowed transitions [39,40]) used to determine the optical bandgap of our ($\bar {2}01$)-oriented single-domain $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ on sapphire. The $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ optical bandgap ($E^{\beta \textrm {-(In}_{0.072}\textrm {Ga}_{0.928})_2\textrm {O}_3}_{\textrm {g}}$) was determined to be approximately 3.93 eV using linear extrapolation. Considering the Tauc plot in Fig. 3(c), at low photon energies ($h \nu < 3.90$ eV), the absorption nonlinearly converges to zero, implying that the material is transparent. Close to the optical bandgap value of 3.93 eV, the absorption level becomes stronger and shows a region of linearity. This linear region has been used to extrapolate to the abscissa to determine the optical bandgap value. Finally, at higher energies ($> 5.50$ eV), the absorption level saturates and the curve deviates from linearity. In the low-energy regime ($h \nu < 3.90$ eV), the deviation from linearity is associated with defect-related absorptive states that are near the band edge (Urbach tail) [41].

 

Fig. 3. (a) Measured transmittance and reflectance spectra, (b) calculated absorbance spectrum, and (c) Tauc plot.

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3.3 X-ray crystallography

We performed out-of-plane (Fig. 4(a)) and $\phi$-scan (Fig. 4(b), 4(c)) XRD measurements to investigate the 80 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film and determine its crystal orientation relationships to $\alpha$-Al$_2$O$_3$. As we can see in the out-of-plane XRD measurements, the ($\bar {2}01$) $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ peak shifted to the left compared to the reference $\beta$-Ga$_2$O$_3$ thin film on sapphire, implying an increased lattice constant. The following orientation relationship was determined from the out-of-plane XRD measurements:

 

Fig. 4. (a) Out-of-plane XRD survey measurements of $\alpha$-Al$_2$O$_3$/$\beta$-Ga$_2$O$_3$ and $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ stacks. $\phi$-scan XRD measurements of (b) ($\bar {2}21$) $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ and (c) ($10\bar {1}2$) $\alpha$-Al$_2$O$_3$. ($\bar {2}21$) $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ peak positions match those of ($10\bar {1}2$) $\alpha$-Al$_2$O$_3$.

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3.4 Electron microscopy analysis

Fig. 5 displays TEM micrographs of the $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin film grown on $\alpha$-Al$_2$O$_3$. The plane spacings ($d_n$, where $n \in \{1,2\}$) of (0003) $\alpha$-Al$_2$O$_3$ and ($\bar {2}01$) $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ were estimated using the HRTEM micrographs shown in Fig. 5(b) and found to be 4.242 Å and 4.749 Å, respectively. The plane spacing values were calculated using the following relations:

 

Fig. 5. (a) Cross-sectional HRTEM micrograph of an $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterojunction stack. (b) Cross-section view of the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface with FFT patterns (a-plane sapphire zone axis). (c) STEM-HAADF and EDX mapping at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface. Note: EDX is not the most reliable method to quantify the concentration of light elements such as oxygen, and a bulk melt-grown single-crystalline sapphire substrate is closer to ideal stoichiometry than a PLD-deposited (InGa)$_2$O$_3$ thin film. This might have led to artifacts or observation errors when the elemental content of present elements is quantified. (d) HRTEM micrographs at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface with a filtered version showing edge dislocations (I) and the $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ lattice with a filtered version showing its crystal structure (II).

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3.5 Heterointerface energy band offset characteristics

To determine the VBO at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface, the conventional relationship reported by Kraut et al. was employed [42]:

The first term in expression (5) accounts for the difference the binding energy of the Ga $2p_{3/2}$ core level and the measured valence band level of $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ as probed from the 80 nm-thick sample (labeled “thick sample” in Fig. 1), while the second term resembles the difference between the Al $2p$ core level and measured valence band level as probed from the bulk $\alpha$-Al$_2$O$_3$ substrate (labeled “sapphire substrate” in Fig. 1). The third term yields the difference between the Ga $2p_{3/2}$ and Al $2p$ core levels of the grown film and substrate, respectively, as probed from the 5 nm-thick sample (labeled “thin sample” in Fig. 1). The 5 nm thickness of the film allows for the simultaneous probing of both materials, which enables us to account for energy value shifts when the materials are brought in contact and share the same Fermi energy level at equilibrium.

The CBO ($\Delta E_\textrm {C}$), on the other hand, can be calculated using

 

Fig. 6. (a) Acquired XPS spectra of bare sapphire substrate and with 5 nm- and 80 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin films. (b) XPS spectra of the Ga $2p_{3/2}$ core level (I) and VBM of the 80 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ sample (II). (c) XPS spectra of the Ga $2p_{3/2}$ (I) and Al $2p$ (II) core levels obtained from the 5 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ sample. (d) XPS spectra of the Al $2p$ core level (I) and VBM of the $\alpha$-Al$_2$O$_3$ sample (II). (e) Schematic representation of band alignment at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ heterointerface.

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Fig. 6(b) shows the XPS spectra of the Ga $2p_{3/2}$ core level and VBM of the 80 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ sample, corresponding to the binding energies at 1117.87 eV and $3.19 \pm 0.05$ eV, respectively. Thus, the difference in binding energy (i.e., $E^{\beta \mbox{-}(\textrm{In}_{0.072} \textrm{Ga}_{0.928})_2 \textrm{O}_3}_{\textrm{Ga} \,\, 2p_{3/2}} - E^{\beta \textrm {-(In}_{0.072} \textrm{Ga}_{0.928} {)} _2 \textrm{O}_3 }_{\textrm {VBM}}$,) can be calculated to be 1114.68 eV. Fig. 6(c) shows the XPS spectra of the Ga $2p_{3/2}$ core level alongside that of Al $2p$. Finally, Fig. 6(d) shows the XPS spectra of the Al $2p$ core level and VBM of an $\alpha$-Al$_2$O$_3$ sample, with the binding energies found to be 74.02 eV and $3.35 \pm 0.05$ eV, respectively. The difference in binding energy (i.e., $E^{\alpha \textrm {-Al}_{2} \textrm{O}_{3} {}}_{\textrm {Al }2p} - E^{\alpha \textrm {-Al}_{2} \textrm{O}_{3} {}}_{\textrm {VBM}}$) is calculated to be 70.67 eV. The binding energies of the Ga $2p_{3/2}$ and Al $2p$ core levels, as examined from the 5 nm-thick $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ layer on $\alpha$-Al$_2$O$_3$ and shown in Fig. 6(c), correspond to 1117.96 eV and 73.95 eV, respectively, and the energy difference (i.e., $E^{\beta \textrm {-(In}_{0.072} \textrm{Ga}_{0.928} {)}_2 \textrm{O}_3 {}}_{\textrm {Ga }2p_{3/2}} - E^{\alpha \textrm {-Al}_{2} \textrm{O}_{3} {}}_{\textrm {Al }2p}$) is thus calculated to be 1044.01 eV. With that, based on expression (5), the VBO is calculated to be $\Delta E_\textrm {V} = 0 \pm 0.1$ eV. To determine the necessary parameters for energy band alignment at the $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ interface, we used the optical bandgaps of $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ (3.93 eV) as measured using UV-visible spectroscopy, and of $\alpha$-Al$_2$O$_3$ as 8.8 eV, a reference value obtained from UV-Visible transmittance measurements from the literature [43] because of our UV-Visible instrument limitations. By substituting the optical bandgaps into expression (6), $\Delta E_\textrm {C}$ yields a value of $4.87 \pm 0.1$ eV. A detailed energy band diagram of the PLD-grown $\alpha$-Al$_2$O$_3$/$\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ interface, as deduced from the above measurements and calculations, is shown as in Fig. 6(e), representing a type-I heterojunction.

4. Concluding remarks

In summary, we have grown high-quality ($\bar {2}01$)-oriented single-domain $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ thin films on sapphire using PLD and determined their interfacial characteristics, including the band alignment at the resulting thermodynamically stable heterointerface. The valence and conduction bands offsets were found to be $0 \pm 0.1$ and $4.87 \pm 0.1$ eV above and below the sapphire valence and conduction bands, respectively. XRD and RBS measurements and HRTEM micrographs confirmed the integrity of the $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ film. HRXPS was employed to measure the core level binding energies of Al 2$p$ and Ga 2$p_{3/2}$ with respect to the valence band maxima of the (In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$ and $\alpha$-Al$_2$O$_3$ layers, respectively, as well as the energy separation between the Al 2p and Ga 2p$_{3/2}$ core levels at the interface of the heterojunction. The dislocations at the interface were characterized using HRTEM, XRD, and FFT algorithms. We discovered the presence of edge dislocations, which we attributed to the lattice mismatch between $\alpha$-Al$_2$O$_3$ and $\beta$-(In$_{0.072}$Ga$_{0.928}$)$_2$O$_3$. By providing a correlated set of extracted material and heterointerface properties, including crystal structure and composition and electronic band alignment, we believe that this work paves the way for designing (In$_x$Ga$_{1-x}$)$_2$O$_3$-based devices.