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## Creator
[Kazuki Koreishi](https://orcid.org/0009-0000-1580-8262), [Kodai Niitsu](https://orcid.org/0000-0002-0430-8868), [Takuto Soma](https://orcid.org/0000-0001-8685-9606), [Kohei Yoshimatsu](https://orcid.org/0000-0001-9288-068X), [Akira Ohtomo](https://orcid.org/0000-0003-0300-4712)
## Rights
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Kazuki Koreishi, Kodai Niitsu, Takuto Soma, Kohei Yoshimatsu, Akira Ohtomo; Lattice-matched (AlxScyGa1−x−y)2O3/β-Ga2O3 heterostructures with widely tunable bandgap. Appl. Phys. Lett. 6 July 2026; 129 (1): 012102 and may be found at https://doi.org/10.1063/5.0326523.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)
## Other metadata
[Lattice-matched (Al x Sc y Ga1− x − y )2O3/ β -Ga2O3 heterostructures with widely tunable bandgap](https://mdr.nims.go.jp/datasets/af24fac8-eac7-43c5-bdc1-c8689dc3826f)
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1 Lattice-matched (AlxScyGa1−x−y)2O3/β-Ga2O3 heterostructures with widely 1 tunable bandgap 2 Kazuki Koreishi1,a), Kodai Niitsu2), Takuto Soma1), Kohei Yoshimatsu1), and Akira Ohtomo1,a) 3 1Department of Chemical Science and Engineering, Institute of Science Tokyo, Ookayama, 4 Meguro, Tokyo 152-8552, Japan 5 2Center for Basic Research on Materials, National Institute for Materials Science, Sengen, 6 Tsukuba, Ibaraki 305-0047, Japan 7 a) E-mail: koreishi.k.aa@m.titech.ac.jp and ohtomo.a.aa@m.titech.ac.jp 8 9 Abstract 10 Bandgap engineering of β-Ga2O3 is essential for advancing its electronic and optoelectronic 11 applications. However, the growth of high-quality heteroepitaxial structures is often hampered by 12 large lattice mismatches. In this study, we design (AlxScyGa1−x−y)2O3 quaternary alloys in the form of 13 both polycrystalline powders and heteroepitaxial films and demonstrate their lattice matching to β-14 Ga2O3. Powder x-ray diffraction (XRD) measurements reveal that the lattice parameters of monoclinic 15 (AlxScyGa0.8)2O3 match those of β-Ga2O3 when x/y = 1.5–3.2. (AlxScyGa1−x−y)2O3 thin films are grown 16 on β-Ga2O3 (100) substrates by pulsed-laser deposition by varying the composition ratio x/y and the 17 total substitutional fraction x + y. Nearly perfect lattice-matched epilayers with uniform composition 18 and crystal structure are obtained up to x + y ~ 0.6, as confirmed by XRD and scanning transmission 19 electron microscopy. Electron energy loss spectroscopy reveals a tunable bandgap from 4.5 to 5.8 eV. 20 These results demonstrate that (AlxScyGa1−x−y)2O3/β-Ga2O3 heterostructures are promising platforms 21 for ultrawide-bandgap semiconductor devices. 22 mailto:koreishi.k.aa@m.titech.ac.jpmailto:ohtomo.a.aa@m.titech.ac.jp2 Main text 23 Monoclinic β-Ga2O3 is an ultrawide-bandgap semiconductor that has received significant 24 research interest over the past decades. Its large bandgap (Eg) of 4.4–5.0 eV,1,2 tunable n-type doping 25 concentration ranging from 1015 to 1020 cm−3,3,4 and large melt-grown single-crystal wafers5 make it a 26 promising candidate for high-voltage power devices.6 In addition, β-Ga2O3 is also promising in 27 optoelectronic applications such as solar-blind UV detection7 and UV-transparent conductive 28 electrodes8 owing to its high transparency down to a wavelength of 280 nm. 29 Bandgap engineering expands the design space of such devices. For example, the bandgap 30 widening of β-Ga2O3 can enhance its durability under high electric fields and tune its spectral response 31 in the UV-C range. Furthermore, heteroepitaxial structures with different Eg enable the control of 32 charge-carrier profiles in electronic and photonic devices, such as modulation-doped field-effect 33 transistors (MODFET), resonant tunneling diodes (RTD), and quantum-well infrared photodetectors 34 (QWIP), which are similar to the applications of III-V semiconductors. 35 In analogy with cubic AlxGa1−xAs and hexagonal AlxGa1−xN, the heteroepitaxy of monoclinic 36 (AlxGa1−x)2O3 has been investigated since the early stages of β-Ga2O3 research,9 although its parent 37 oxides exhibit different crystal structures. The (010)-oriented (AlxGa1−x)2O3/β-Ga2O3 heterojunctions 38 with x up to ~0.2 were implemented in MODFET10 and RTD.11 However, the lattice mismatches 39 between (AlxGa1−x)2O3 and β-Ga2O3 amount to 3.2–4.4% when x = 1.12,13 As a result, heteroepitaxy of 40 (AlxGa1−x)2O3 on β-Ga2O3 has faced some constraints depending on the crystal orientation. On the β-41 Ga2O3 (010) substrate, phase transformation to the spinel-like γ-phase limits x to less than 0.27,14 and 42 crack formation occurs in epilayers thicker than 100 nm when x > 0.1.15 On the β-Ga2O3 (100) 43 substrate, strain relaxation proceeds in 50-nm-thick epilayers with x = 0.28,16 while 5-nm-thick 44 epilayers (AlxGa1−x)2O3 can be epitaxially stabilized in the entire composition range.17 On the β-Ga2O3 45 (001) substrate, inhomogeneous cation distribution occurs in epilayers with an average x = 0.14.18 46 Substantially, the tunable Eg increment without introducing lattice disorders is approximately 0.4 eV19, 47 3 which is recognized as the upper limit of the design space with (AlxGa1−x)2O3. 48 A lattice-matched quaternary alloy is an effective approach to address these issues. 49 Considering the ionic radius, (Al,Ga,In)2O3 and (Al,Sc,Ga)2O3 alloys can maintain lattice parameters 50 close to those of β-Ga2O3 under specific Al:In or Al:Sc ratios, since the ionic radii of Al3+ (Sc3+ and 51 In3+) are smaller (larger) than those of Ga3+.20 Recently, (Al,Ga,In)2O3 quaternary alloys were 52 investigated both theoretically21 and experimentally.22,23 However, the lattice-matched 53 (Al0.17Ga0.76In0.07)2O3/β-Ga2O3 (010) heterostructure exhibited inhomogeneous In incorporation and 54 local γ-phase inclusion. On the other hand, (Al,Sc,Ga)2O3 alloys gain an advantage over (Al,Ga,In)2O3 55 since both Al- and Sc-substitutions contribute to the increase in Eg,16,19,24,25 while co-substitution by 56 Al and In partially cancels Eg variation.21–23 Additionally, Sc incorporation appears easier than In due 57 to the absence of competitive suboxide reactions as observed for In.26,27 We thus examine the variation 58 in lattice parameters in polycrystalline (AlxScyGa1−x−y)2O3 powder samples to identify the lattice-59 matching composition ratio x/y and fabricate (100)-oriented (AlxScyGa1−x−y)2O3 epilayers with the 60 appropriate ratios to demonstrate lattice-matched heterostructures with large tunability of Eg. 61 62 Polycrystalline (AlxScyGa1−x−y)2O3 powders (Toshima Manufacturing, 3N purity) were 63 prepared to investigate their crystal structures. For simplicity, the substitutional molar fraction was 64 fixed at x + y = 0.2, while the x:y ratio was varied as 20:0, 15:5, 10:10, 5:15, and 0:20. 65 (AlxScyGa1−x−y)2O3 epilayers were grown on β-Ga2O3 (100) substrates (Novel Crystal 66 Technology) by oxygen-radical-assisted pulsed-laser deposition (PLD).28 For all runs, the substrate 67 temperature, fluence, and frequency of the KrF laser pulses were kept at 750 °C, 0.4 J cm−2, and 10 68 Hz, respectively. Oxygen radicals were supplied from an RF plasma cell operating at 200 W with an 69 O2 flow rate of 1.00 sccm, corresponding to a constant pressure of 1.5×10−4 Torr in the PLD chamber. 70 The epilayers were grown either by ablating a single target or by alternately ablating two different 71 4 targets, which were ceramics or single crystals. The layer thickness was regulated using the intensity 72 oscillation period of the reflection high-energy electron diffraction (RHEED) spots. Further details of 73 the deposition procedure are provided in the supplementary material. 74 To investigate structural properties, x-ray diffraction (XRD) measurements were carried out 75 on the polycrystalline powder and the epilayer samples with Cu Kα and Cu Kα1 radiation, respectively. 76 The composition of the epilayers was analyzed by Auger electron spectroscopy (AES) using scanning 77 electron microscopy (JAMP-9500F, JEOL). (AlxGa1−x)2O3 and (ScyGa1−y)2O3 ceramics were used as 78 standards for calibrating the composition. To investigate microstructures and composition of the 79 epilayers, cross-sectional scanning transmission electron microscopy (STEM) observations were 80 performed using an aberration-corrected STEM (Spectra Ultra, Thermo Fisher Scientific) equipped 81 with an energy-dispersive x-ray spectroscopy (EDS) detector. A cross-sectional thin-foiled specimen 82 with a thickness of approximately 100 nm was prepared by focused ion beam process using NB5000 83 (Hitachi High-Tech) dual-beam system, followed by Ar ion milling using a PIPS II (Gatan). The Eg 84 values were estimated by reflection electron energy loss spectroscopy (REELS) in the AES apparatus. 85 86 Powder-XRD measurement confirmed that all the (AlxScyGa0.8)2O3 samples maintained a 87 pure monoclinic phase (see Fig. S1 in the supplementary material). Table I summarizes their lattice 88 parameters. As shown in Fig. 1(a), the lattice parameters a, b, and c (β) increased (decreased) as the 89 Sc content increased. From linear regression, the x- and y-dependencies of the lattice parameters’ 90 variations with respect to β-Ga2O3 were formulated to be Δa = −0.47x + 1.1y (Å), Δb = −0.13x + 0.26y 91 (Å), Δc = −0.17x + 0.26y (Å), and Δβ = 0.71x − 2.3y (deg). Therefore, the individual lattice parameters 92 match those of β-Ga2O3 when x/y is between 1.5 and 3.2. This range of x/y values is reasonable, as it 93 centers on a specific ratio of x/y = 2.4, where the average cation radius of Al3+ and Sc3+ is equal to that 94 of Ga3+. 20 Although exact lattice matching is unattainable in monoclinic β-Ga2O3 due to four lattice 95 parameters varying independently, a nearly perfect lattice-matched (AlxScyGa1−x−y)2O3/β-Ga2O3 96 5 heterostructure is feasible within this compositional range. 97 Having established the lattice-matching x/y range, ~60-nm-thick (AlxScyGa1−x−y)2O3 epilayers 98 were grown on a 5×10 mm2 substrate using a combinatorial approach. A continuous composition 99 gradient was created such that the x/y ratio varied along the 10-mm-length direction, while the total 100 substitutional fraction x + y was fixed to 0.45±0.02. This total amount of substitution was beyond the 101 composition thresholds for strain relaxation in ternary (AlxGa1−x)2O3 and (ScyGa1−y)2O3 epilayers 102 having similar thicknesses.16,24 Figure 1 (b) shows reciprocal space maps (RSMs) around 710 103 reflections from the selected sample area, corresponding to epilayers with (x, y, x/y) = (0.23, 0.21, 1.1), 104 (0.30, 0.15, 2.0), (0.35, 0.12, 2.9), and (0.36, 0.07, 5.1), respectively. An increase in Qz of the 105 reflections from the epilayers reflects the shrinkage of the out-of-plane lattice spacing with increasing 106 (decreasing) Al (Sc) fraction, as indicated by the a/a0 of the powder samples. All of the primary 107 reflections from the epilayers were found at the same Qx value as the substrate, regardless of the 108 composition, indicating that the epilayers were coherently strained along the [010] direction. In 109 addition, the sample with the highest Sc content exhibited a diffuse component, and its centroid shifted 110 toward a smaller Qx compared to that of the substrate. These features suggest not only partial 111 relaxation of the compressive strain arising from out of the lattice-matching x/y range but also the 112 reduction of the lateral coherence length29 along the [010] direction. Similar features were observed 113 in the sample with the highest Al content. However, the direction of the centroid shift was opposite to 114 that of the Sc‑rich case due to the relaxation of opposite strain, i.e., tensile strain. In contrast, the other 115 two samples, having x/y = 2.0 and 2.9, showed only sharp reflection spots, indicating an absence of 116 strain relaxation owing to the compositions within the lattice-matching range (1.5 ≤ x/y ≤ 3.2). 117 Next, a series of nearly lattice-matched ~20-nm-thick (AlxScyGa1−x−y)2O3 epilayers was grown 118 using single ceramic targets with fixed x/y = 2 and various x + y values of 0.2, 0.4, and 0.6. The 119 composition parameters (x, y, x/y) of the epilayers were (0.21, 0.07, 3.0), (0.31, 0.11, 2.8), and (0.48, 120 0.15, 3.2), respectively. A slight deviation from the target compositions is likely due to differences in 121 6 the laser ablation efficiency and/or preferential scattering of constituent cations.30 Figure 2 shows out-122 of-plane XRD profiles around the substrates’ 400 reflection for the epilayers. The 400 reflections of 123 the epilayers overlapped with those of the substrates at 2θ ~ 30°. In contrast, oscillatory fringes 124 appeared in their tails, known as Laue oscillations, indicating structural homogeneity and smooth 125 surface/interfaces31 even at a very high substitutional fraction of x + y = 0.63. 126 Cross-sectional STEM observations were performed along the [010] zone axis of an 127 (AlxScyGa1−x−y)2O3 epilayer. A high-angle annular dark-field (HAADF)-STEM image and the 128 corresponding EDS chemical maps, presented in Figs. 3(a–d), determined the layer thickness and 129 average composition parameters to be 73 nm and (x, y, x/y) = (0.38, 0.18, 2.1), respectively. As the 130 intensity in a HAADF-STEM image correlates with the atomic number of the constituent elements, 131 the homogeneous, darker contrast of the epilayer informs a higher x + y value without noticeable 132 segregation of Al and Sc at the observed scale. The homogeneous cation distribution was also 133 confirmed by the EDS maps of Al, Sc, and Ga, as shown in Figs. 3(b–d), respectively. 134 Figure 3(e) shows a HAADF-STEM image near the substrate/epilayer interface, revealing an 135 atomically flat and compositionally abrupt interface. In the epilayer, however, the cation arrangement 136 is partially altered, which is attributed to twinning along the [001] direction, as illustrated in Fig. 3(f). 137 Such twinning has been reported during the epitaxial growth of (100)-oriented β-Ga2O3 and 138 (AlxGa1−x)2O3.32,33 The observed stacking sequence in Fig. 3(f) can be described as follows: (i) 139 stacking of one and a half unit cells along the [100] direction, (ii) stacking of a half twinned unit cell 140 with a displacement of c/2, forming a twin boundary on the (100)A plane [TB(100)A],34 (iii) stacking of 141 one twinned unit cell that coalesces with untwinned regions, forming a second TB(100)A and twin 142 boundaries on the (1̅02) plane [TB(−102)]34 arranged with a spacing of c, and (iv) stacking of two or 143 more unit cells on a third TB(100)A. TB(100)A can be readily formed due to its low formation energy, 144 whereas TB(−102) has a much higher formation energy,34 which likely causes TB(−102) to terminate 145 within one unit cell along the growth direction, being consistent with the STEM observations. Among 146 7 the observed TBs, TB(−102) is classified as an incoherent TB that deteriorates the electrical transport 147 properties.32 Generally, growth on miscut substrates is effective for eliminating stacking faults and/or 148 TBs. Indeed, the use of a 6°-off (100) substrate along the [001̅] direction has enabled TB-free step 149 flow growth in homoepitaxy.35,36 150 Figure 4 (a) shows the room-temperature energy loss spectra measured for ~20-nm-thick 151 (AlxScyGa1−x−y)2O3 epilayers (which are identical to those shown in Fig. 2) together with a reference 152 homoepitaxial β-Ga2O3 (100) film. In the spectra, the energy of the intensity onset (Eonset) shifts to the 153 higher loss-energy side, and the intensity above 8 eV increases with increasing x + y value. The former 154 reflects an increase in Eg, while the latter is attributed to an increase in the unoccupied Sc 3d density 155 of states. The Eonset values were determined by extrapolating the linear portions of the slopes to the 156 background level. Since the Eonset value of β-Ga2O3 (4.5 eV) agrees with the lowest direct optical 157 bandgap (4.48 eV) of a bulk single crystal,1 it can be regarded as a proxy for Eg. Figure 4(b) compares 158 Eonset values of quaternary (AlxScyGa1−x−y)2O3 epilayers as a function of out-of-plane lattice spacing 159 d100 with those of ~20-nm-thick ternary (AlxGa1−x)2O3 and (ScyGa1−y)2O3 epilayers. The d100 values 160 for the ternary epilayers were determined from the 2θ peak positions of the 400 reflections in the XRD 161 profiles, whereas for the quaternary epilayers, the d100 value of the β-Ga2O3 substrate was used. An 162 attainable Eonset value of the lattice-matched (AlxScyGa1−x−y)2O3 epilayers was up to 5.8 eV, whereas 163 that of the coherently strained (AlxGa1−x)2O3 and (ScyGa1−y)2O3 epilayers was limited to 5.3 eV and 5.2 164 eV, respectively, due to the strain relaxation. 165 The Eonset range between β-Ga2O3 and (AlxScyGa1−x−y)2O3 spans 4.5−5.8 eV, which is larger 166 in both absolute energy and energy width than those reported for conventional lattice-matched 167 heterojunctions [Fig. 4(c)]. Furthermore, since the valence band maximum of β-Ga2O3 is primarily 168 composed of O 2p states, a small valence-band offset, and consequently, a large conduction-band offset 169 (ΔEc) are anticipated at the (AlxScyGa1−x−y)2O3/β-Ga2O3 heterojunction. These features enable the 170 formation of lattice-matched ultrawide-bandgap heterostructures with high structural quality and wide 171 8 tunability of Eg and ΔEc. Such wide tunability is particularly advantageous for high-temperature and 172 high-voltage device operation of MODFETs and RTDs, where both high breakdown field and carrier 173 confinement are required. 174 175 This study presents structural and electronic properties of quaternary (AlxScyGa1−x−y)2O3 176 lattice matched to β-Ga2O3. Monoclinic (AlxScyGa0.8)2O3 polycrystals were successfully synthesized, 177 and their lattice parameters varied by x and y, reflecting the differences in ionic radii. The four 178 independent lattice parameters were found to match those of β-Ga2O3 in the x/y range of 1.5–3.2. 179 Epitaxial growth of (AlxScyGa1−x−y)2O3 on β-Ga2O3 (100) substrates, as confirmed by RSM 180 measurements, yielded coherently strained epilayers with x + y ~ 0.45, exceeding the critical 181 composition achievable in ternary (AlxGa1−x)2O3 and (ScyGa1−y)2O3 epilayers. Additionally, a high 182 substitutional fraction up to x + y = 0.63 was achieved in nearly lattice-matched (AlxScyGa1−x−y)2O3 183 epilayers. STEM and EDS measurements of the (Al0.38Sc0.18Ga0.44)2O3 epilayer revealed its 184 homogeneous cation distribution and a compositionally abrupt substrate/epilayer interface. The 185 formation of twin boundaries was also observed due to the specific substrate orientation, which could 186 be eliminated by the use of miscut substrates. The REELS spectra of the quaternary epilayers 187 exhibited an increase in Eonset from 4.5 eV (x = y = 0) to 5.8 eV (x = 0.48, y = 0.15). Therefore, this 188 quaternary system uniquely realizes wide Eg tunability while maintaining near lattice-matching to β-189 Ga2O3, which is not achievable with ternary alloys. Furthermore, the large Eg and its wide tunability 190 are exceptional among lattice-matched heterojunctions. These capabilities open a pathway to β-191 Ga2O3-based bandgap-engineered ultrawide-bandgap power electronic and optoelectronic devices, 192 particularly those relying on high-quality heterojunctions. 193 194 See the supplementary material for detailed descriptions of the epitaxial growth and XRD 195 patterns of the (AlxScyGa1−x−y)2O3 powder samples available online. 196 9 Acknowledgements 197 The Authors thank M. Tada for AES and REELS measurements. This study was supported 198 by JSPS KAKENHI (Grant Nos. JP21H02026, JP22H04505, and JP24H00480), JST PRESTO (Grant 199 Nos. JPMJPR22Q3 and JPMJPR22Q6), and JST SPRING (Grant No. JPMJSP2180). This work was 200 the result of using research equipment (JAMP-9500F) shared in the MEXT Project for promoting 201 public utilization of advanced research infrastructure (Program for supporting construction of core 202 facilities, Grant No. JPMXS0420900524). This work contains the results using the research equipment 203 (SmartLab) shared in PAIMS (Platform of Analytical Instruments for Chemistry and Materials 204 Science) in Institute of Science Tokyo. A part of this study was supported by the Electron Microscopy 205 Unit, National Institute for Materials Science (NIMS). 206 207 TABLE Ⅰ. Lattice parameters of (AlxScyGa1−x−y)2O3 powder samples calculated from powder XRD 208 data. 209 x y a (Å) b (Å) c (Å) β (deg) 0 0 12.22 3.04 5.81 103.84 0 0.20 12.44 3.09 5.86 103.39 0.05 0.15 12.37 3.07 5.84 103.55 0.10 0.10 12.29 3.05 5.82 103.68 0.15 0.05 12.21 3.03 5.80 103.84 0.20 0 12.13 3.01 5.78 103.99 210 10 References 211 1 T. Onuma, S. Saito, K. Sasaki, T. Masui, T. Yamaguchi, T. Honda, and M. Higashiwaki, Jpn. J. 212 Appl. Phys. 54, 112601 (2015). 213 2 A. Mock, R. Korlacki, C. Briley, V. Darakchieva, B. Monemar, Y. Kumagai, K. Goto, M. 214 Higashiwaki, and M. Schubert, Phys. Rev. B 96, 245205 (2017). 215 3 C. Peterson, A. Bhattacharyya, K. Chanchaiworawit, R. Kahler, S. Roy, Y. Liu, S. Rebollo, A. 216 Kallistova, T.E. Mates, and S. Krishnamoorthy, Appl. Phys. Lett. 125, 182103 (2024). 217 4 H.M. Jeon, K.D. Leedy, D.C. Look, C.S. Chang, D.A. Muller, S.C. Badescu, V. Vasilyev, J.L. 218 Brown, A.J. Green, and K.D. Chabak, APL Mater. 9, 101105 (2021). 219 5 T. Igarashi, Y. Ueda, K. Koshi, R. Sakaguchi, S. Watanabe, S. Yamakoshi, and A. Kuramata, Phys. 220 Status Solidi 262, 2400444 (2025). 221 6 A.J. Green, J. Speck, G. Xing, P. Moens, F. Allerstam, K. Gumaelius, T. Neyer, A. Arias-Purdue, 222 V. Mehrotra, A. Kuramata, K. Sasaki, S. Watanabe, K. Koshi, J. Blevins, O. Bierwagen, S. 223 Krishnamoorthy, K. Leedy, A.R. Arehart, A.T. Neal, S. Mou, S.A. Ringel, A. Kumar, A. Sharma, K. 224 Ghosh, U. Singisetti, W. Li, K. Chabak, K. Liddy, A. Islam, S. Rajan, S. Graham, S. Choi, Z. Cheng, 225 and M. Higashiwaki, APL Mater. 10, 029201 (2022). 226 7 J. Xu, W. Zheng, and F. Huang, J. Mater. Chem. C 7, 8753 (2019). 227 8 J. Zhang, J. Willis, Z. Yang, X. Lian, W. Chen, L.-S. Wang, X. Xu, T.-L. Lee, L. Chen, D.O. 228 Scanlon, and K.H.L. Zhang, Cell Reports Phys. Sci. 3, 100801 (2022). 229 9 T. Oshima, T. Okuno, N. Arai, Y. Kobayashi, and S. Fujita, Jpn. J. Appl. Phys. 48, 070202 (2009). 230 10 Y. Zhang, A. Neal, Z. Xia, C. Joishi, J.M. Johnson, Y. Zheng, S. Bajaj, M. Brenner, D. Dorsey, K. 231 Chabak, G. Jessen, J. Hwang, S. Mou, J.P. Heremans, and S. Rajan, Appl. Phys. Lett. 112, 173502 232 (2018). 233 11 H. Okumura, Jpn. J. Appl. Phys. 59, 075503 (2020). 234 12 J. Åhman, G. Svensson, and J. Albertsson, Acta Crystallogr. Sect. C Cryst. Struct. Commun. 52, 235 1336 (1996). 236 13 Y.R. E. Husson, Eur. J. Solid State Inorg. Chem. 33, 1223 (1996). 237 14 A.F.M.A.U. Bhuiyan, Z. Feng, J.M. Johnson, H.-L. Huang, J. Sarker, M. Zhu, M.R. Karim, B. 238 Mazumder, J. Hwang, and H. Zhao, APL Mater. 8, 031104 (2020). 239 15 J.S. Lundh, K. Huynh, M. Liao, W. Olsen, K. Pan, K. Sasaki, K. Konishi, H.N. Masten, J.K. Hite, 240 M.A. Mastro, N.A. Mahadik, M. Goorsky, A. Kuramata, K.D. Hobart, T.J. Anderson, and M.J. 241 Tadjer, Appl. Phys. Lett. 123, 222104 (2023). 242 11 16 R. Wakabayashi, M. Hattori, K. Yoshimatsu, K. Horiba, H. Kumigashira, and A. Ohtomo, Appl. 243 Phys. Lett. 112, 232103 (2018). 244 17 R. Wakabayashi, K. Yoshimatsu, M. Hattori, J.-S. Lee, O. Sakata, and A. Ohtomo, Cryst. Growth 245 Des. 21, 2844 (2021). 246 18 A.F.M.A. Uddin Bhuiyan, L. Meng, H.L. Huang, J. Sarker, C. Chae, B. Mazumder, J. Hwang, and 247 H. Zhao, APL Mater. 11, 041112 (2023). 248 19 M. Hilfiker, U. Kilic, A. Mock, V. Darakchieva, S. Knight, R. Korlacki, A. Mauze, Y. Zhang, J. 249 Speck, and M. Schubert, Appl. Phys. Lett. 114, 231901 (2019). 250 20 R.D. Shannon, Acta Crystallogr. Sect. A 32, 751 (1976). 251 21 S. Seacat, J.L. Lyons, and H. Peelaers, Phys. Rev. Mater. 8, 014601 (2024). 252 22 L. Vasylechko, V. Hreb, Y. Zhydachevskyy, Y. Hizhnyi, A. Smaliuk, V. Stasiv, V. Stadnik, Y. 253 Hirskyi, H. Zhydachevska, V. Mykhaylyk, and A. Suchocki, Sci. Rep. 15, 37128 (2025). 254 23 S. Schaefer, M. Smeaton, K. Egbo, S. Hasan, W. Callahan, G. Teeter, A. Zakutayev, and M.B. 255 Tellekamp, Appl. Phys. Lett. 125, 172106 (2024). 256 24 K. Koreishi, T. Soma, H. Kumigashira, and A. Ohtomo, Appl. Phys. Lett. 125, 152101 (2024). 257 25 Q. Wang, P. Huang, Q. Liu, Y. Li, Q. Qu, M. Li, K.P. Homewood, Y. Lu, and Y. He, J. Alloys 258 Compd. 834, 155036 (2020). 259 26 P. Mazzolini, C. Wouters, M. Albrecht, A. Falkenstein, M. Martin, P. Vogt, and O. Bierwagen, 260 ACS Appl. Mater. Interfaces 16, 12793 (2024). 261 27 S. Schaefer, D. Febba, K. Egbo, G. Teeter, A. Zakutayev, and B. Tellekamp, J. Mater. Chem. A 262 12, 5508 (2024). 263 28 R. Wakabayashi, T. Oshima, M. Hattori, K. Sasaki, T. Masui, A. Kuramata, S. Yamakoshi, K. 264 Yoshimatsu, and A. Ohtomo, J. Cryst. Growth 424, 77 (2015). 265 29 R. Chierchia, T. Böttcher, H. Heinke, S. Einfeldt, S. Figge, and D. Hommel, J. Appl. Phys. 93, 266 8918 (2003). 267 30 S. Wicklein, A. Sambri, S. Amoruso, X. Wang, R. Bruzzese, A. Koehl, and R. Dittmann, Appl. 268 Phys. Lett. 101, 131601 (2012). 269 31 A.M. Miller, M. Lemon, M.A. Choffel, S.R. Rich, F. Harvel, and D.C. Johnson, Zeitschrift Für 270 Naturforsch. B 77, 313 (2022). 271 32 A. Fiedler, R. Schewski, M. Baldini, Z. Galazka, G. Wagner, M. Albrecht, and K. Irmscher, J. 272 Appl. Phys. 122, 165701 (2017). 273 33 A.F.M.A.U. Bhuiyan, L. Meng, H.L. Huang, C. Chae, J. Hwang, and H. Zhao, Phys. Status Solidi 274 RRL 17, 2300224 (2023). 275 12 34 M. Wang, S. Mu, J.S. Speck, and C.G. Van de Walle, Adv. Mater. Interfaces 2023, 2300318 276 (2023). 277 35 R. Schewski, M. Baldini, K. Irmscher, A. Fiedler, T. Markurt, B. Neuschulz, T. Remmele, T. 278 Schulz, G. Wagner, Z. Galazka, and M. Albrecht, J. Appl. Phys. 120, 225308 (2016). 279 36 P. Mazzolini, A. Falkenstein, Z. Galazka, M. Martin, and O. Bierwagen, Appl. Phys. Lett. 117, 280 222105 (2020). 281 37 K. Momma and F. Izumi, J. Appl. Crystallogr. 44, 1272 (2011). 282 38 I. Vurgaftman, J.R. Meyer, and L.R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001). 283 39 S.N. Alam, V.Z. Zubialevich, B. Ghafary, and P.J. Parbrook, Sci. Rep. 10, 16205 (2020). 284 285 286 13 Figures and figure captions 287 288 FIG. 1. (a) Lattice parameters of (AlxScyGa1−x −y)2O3 powder samples having x + y = 0.2 with respect 289 to those of β-Ga2O3. Individual lattice parameters match those of β-Ga2O3 within the highlighted 290 region. (b) Reciprocal space maps around 710 reflections for ~60-nm-thick (AlxScyGa1−x −y)2O3 291 epilayers having x + y ~ 0.45 grown on β-Ga2O3 (100) substrates. 292 293 294 FIG. 2. Out-of-plane XRD profiles around substrates’ 400 reflections for ~20-nm-thick 295 (AlxScyGa1−x−y)2O3 epilayers. The inset shows ω scans of substrates’ 400 reflections. Particularly 296 broad peak shapes that are observed in the upper (red) and middle (blue) profiles stem from substrate 297 bending confirmed in the corresponding ω scans. The substrate bending is sometimes initiated by the 298 cutting process and/or clamping during the growth. 299 14 300 FIG. 3. Cross-sectional HAADF-STEM images and EDS maps of 73-nm-thick (Al0.38Sc0.18Ga0.44)2O3 301 epilayer. The solid lines in (a–e) indicate interfaces between the epilayer and β-Ga2O3 substrate. The 302 atomic model in (f) shows one and a half cells of twinned and untwinned β-Ga2O3, where overlaid 303 light- and deep-green balls represent cations at the oxygen tetrahedral and octahedral sites, respectively. 304 The models were generated by VESTA.37 These data were acquired at an acceleration voltage of 200 305 kV. 306 307 FIG. 4. (a) Energy loss spectra near the onset of loss peaks measured for ~20-nm-thick 308 (AlxScyGa1−x−y)2O3 epilayers. The intercepts of the dashed lines correspond to Eonset. (b) Eonset as a 309 function of out-of-plane lattice spacing d100. Error bars along the x-axis for (AlxScyGa1−x−y)2O3 and the 310 y-axis correspond to the full width at half-maximum of substrates’ 400 reflection in XRD and standard 311 deviations of the intercept by linear fits in (a), respectively. The solid and open symbols represent 312 coherently-strained and partially-relaxed epilayers, respectively. (c) Eg values vs. average bond length 313 of selected semiconductors that can construct lattice-matched heterojunctions.38,39 Subscripts denoting 314 the chemical composition are omitted. In AlScGaO/GaO, Eg is replaced with Eonset. 315