Recent progress on the electronic structure, defect, and doping properties of Ga 2 O 3

Gallium oxide (Ga 2 O 3 ) is an emerging wide bandgap semiconductor that has attracted a large amount of interest due to its ultra-large bandgap of 4.8 eV, a high breakdown field of 8 MV/cm, and high thermal stability. These properties enable Ga 2 O 3 a promising material for a large range of applications, such as high power electronic devices and solar-blind ultraviolet (UV) photodetectors. In the past few years, a significant process has been made for the growth of high-quality bulk crystals and thin films and device optimizations for power electronics and solar blind UV detection. However, many challenges remain, including the difficulty in p -type doping, a large density of unintentional electron carriers and defects/impurities, and issues with the device process (contact, dielectrics, and surface passivation), and so on. The purpose of this article is to provide a timely review on the fundamental understanding of the semiconductor physics and chemistry of Ga 2 O 3 in terms of electronic band structures, optical properties, and chemistry of defects and impurity doping. Recent progress and perspectives on epitaxial thin film growth, chemical and physical properties of defects and impurities, p -type doping, and ternary alloys with In 2 O 3 and Al 2 O 3 will be discussed.

Ga 2 O 3 is also deemed as a rising star in the field of solar-blind photodetectors, again due to its wide bandgap. The solar-blind ultraviolet photodetectors have been broadly investigated with the goal of acquiring precise and accurate information of weak signal by night and day through the absence of solar-blind region irradiation (200-280 nm) at the Earth's surface. 6-10 Ga 2 O 3 based photodetectors possess the cutoff wavelength range of 250-280 nm, which fulfills the requirements of detection over a deep ultra-violet (DUV) region and insensitivity to visible and infra-red wavelength. 11,12 From a more practical point of view, the ease of fabrication of large area native substrates, control of carrier concentration, and inherent thermal stability also motivate the development of Ga 2 O 3based devices. N-type doping of Ga 2 O 3 with Si or Sn has shown good controllability with a broad range from 10 15 cm −3 to 10 20 cm −3 . 13,14 Although some UWBG semiconductors (such as AlN, c-BN, and diamond) beat Ga 2 O 3 in the BFOM chart, their wide utilization is strongly constrained by practical limits: AlN, c-BN, and diamond still suffer from a lack of proper substrates for high quality epitaxial growth. 15,16 FIG. 2. Baliga's figure of merit (BFOM) of common wide bandgap (WBG) and ultra-wide bandgap (UWBG) semiconductors. 3 Although Ga 2 O 3 based devices have become the focus of research only in recent years, the explorations of Ga 2 O 3 may date back to several decades ago (as shown in Fig. 3). The first report was on the optical properties of Ga 2 O 3 in early nineteenth century, when the French scientist Lecoq de Boisbaudran found that "gallium oxide which contains chromium shows a red fluorescence in a vacuum" right after his discovery of the new element gallium. 17 Most of the early publications mainly focused on the basic physical properties and chemical synthesis of Ga 2 O 3 . [18][19][20][21][22] In 1952, five different polymorphs of Ga 2 O 3 , their crystal structure, and phase stability have been explicitly illustrated by Roy et al. 23 The investigations of Ga 2 O 3 in the period of 1960s-1980s were mostly based on materials with poor crystallinity or even in amorphous forms, though some attempts for making Ga 2 O 3 single crystals started to appear. 24,25 For example, small flasks of single crystals grown by Chase 24 revealed the optical properties of β-phase Ga 2 O 3 , which established a bandgap value of 4.7 eV based on the observation of a band-to-band transition at 270 nm. 26 The bandgap values were in consistency with values measured from bulk crystals and epitaxial thin films with much better quality. 2,27,28 Because a native layer of Ga 2 O 3 naturally forms on the surfaces of GaAs and GaN compound semiconductors, Ga 2 O 3 thin films, mostly in amorphous or α-phase polycrystalline forms, were also used as passivating layers for GaAs based complementary metal-oxide-semiconductor (CMOS) devices or as anti-reflective coating on GaAs light emitting diodes [29][30][31][32][33] and as dielectric layers on GaN for MOS devices (native Ga 2 O 3 on the GaN structure was chemically stable and supposed to be correlated with the low density of interface states) 34 or Ga 2 O 3 /GaN dielectrics. 35,36 Ga 2 O 3 bulk crystals have also been used as substrates for the growth of GaN. [37][38][39][40] Nevertheless, no significant progress has been made in this attempt because of poor control over the interface, film quality, and device performance. In fact, it is generally believed that Ga 2 O 3 plays a negative role in GaAs and GaN technology, in which the naturally occurred Ga 2 O 3 must be carefully removed before device processes. [41][42][43] From the 1990s to 2010s, significant breakthroughs have been made in successful growth of a bulk single crystal of high quality and large size. For example, a large Ga 2 O 3 single crystal with size up to 70 mm × 50 mm × 3 mm was realized by the edgedefined film-fed growth (EFG) method, making EFG one of the most promising methods for large-scale production. 44,45 Commercially available large β-phase Ga 2 O 3 bulk crystals and wafers with a size up to 2 in. and 4 in. have been achieved by the Czochralski method 46 and EFG method, 47,48 respectively. Figure 4 shows the picture of a 4-in. single crystal grown by the EFG technique. The availability of large area substrates has in-turn motivated the homoepitaxial growth of high quality Ga 2 O 3 thin films with more sophisticated controlling of doping, defects, modulation doping, superlattice, etc. 13,[49][50][51] Triggered by the growth of large-size bulk crystals, Ga 2 O 3based device research, including Ga 2 O 3 based field-effect transistors (FETs), 3,48 Schottky barrier diodes (SBDs), 4,52-57 and solarblind ultraviolet detectors, 11,12,58,59 has been experiencing a rapid rise in the past few years. Some representative device structures are shown in Fig. 5. In 2012, Higashiwaki et al. 60 from the Novel Crystal Technology, Inc. reported the metal-semiconductor fieldeffect transistors (MESFETs) based on the Ga 2 O 3 epitaxial layer grown on the β-Ga 2 O 3 (010) substrate, which raised a boom in developing Ga 2 O 3 -based transistors with a variety of architectures. Ga 2 O 3 MOSFETs with undoped or n-type channels utilizing dielectrics such as SiO 2 61 or Al 2 O 3 62 as well as normally off Ga 2 O 3 MOSFETs 63 have all been extensively investigated. 64 Breakthroughs are also achieved in transistor architectures, including heterostructure field-effect transistors (HFETs), 65 current aperture vertical electron transistors (CAVETs), 66 and fin-based vertical junction field-effect transistors (JFETs). 67 Lateral FET with a breakdown voltage of 755 V and channel current of 100 mA/mm has been demonstrated in 2016. 68 It is worth mentioning that twodimensional electron gas (2DEG) was achieved in the ternary HFETs with the modulation-doped β-(AlxGa 1−x ) 2 O 3 /Ga 2 O 3 interface by Zhang et al. 65 SBDs based on epitaxial layers of β-Ga 2 O 3 have exhibited power figure-of-merits (V B 2 /R ON ) with great promises, in terms of a high reverse breakdown field (V B ) together with a low on-resistance (R ON ) value. 69 Benefiting from the recent development of homoepitaxial growth techniques such as halide vapor phase epitaxy (HVPE) and low-pressure chemical vapor deposition (LPCVD), capable of growing thick (>1 μm) and high-quality layers, Ga 2 O 3 SBDs had developed rapidly in the last four years. [52][53][54][55] The breakdown strength of SBDs based on β-Ga 2 O 3 has reached up to 4.2 MV/cm with an extrinsic R ON of 3.9 mΩ cm 2 , 70 exceeding the theoretical limits of 4H-SiC (2.2 MV/cm) and GaN (3.3 MV/cm). 69 Solar-blind UV photodetectors based on Ga 2 O 3 single crystal substrates were initially developed by Oshima et al. 6 and Suzuki et al. 7 in 2008. Their pioneering works paved the way for the increase of investigations in this field. Ga 2 O 3 solar-blind UV photodetectors have been broadly studied in the types of metal-semiconductormetal (MSM) photodetectors, Schottky barrier photodetectors, and p-n or n-n junction photodiodes using Ga 2 O 3 bulk crystals, 6,7,71,72 films, 8,[73][74][75][76] and micro/nanostructures. 9,77 Compared with the widely used AlxGa 1−x N 78, 79 and MgxZn 1−x O, 80 whose detectivity is limited due to their serious alloying composition fluctuation or even phase segregation, a Ga 2 O 3 -based photodetector is highly suitable for practical applications of solar-blind photodetection with improved photoresponsivity and response speed. 12
β-Ga 2 O 3 has a monoclinic crystal structure with a space group C2/m, as shown in Fig. 6(b). The lattice parameters are a = 12.21 Å, b = 3.04 Å, c = 5.80 Å, and β = 103.8 ○ , and the unit cell volume is 208.85 Å 3 . A detailed crystal structure of β-Ga 2 O 3 has been reported by Åhman et al. 81 Briefly, the unit cell of β-Ga 2 O 3 [ Fig. 6(b)] contains two crystallographically different Ga cations and three O anions. Half of the Ga cations are in distorted tetrahedral coordination (Ga1), and the other half are in distorted octahedral coordination (Ga2). O anions are packed in a distorted cubic structure with two threefold coordinated types (O1 and O2) and one fourfold coordinated type (O3). Therefore, different bonding environments could be found in β-Ga 2 O 3 : the tetrahedrally (T d ) coordinated Ga1 shares bonds with one O1 ion with a bond length of 1.835 Å, one O3 ion with a bond length of 1.833 Å, and two O2 ions with a bond length of 1.863 Å. The octahedrally (O h ) coordinated Ga2 ions share bonds with two O1 ions with a bond length of 1.937 Å, one O2 ions (1.937 Å), and three O3 ions (one with 2.005 Å and two within the bc-plane with 2.074 Å). The low crystallographic symmetry of the monoclinic phase leads to anisotropy of the physical, optical, and electrical properties, as both predicted theoretically and observed experimentally. The (010) and (201) planes are the most commonly used crystal surfaces for device application and thin film growth.
Polymorphs other than the β-phase are metastable phases and cannot be grown as bulk crystals from the melt. 1 However, they could be epitaxially grown as thin films stabilized on substrates.

B. Electronic band structure and optical properties
The fundamental electronic structure of β-Ga 2 O 3 and optical properties have been studied by numerous first principle calculation and a few photoemission spectroscopic experiments. [100][101][102][103][104][105][106][107] There is general consensus that β-Ga 2 O 3 has a direct bandgap of ∼4.87 eV (though with a slightly smaller indirect bandgap of 4.83 eV). The conduction band (CB) is mainly composed of delocalized Ga 4s derived states, giving rise to a dispersive band with a low electron effective mass, while the valence band (VB) is mainly formed by occupied O 2p 6 derived states with minor hybridization with Ga 3d, 4p, and 4s orbitals.
The band structure of β-Ga 2 O 3 has been calculated by density functional theory (DFT), 100,101 hybrid HF-DFT, 102 and GW methods. [103][104][105][106] Standard DFT results in an underestimate bandgap because of the approximations in the calculation of electron exchange correlation (XC) energy. [108][109][110] Hybrid B3LYP or GW methods were proven to provide results with better agreement with the experimental bandgap and lattice parameters. Figure 7(a) shows the calculated band structure of β-Ga 2 O 3 by Varley et al. 107 using hybrid B3LYP. It can be seen that the bottom of CB, of mainly the Ga 4s character, shows a highly dispersive feature at the Γ point.
On the other hand, the top of VB is mainly composed of localized O 2p orbitals, exhibiting very low dispersion. This results in a large hole effective mass, in agreement with other calculations for Ga 2 O 3 and the situations for other post-transition metal oxide semiconductors. 107 An indirect bandgap of 4.83 eV was found for Ga 2 O 3 , with the VB maximum (VBM) located just off the M point, slightly smaller than the direct bandgap of 4.87 eV at Γ. 107 Vertical transitions at the Γ point and VB maximum (VBM) are both dipole-allowed, but indirect transition probability at VBM are around one tenth of the strength of direct transition at the Γ point, as revealed by the dipole matrix analysis. The relatively weak indirect transitions as well as the slight difference between indirect and direct bandgaps make β-Ga 2 O 3 a "pseudo-indirect" semiconductor, as shown experimentally in a sharp absorption edge at roughly 4.9 eV. 111 The electronic structure of β-Ga 2 O 3 was also investigated experimentally by angle resolved photoemission spectroscopy (ARPES), showing the VB dispersion along the Γ-A and A-M direction of the Brillouin zone, as shown in Fig. 8. 112 The experimental VB band structures also exhibit weak dispersion, which fits well with the calculated band structure. The position of conductionband minimum (CBM) was also measured to be at the Γ-point. The experimental direct and indirect bandgaps are Eg dir = 4.9 eV and Eg ind = 4.85 eV, respectively.
The VB spectra have been measured by photoemission spectroscopy excited with photon energies ranging from 27 eV to 39 Figure 9 shows the comparison of the experimentally measured VB spectra excited with photon energies of 150 eV and 8000 eV, with VB density of states (DOS) calculated by DFT. The measured VB spectra in conjunction with calculated total and partial DOSs weighted by photoionization cross sections reached the conclusion that the VB spectra of β-Ga 2 O 3 mainly consist of O 2p with a bandwidth of 7.7 eV. The VB of β-Ga 2 O 3 shows three main regions: region I at 0-2 eV below the VBM, region II at 2-6 eV below the VBM, and region III at 6-8 eV, corresponding to the occupied O 2p 6 states slightly hybridized with Ga 3d, 4p, and 4s states, respectively. The optical properties of β-Ga 2 O 3 show notable anisotropy due to the asymmetry of the crystal structures, as mentioned earlier. This optical anisotropy has come into the view of physicists for a long time. Optical absorption measurement of β-Ga 2 O 3 by Tippins in 1965, 26 though all conducted with light in the same polarization, still recognized the occurrence of the absorption shoulder which was assigned to different transition energies between T d coordinated Ga1 and O1/O2 [ Fig. 10(a)]. A more systematic study on the pleochroism of vapor phase reaction grown Ga 2 O 3 single-crystalline platelets was conducted by Matsumoto et al. using incident light polarized in six different orientations, in which they observed the highest absorption edge at room temperature to be 4.90 eV for E//b shown in Fig. 10(b). 119 The absorption edge in other geometries at room temperature was also measured for E//c and E b&c with the value of 4.54 eV and 4.56 eV, respectively. Moreover, larger energies were found at 77 K for both E//b and E//c with the corresponding magnitude of 40 meV and 220 meV.
Optical floating zone (OFZ) grown single crystals were also investigated for pleochroism by Ueda et al. 27 Smaller absorption edges measured for light polarized E//b and E//c were found to be 4.90 eV (253 nm) and 4.59 eV (270 nm), as shown in Fig. 10(c). Moreover, increasing the angle φ between E and c could result in the appearance of a shoulder at a shorter wavelength in optical transmission spectra. The shoulder transmittances also become stronger with an increase in φ.
Conditions for material synthesis, defects, and doping also show a great influence on optical properties of β-Ga 2 O 3 . Ueda et al. studied the influence of O 2 annealing on Ga 2 O 3 crystals grown by the OFZ method and found that the transmittance of Ga 2 O 3 increased with the elongation of annealing time. 120 Galazka et al. 46 reported that Ga 2 O 3 crystals with lower concentration of free electrons (controlled with different growth atmospheres and dopants by the Czochralski method) showed better transmittance.
There are fewer studies on the electronic structure for other metastable phases of Ga 2 O 3 , mostly based on theoretical works. A few experimental 121,122 and theoretical [123][124][125][126]  methods. The bandgap of α-Ga 2 O 3 has been measured to be in the range of 4.9-5.6 eV, 83,86,[127][128][129] slightly larger than that of β-Ga 2 O 3 . Figure 7(b) shows the calculated band structure of α-Ga 2 O 3 using the Heyd-Scuseria-Ernzerh (HSE) hybrid functional reported by Kobayashi et al. 126 The band structure of α-Ga 2 O 3 is very similar to that of β-Ga 2 O 3 , with highly dispersive CBM of Ga 4s. The VB also exhibits similar flatness as β-Ga 2 O 3 attributed to localized O 2p. α-Ga 2 O 3 has the same CBM at Γ as well as VBM at the L or F point. α-Ga 2 O 3 is also an indirect semiconductor with a calculated bandgap of 5.39 eV. The band structure of ε-Ga 2 O 3 is also investigated both theoretically [130][131][132] and experimentally. 132 Similar flatness in VBM and strong dispersion in CBM are also found in the band structure of ε-Ga 2 O 3 as well. The calculated bandgap for ε-Ga 2 O 3 is reported to be 4.26 eV by Mulazzi et al. 131 using the HSE functional and 4.62 eV by Pavesi et al. 132 using the B3LYP functional. The ARPES results suggest a lower bandgap value of 4.41 eV, 131 while optical absorption and photoconductivity measurements suggest a bandgap value of 4.6 eV. 132 The band structure of γ-Ga 2 O 3 was calculated by Gake et al. 133 The calculated direct and indirect bandgaps were 5.30 eV and 5.15 eV, respectively.

III. MATERIALS SYNTHESIS
High quality bulk crystals and thin films are the starting point for the fundamental study of the structural, electrical, and optical properties and for further device fabrication. In the last decade, achievement in growing large scale and high-quality bulk crystals has triggered enormous research efforts in the use of Ga 2 O 3 for high power electronics and solar-blind photodetectors. Recently, 4-in. high quality β-Ga 2 O 3 (201) wafers, with the full width at half maximum (FWHM) for the rocking-curve (402) diffraction below 17 arcsec and etch pit density (EPD) as low as 10 3 cm −2 , were achieved using the EFG-growth method 47 and also commercially available from Novel Crystal Technology, Inc. Furthermore, highpurity, 1.25 μm-thick (010) β-Ga 2 O 3 homoepitaxial thin films, with record-high carrier electronic mobilities of 184 cm 2 /V s and low carrier concentrations of 2.5 × 10 16 cm −3 at room temperature, have been achieved by MOCVD. 134 Using Si, Sn, or Ge as dopants, a controllable n-type doping with free carrier concentration ranging from 10 16 to 10 20 cm −3 and mobility decreasing from 140 to 40 cm 2 /V s has been achieved for MBE grown homoepitaxial films. 13,49 Recently, using modulation doped β-(AlxGa 1−x ) 2 O 3 /Ga 2 O 3 heterostructures to form two-dimensional electron gas (2DEG) at the interface, a record room-temperature channel mobility of 180 cm 2 /V s and low temperature peak mobility of 2790 cm 2 /V s have been demonstrated. 50 Clearly, the availability of large volume and high structural quality substrates with high electrical and optical parameters at reasonable costs will accelerate the development of devices and circuits, as in the case of SiC and GaN.
This section will briefly introduce the progress on the growth technique for bulk single crystals and homo-and hetero-epitaxial thin films.

A. Bulk single crystals
For the growth of β-Ga 2 O 3 bulk single crystals, a variety of techniques have been used, including the Verneuil method, OFZ method, Czochralski method, Vertical Bridgman (VB) method, and EFG method. 135 Earlier trials of growing Ga 2 O 3 bulk crystals were performed by Chase 24 and Lorenz et al. 25 using the Verneuil method. The largest dimension achieved by the Verneuil method was 20 × 8 × 2 mm 3 with a Hall mobility of about 100 cm 2 /V s at room temperature. 25 The Verneuil growth of β-Ga 2 O 3 was merely used in these days due to the high mechanical stresses caused by the growth PERSPECTIVE scitation.org/journal/apm processes and limited size obtained. The use of the OFZ method in growing β-Ga 2 O 3 crystals was initially introduced by Víllora et al., 136 achieving the growth of substrate-level crystals (∼1 in.) in 2004. The OFZ growth of β-Ga 2 O 3 has shown great controllability in both crystal quality and doping level. A wide range of conductivity (<10 −9 S cm −1 to 38 S cm −1 ) could be reached through the change in growth atmosphere and doping concentration. 120 However, the achievement of a large crystal via the OFZ method is limited by optical heating. 137 The Czochralski growth of β-Ga 2 O 3 single crystals was first reported by Tomm et al., 138 and the growth of 2-in. in diameter β-Ga 2 O 3 single crystals was already achieved by Galazka et al. 46 in 2014. However, the growth of larger crystals was impeded by their higher oxygen content during growth. 139 Among those methods, EFG is one of the leading candidates to produce large-size wafers beyond 2-in. with low defect density and high crystal quality. This method has also been widely used for mass production of sapphire wafers. 140 Fig. 11.

MBE
MBE has the potential for generating exceedingly pure and defect-free films by virtue of the high purity levels available in commercially available metals and O 2 , as well as the low energy (∼1 eV) of the incident species. 223,224 MBE has a typical growth rate ranging from 12 nm h −1 to 700 nm h −1 and a growth temperature of 700 ○ C-900 ○ C. The system also houses a reflection highenergy electron diffraction (RHEED) system, allowing the monitoring of surface structure and morphology in real time during growth with atomic layer precision. 225 MBE is one of the two predominant growth methods used in GaAs and GaN semiconductor technology and also the commonly used technique for the epitaxial growth of oxide semiconductors, such as In 2 O 3 226-229 and Ga 2 O 3 . 13,49,50,[230][231][232][233][234] Due to its ultrahigh vacuum (UHV) environment and high purity source materials, electrically insulating 0.7 μm-thick undoped films with a smooth surface morphology have been achieved on (010) Ga 2 O 3 substrates by MBE. 13,49 It has a low residual carrier concentration of <2.5 × 10 16 cm −3 and carrier mobility of >140 cm 2 /V s. Intentional Sn or Ge doping can induce the n-type electrical conductivity. For example, by increasing Sn dopant flux, the free electron concentration can be accurately controlled in a wide range from ∼10 16 cm −3 up to 1 × 10 20 cm −3 with mobility decreasing from 120 to 40 cm 2 /V s. 13,49 At present, (010) β-Ga 2 O 3 homoepitaxial wafers with a 0.5 μm thick unintentional doping or Si doped Ga 2 O 3 layer or 60 nm-thick (AlxGa 1−x ) 2 O 3 (x < 0.23) layer grown by MBE are commercially available.
Because of the controllability over the growth at atomic precision, MBE is a promising method to fabricate modulation doping β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 heterojunction or superlattice for an abrupt band discontinuity and confinement of high mobility twodimensional electron carrier at the interface. It has been demonstrated that β-(AlxGa 1−x ) 2 O 3 solid solution with x as high as 0.20 at 650 ○ C 51 and 0.61 at 800 ○ C 230,231 or higher can be grown by MBE. However, the MBE growth temperature is usually limited to less than 700 ○ C, in order to avoid the decomposition of Ga 2 O 3 in vacuum. 23 Therefore, the Al composition is limited at x = 0.20. Most interestingly, β-(AlxGa 1−x ) 2

MOCVD
MOCVD is in essence a CVD system that uses metal-organic compounds as some of or all its precursors. It is highly scalable with a large deposition area, suitable for large scale production. At present, MOCVD is a mature technique for mass production of GaN based semiconductors and GaN can be epitaxially grown on an 8-in. Si wafer with reasonably high growth rate. 235,236 Recently, benefitting from the low background charge and compensation concentration by optimizing the growth pressure, high quality 1.25 μm thick β-Ga 2 O 3 films with record-high electron mobility values of 184 cm 2 /V s at room temperature and 4984 cm 2 /V s at 45 K were achieved on (010) Fe-doped Ga 2 O 3 substrates using MOCVD. 134 The room temperature mobility approaches the predicted theoretical limit of 220 cm 2 /V s. 237 Using Si and Sn as dopants, a controllable carrier concentration ranging from 1 × 10 17 cm −3 to 8 × 10 19 cm −3 with a decrease in mobility from ∼130 cm 2 /V s to ∼50 cm 2 /V s was achieved. 238 The feasibility of achieving low background impurity concentration and high electron mobility will inspire more extensive studies on MOCVD for the fabrication of high-performance power electronics.
Furthermore, due to its higher growth temperature (>800 ○ C) than that of MBE and smooth surface morphology compared to that of MBE, MOCVD can grow β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 heterojunction or superlattice with abrupt heterointerfaces and a higher Al content (x > 0.4). 239 These features in combination with its high growth rates (0.8 μm/h, much higher than typical 0.2 μm/h by MBE) make MOCVD very promising for mass production of β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 MODFETs.
Although encouraging results were obtained on (010) substrates, their preparation in large scale remains challenging because of the limited availability of large size (010) wafers. Because the (010) substrates must be sliced perpendicularly to both easy cleavage planes, its largest scale commercially available from the EFG method (Novel Crystal Technology, Inc.) is 25 × 25 mm 2 . Recently, 2 in. diameter cylindrical crystals grown by the Czochralski method in the [010] direction were demonstrated. 240,241 Thus, potentially 2-in. epi-wafers grown by MOCVD could be prepared.

Mist-CVD
Mist-CVD is a relatively simple and cost-effective technique. This modified CVD technique uses a fine mist of precursors in a vapor phase reaction on the substrate. 88 It has been extensively used for the deposition of metal-oxide semiconductors, such as ZnO 242,243 and MgxZn 1−x O. 244 Mist-CVD is a promising method to grow α-Ga 2 O 3 other than the β-phase on the Al 2 O 3 substrate.
Due to the similar corundum structure with an in-plane lattice mismatch of 4.6%, α-Ga 2 O 3 can be grown on α-Al 2 O 3 substrates with a typical edge dislocation density of 7 × 10 10 cm −2 but with a relatively low electron mobility of 2.8 cm 2 /V s. 83,172,245 By applying quasi-graded α-(AlxGa 1−x ) 2 O 3 buffer layers, the total density of dislocations in the α-Ga 2 O 3 thin films can be further reduced to ∼10 8 cm −2 and the electron mobility is increased to 24 cm 2 /V s with a carrier concentration of 10 18 cm −3 . 85 Currently, a high quality 5 μm-thick α-Ga 2 O 3 layer grown on Al 2 O 3 (0001) substrates with a size of 4-in. in diameter is commercially available from FLOSFIA, Inc.
On the other hand, taking advantage of the misfit dislocations and strain accumulated at the interface of the α-Ga 2 O 3 layer and Al 2 O 3 substrate, the epi-structure can be exfoliated from the substrate and mounted on a heat sink. 245 This not only simplifies backside Ohmic contact deposition but also is important to efficiently remove the heat from the device. The latter is of particular interest in the Ga 2 O 3 technology as this material suffers from poor intrinsic thermal conductivity. 247,248 However, mist-CVD is a relatively new technique (designed by Kyoto University in 2008) 83 and has not been applied to massproduction of semiconductor epi-wafers. The highest electronic mobility (24 cm 2 /V s) achieved in α-Ga 2 O 3 is still much lower than its theoretical value (300 cm 2 /V s) and the reported values of β-Ga 2 O 3 . In order to utilize α-Ga 2 O 3 for high performance power devices, it is necessary to realize the growth of high-quality defect-free α-Ga 2 O 3 thin films, and the realization requires a steady effort to accumulate technical knowledge of mist-CVD.

PLD
PLD is a versatile technique for the deposition of complex oxide thin films, heterostructures, and interfaces. 223,249 The composition of targets is preserved in the film, enabling impurity doping or alloying by varying the composition of targets. However, ions from targets can be of very high (∼100 eV) energy and, thus, can create point defects, giving rise to unwanted electrical properties in the epitaxial film. Similar to MBE, RHEED can also be used here to monitor surface structure and morphology. 250, 251 Recently, a record-high conductivity of 798 S cm −1 with a carrier concentration of 1.74 × 10 20 cm −3 was achieved by PLD on a (010) Ga 2 O 3 substrate from a 1 wt. % SiO 2 -Ga 2 O 3 target. 173 Its high conductivities are critical to address a known problem of Ohmic contact formation including in β-Ga 2 O 3 and have extensive implications on forming low on-resistance for both power switching and radio frequency (RF) applications. However, the highest mobility (27 cm 2 /V s) 173 achieved until now in PLD-grown films is still much lower than those grown by MOCVD (184 cm 2 /V s), 134 MBE (120 cm 2 /V s), 13,49 and HVPE (149 cm 2 /V s) and bulk single crystals grown by EFG-grown (123 cm 2 /V s), 252 which is likely due to the ionized impurity scattering of the high density of Si dopants (>3 × 10 19 cm −3 ). 174 Therefore, steady efforts are required in future to optimize target compositional control and deposition parameters to achieve a higher mobility.
Noted that due to high temperature (several thousand degrees) and high energy of ions and electrons from the target during growth, the solubility of Al in β-(AlxGa 1−x ) 2 O 3 by PLD is up PERSPECTIVE scitation.org/journal/apm to x = 0.8 at a relatively low temperature of 400 ○ C, 230,253 which is comparable to x = 0.8 in bulk polycrystals prepared by solid state synthesis in the 850-1950 ○ C temperature range 254 and much higher than x = 0.18 in thin films prepared by MBE at a typical temperature of 650 ○ C. 51 Therefore, with the characteristics of the higher solubility of Al at a low growth temperature, it seems reasonable to push the CB bottom higher by increasing the Al content in the β-(AlxGa 1−x ) 2 O 3 barrier by PLD, enabling the enhancement of 2DEG channel mobility and realization of high- However, the fabrication of such FETs by PLD is still in its infancy, and much effort is needed to optimize deposition parameters and conditions.

HVPE
HVPE is an old epitaxy growth method that was previously used for the growth of III-V and GaN compound semiconductors. 255 HVPE has the highest growth rate (250 μm/h) for growth of β-Ga 2 O 3 and is promising for growing thick layers with high productivity. However, it typically results in rough surface morphology containing a high density of defects and pits, even when grown on native substrates. 192,195 Therefore, chemical and mechanical polishing processes need to be applied prior to device fabrication. 248 Recently, 5 μm-thick high quality β-Ga 2 O 3 layers, with a low effective donor concentration below 10 13 cm −3 , have been homoepitaxially grown on (001) β-Ga 2 O 3 substrates by HVPE with a high growth rate of 5 μm/h. 192 Controllable n-type concentration in the range of 10 15 cm −3 to 10 18 cm −3 with the carrier mobility decreasing from 149 to 88 cm 2 /V s has been obtained by intentional Si doping. 194 The mobility is almost equal to those of bulk crystals. At present, (001) β-Ga 2 O 3 homoepitaxial wafers with a 10 μm-thick Sidoped layer grown by HVPE are commercially available from Novel Crystal Technology, Inc.
HVPE can also be utilized to grow high purity α-Ga 2 O 3 on Al 2 O 3 substrates typically at 500-600 ○ C. 86 The structural quality of HVPE-grown α-Ga 2 O 3 is similar to that of mist-CVD grown films, with the dislocation density measured by plan-view TEM of typically ∼10 10 cm −2 . 75,76, Using the epitaxial lateral overgrowth (ELO) technique, the dislocation density in laterally grown wing regions can also be reduced down to less than 5 × 10 6 cm −2 . 196 The Ge doped α-Ga 2 O 3 films show a Hall mobility of 28 cm 2 /V s and carrier concentration of 3 × 10 19 cm −3 , 88 which are comparable to those of Sn doped films grown by mist-CVD (24 cm 2 /V s and 10 18 cm −3 ). 85 Moreover, as achieved in mist-CVD grown α-Ga 2 O 3 85 and III-V compound semiconductors, 256,257 inserting a buffer layer can confine misfit dislocations within the buffer layers and significantly improve the crystalline quality of the films grown after. Inserting a buffer layer seems a promising strategy to overcome the lattice mismatch between α-Ga 2 O 3 and Al 2 O 3 and to reduce the dislocations in HVPE-grown α-Ga 2 O 3 . The realization of free-standing α-Ga 2 O 3 wafers by HVPE can also be expected as it happened in GaN industry and α-Ga 2 O 3 by mist-CVD.
To summarize this section, as described above, different epitaxial techniques have been applied to grow Ga 2 O 3 thick layers or thin films. Heteroepitaxial β-Ga 2 O 3 layers are often polycrystalline, containing a high density of defects and show low conductivity <10 S cm −1 and low mobility <1 cm 2 /V s. 173,188,258,259 Although such heteroepitaxial layers might be good enough for some applications, such as gas sensing 218,260 and a solar-blind UV detector, 154 high crystal quality layers are still demanded for high-power electronic and optoelectronic applications. 261 Homoepitaxial growth on native substrates is needed to reduce the epitaxial dislocations, defects, and impurities, and to optimize electrical and optical properties of the materials. One of the major advantages of the Ga 2 O 3 technology is that high quality single-crystal substrates can be grown by melt methods, as reviewed above. High quality homoepitaxial β-Ga 2 O 3 layers, with a low residual carrier concentration below 5 × 10 16 cm −3 and mobility higher than 150 cm 2 /V s, have been grown by MBE, MOCVD, and HVPE. Their growth kinetics and thermodynamics have been well understood, which are important to achieve the required structural quality and controllable electrical properties, with a reasonable growth rate. Among them, MOCVD and HVPE with a typically high grow rate >0.8 μm/h can be used to grow thick layers for vertical devices including SBDs, while MBE, with a control over the growth at atomic precision and a typical growth rate of 200 nm/h, has promising potential to grow thin films for lateral devices, such as β-( The mist-CVD system is relatively new, and its growth kinetics and thermodynamics are not well understood. However, this growth system and HVPE are both suitable for growth of highly crystalline α-Ga 2 O 3 thick films on an inexpensive sapphire. Both methods can be or are expected to realize free-standing α-Ga 2 O 3 wafers (>4-in. in diameter) by lift-off technology, providing an alternative platform to realize high performance power devices at low cost and solve the problem of poor thermal conductivity of Ga 2 O 3 on native substrates, as it happened in GaN industry. However, the highest reported mobilities for α-Ga 2 O 3 films grown by mist-CVD and HVPE are still below 30 cm 2 /V s. Thus, much effort is needed to optimize the growth condition or use a buffer layer at the interface to reduce the dislocation. Based largely on its relative ease of use and higher solubility of Al at a low growth temperature, PLD has potential to enhance the 2DEG channel mobility in modulation-doped β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 FETs.

IV. DEFECT AND DOPING (ELECTRONIC STRUCTURE, OPTICAL, MOBILITY, AND TRANSPORT)
In the undoped stoichiometric state, Ga 2 O 3 should be a transparent insulator because of its ultra-large bandgap of 4.87 eV. However, Ga 2 O 3 exhibits an unintentionally n-type conductivity, 47,262,263 and the origin of the unintentional doping is still under debate. Defects such as oxygen vacancies (V O ), hydrogen interstitials (Hi) and substitutions (HO), Ga interstitials (Gai), and other impurities have been proposed. 264-267 Ga 2 O 3 is also amenable to n-type doping with Si, 268 Sn, 47 Ge, 13 Nb, 269 Ta, 270 and so on. The free electron concentration could be controlled by growth conditions, post-growth treatment, or intentional doping, in the range of 10 16 -10 19 cm −3 for bulk crystals 49,268 and in the range of 10 14 -10 20 cm −3 for epitaxial thin films 188,194,258 with a corresponding Hall mobility of up to about 140 and 184 cm 2 /V s, 13,134,194 respectively. On the other hand, as discussed earlier, p-type doping in Ga 2 O 3 would be fundamentally difficult because of the very flat VBM of O 2p in nature and self-compensation. 271 278 have carried out a critical assessment of the specific on-resistance (Ronsp) and breakdown voltage of Schottky diodes containing defect states at 110 meV below the CBM, as shown in Fig. 12; to achieve 20 kV breakdown voltage in Ga 2 O 3 (comparable to SiC devices), the concentration of these defects must be below 5 × 10 14 cm −3 , while at present, only a 1.1 kV device has been demonstrated with a defect concentration of 1 × 10 16 cm −3 .
In this section, we will review the defects and doping chemistry in Ga 2 O 3 and its impact on electrical conductivity, mobility, and optical properties. We will begin with a brief introduction on the fundamental semiconductor physics for doping and defects in oxide materials.

A. Fundamental semiconductor physics of doping and defects in Ga 2 O 3
The fundamentals of doping and defects can be understood by the physics of semiconductors. The electrical conductivity (σ) of a semiconductor is directly related to its carrier concentration (n) and carrier mobility (μ), according to the relation σ = neμ, where e is the elementary charge. These parameters are fundamentally related to the electronic structure of oxides. n is determined by the intrinsic ease of generation of mobile carriers (electrons for n-type and holes for p-type) by defects or dopants. The carrier mobility μ is directly proportional to the free carrier scattering time, τ, and is inversely proportional to the carrier effective mass, m * , via μ = eτ/m * . τ largely depends on extrinsic factors such as ionized dopants, defects, and grain boundaries determined by film preparation procedures. m * is an intrinsic property of the materials, a tensor whose components are obtained from the electronic band structure by analyzing the variation of energy (E) with momentum (k). Thus, a highly dispersive VBM or CBM gives rise to small m * and hence potentially a high μ.

Effective mass and doping
For Ga 2 O 3 , the top of VB is primarily formed by fully filled O 2p 6 states and the CBM mainly by the unoccupied Ga 4s 0 orbitals. The Ga 4s 0 derived CBM is the key for achieving a high n-type conductivity and mobility in Ga 2 O 3 for the following two reasons.
First of all, the 4s orbital normally has large spatial distributions and their wavefunctions overlap with each other [inset in Fig. 7(a)], leading to a facile pathway for the conduction of electrons. In the view of band structure [ Fig. 7(a)], the s orbitals form a highly dispersive CBM at the Γ point, giving rise to a small m * . m * for β-Ga 2 (201) surface. 282 A small m * is also true for other wide bandgap oxide semiconductors, including In 2 O 3 , [283][284][285] ZnO, 286,287 and SnO 2 , 288,289 which typically have small electron effective masses of 0.20-0.35 me. On the other hand, the effective masses for holes are as large as 10 me, suggesting the fundamental limitation to obtaining highly mobile holes at the VBM. This is reflected in part by numerous attempts at p-type doping of ZnO 290-292 and In 2 O 3 , 293,294 but no encouraging results have been achieved so far, and there are still problems concerning the reproducibility of the results.
Second, owing to the Ga 3d contraction, the energy of Ga 4s is relatively lower than those of pre-transition metals (e.g., MgO). This gives rise to a relatively high electron affinity that facilitates n-type doping. 295 Ga 2 O 3 has an electron affinity of 4.0 eV, 296 compared to 1.4 eV for MgO. 297 For Ga 2 O 3 , substitution of Ga 3+ by Si 4+ , Ge 4+ , and Sn 4+ introduces dopant energy levels with ionization energy less than ∼50 meV below the CBM. 298 The extra electrons can be easily activated into the CBM as free carriers, inducing a significant increase in conductivity. The activation energy (Ea) for donors depend on the doping concentration (N d ), i.e., Ea decreases with an increase in N d , resulting from a combined effect of screening of the dopant's Coulomb potential by free carriers and charged impurities and of spatial fluctuations of the CB edge induced by the potentials of randomly distributed charged impurities. Generally, ΔEa decreases according to where ΔE 0 is the activation energy for isolated donors and β is a constant. For example, Irmscher et al. 299 300 and an electron effective mass is m * = 0.28 me, 112,280 giving an effective Bohr radius of a 0 * = a 0 ε(0)/(m * /me) = 1.92 nm. Thus, nc is calculated to be 2.48 × 10 18 cm −3 . For example, a carrier concentration of 1.74 × 10 20 cm −3 can be achieved, together with a typically electron mobility of 26.5 cm 2 /V s, yielding a high conductivity of 732 S cm −1 . 173 It should be noted that dopants and other defects such as vacancies or interstitials in the lattice behave as point scatters of electrons and such scattering events limits electron mobility. The free electrons in the CB can oscillate with an external electromagnetic field, such as the free electrons in metals (plasma oscillations). Below the plasma energy, any material exhibits a high reflectivity. The plasma frequency, ωp, is given by where n is the free carrier density, m * is the electron effective mass, and ε 0 is the permittivity of free space. The plasma frequency depends on the carrier concentration. 301,302 For a carrier concentration of order 10 18 cm −3 , the plasma energy is typically in the nearinfrared (NIR) region at around 0.4-0.7 eV. Bluish coloration due to reflectivity in the NIR has typically been observed for electrically conductive specimens. 46 Insulating specimens were colorless and, therefore, transparent in the UV, visible, and IR regions, as shown in Fig. 14(b). Therefore, the "optical window" for doped Ga 2 O 3 is set at short wavelengths by its optical bandgap and at longer wavelengths by its reflectivity plasma edge ( ̵ hωp).

Intrinsic mobility limits in Ga 2 O 3
We now turn back to discuss the electron mobility in Ga 2 O 3 . As mentioned above, β-Ga 2 O 3 has a small m * of 0.28-0.33 me because the CBM derives mostly from the dispersive Ga 4s states. The m * of β-Ga 2 O 3 and its character are quite similar to those of GaN. 303 One may initially expect that the electron mobility of Ga 2 O 3 is similar to that of GaN of 1500 cm 2 /V s. 237 However, so far, the best room temperature mobility in β-Ga 2 O 3 is in the range of 150-184 cm 2 /V s, 134,194 nearly an order of magnitude lower than GaN. One critical question is whether the reported lower mobilities in β-Ga 2 O 3 are intrinsic or extrinsic which can be improved by eliminating defects/impurities. Ma et al. 237

PERSPECTIVE
scitation.org/journal/apm β-Ga 2 O 3 with a higher density of defects and impurities, the electron mobility is limited by scattering at ionized impurities. POP scattering was also reported by Ghosh and Singisetti 304 and Parisini and Fornari. 305

Deep level states
Several deep level states in β-Ga 2 O 3 bulk crystals and thin films have been identified using deep level transient spectroscopy (DLTS), deep level optical spectroscopy (DLOS), and combination with other techniques and DFT calculations. Using DLTS, Irmscher et al. 299 found three deep trap states in undoped β-Ga 2 O 3 crystals grown by the Czochralski method, including E 1 with energy level located at 0.54 eV below CB (E C -0.54 eV), E 2 at 0.72 eV below CB (E C -0.72 eV), and E 3 at 1.04 eV below CB (E C -1.04 eV). E 2 is the dominating trap with a concentration of 2-4 × 10 16 cm −3 and is detected in all samples. E 3 is only present in some samples prepared with specific conditions but with comparable concentration to E 2 . E 1 has a concentration of one order of magnitude lower than that of E 2 and E 3 (3 × 10 14 -6 × 10 15 cm −3 ). The deep level states can act as compensating acceptors. Although more works should be done to identify the microscopic and chemical nature of the deep level states, Irmscher et al. 299 proposed that transition metal impurities such as Fe 3+ and Co 2+ may be responsible for some of the deep traps because EPR detected the presence of Fe 3+ and Co 2+ in their samples.
Zhang et al. 306 performed DLTS and DLOS to probe the deep level states in bulk β-Ga 2 O 3 single crystals grown by EFG, in which five distinct deep states have been detected. Their energy levels and concentrations are shown in Fig. 15. Three states, E 1 (E C -0.62 eV), E 2 (E C -0.82 eV), and E 3 (E C -1.00 eV), detected by DLTS are very similar to those found in the work by Irmscher et al. 299 Moreover, DLOS allowed to identify another two deeper states than DLTS, including E 4 (E C -2.16 eV) and E5 (E C -4.4 eV, i.e., 0.43 eV above VB). E 2 and E5 are the dominant ones, with a concentration of ∼10 16 cm −3 . The authors also speculated that E 2 may be associated with either Sn Ga or V O point defects, and E 4 may be with Ga vacancies (V Ga ). However, more work is needed to verify these interesting but speculative assignments.
Ingebrigtsen et al. 307 combined DLTS, proton radiation, secondary ion mass spectrometry (SIMS), and hybrid DFT calculations to study the deep level states in β-Ga 2 O 3 synthesized by different methods, including EFG single crystals and homoepitaxial film grown by MBE and HVPE. For the EFG single crystals, they found similar trap distribution to those measured by Irmscher et al. 299 and Zhang et al. 306 with E 2 dominating. However, for the epitaxial films by MBE and HVPE, E 2 has 2 orders of magnitude lower concentration. As further confirmed by SIMS measurements, they concluded that E 2 has an extrinsic origin, associated with residual Fe 3+ impurities occupying Ga sites. More interestingly, their results also revealed another deep state, E 2 * at 0.72 eV below CB (E C -0.72 eV).
E 2 * was identified as having an intrinsic origin, perhaps from Ga vacancies or its complexes. Similar results were also reported by Polyakov et al. 308 based on HVPE-grown β-Ga 2 O 3 epitaxial films which exhibit E 1 , E 2 , and E 3 deep states near E C -0.6 eV, E C -0.75 eV, and E C -1.05 eV, but the concentration of these traps in the HVPE film is 1-2 orders of magnitude lower than that in bulk crystals. However, proton irradiation increases the concentrations of E 2 and E 4 states, suggesting that these states are associated with intrinsic defects, different from the conclusion by Irmscher et al. 299 and Ingebrigtsen et al. 307 To summarize this part, although several deep level states in bulk crystals and thin films of β-Ga 2 O 3 have been identified, their physical origin remains elusive. More works such as high-resolution photoemission spectroscopy, photoluminescence, and DFT calculations should be performed to clarify their origins. Knowledge of the natures of these types of deep levels is critical for further developing Ga 2 O 3 -based optoelectronic devices.

B. Unintentional doping and intrinsic defects (oxygen Vo and hydrogen H i and Ho)
It is often observed that β-Ga 2 O 3 bulk crystals and thin films exhibit an intrinsic n-type conductivity (with a background free electron concentration), despite the absence of intentional doping. 47,262,263 Such unintentional n-type conductivity is also commonly observed for other wide bandgap oxide semiconductors (ZnO, 273,309 In 2 O 3 , 226,283,310 and SnO 2 311,312 ). Table I summarizes unintentional doping electron concentration and mobility for Ga 2 O 3 single crystals (bulk and epitaxial thin films) grown by different methods and at different conditions. The resulting electron concentrations between 10 16 cm −3 and 10 19 cm −3 would correspond to a donor concentration of 0.000 01%-0.01%. Despite intense research in the last few years, the origin of the unintentional doping is still not settled. The proposed electron donors include oxygen vacancies (Vo), hydrogen, Ga interstitial (Ga i ), and other impurities from the material synthesis process, but no conclusive agreement has been reached yet.

Oxygen vacancies (Vo)
It is often experimentally observed that the growth of Ga 2 O 3 or post-growth annealing in high oxidizing environments reduces the free electron density whereas in reducing conditions (nitrogen, hydrogen, or ultra-high vacuum) leads to an increase in n-type conductivity. Table I    On the other hand, the conductive crystals became insulating after annealing in O 2 . Furthermore, the dependence of conductivity on oxygen partial pressure (P O2 ) was investigated by Cojocaru and Alecu 313 and Fleischer and Meixner 314 using Ga 2 O 3 polycrystalline thin films: Ga 2 O 3 shows a characteristic (P O2 ) −1/4 dependence of conductivity with a relation of σ ∼ (P O2 ) −1/4 . Because of the inverse correlation between conductivity and oxygen partial pressure, the n-type conductivity in Ga 2 O 3 was commonly attributed to the presence of Vo. 262,264,275,315,316 In order to preserve the charge neutrality, a Vo captures two electrons and is denoted as a neutral vacancy Vo x . Free carriers can be generated, by single or double ionization of Vo x , resulting in Vo • or Vo •• , respectively. The donor state energy levels were experimentally determined to be located only ∼0.02-0.03 eV below the CBM. 315 Aubay and Gourier 317 synthesized β-Ga 2 O 3 single crystals using the Verneuil method. The samples showed a very high conductivity of 200 S/cm and slightly blue color, when synthesized under reducing conditions (H 2 /O 2 flow rate of 2:3). In normal conditions, the sample was insulating with a conductivity of 10 −6 S cm −1 and transparent. They also performed a detailed EPR study on the magnetic bistability and Overhauser shift of conduction electrons and concluded that Vo forms a partially occupied shallow impurity donor and is responsible for the low-temperature conductivity. Using EPR, Yamaga et al. 264 provided further microscopic evidence that among the three oxygen sites, the one in fourfold coordination acts as a shallow donor, trapping a single unpaired electron (Vo • ), i.e., each Vo donates one delocalized electron responsible for conductivity, while the other is localized.

PERSPECTIVE scitation.org/journal/apm
However, this assumption was questioned by Varley et al. 298 and others 318 who performed first-principle calculations based on hybrid DFT of various impurities and Vo in β-Ga 2 O 3 . According to these calculations, Vo acts as a deep donor with an ionization energy of more than 1 eV and, thus, cannot be the source of n-type conductivity. This would be similar to the case of other oxide semiconductors (In 2 O 3 , 319 SnO 2 , 311,312 and ZnO 273,309 ), where the energy level of Vo is too deep to be ionized for n-type conductivity. 320 The deep level states of Vo in Ga 2 O 3 may also be associated with the observations of blue luminescence emissions arising from the recombination of a localized donor state (attributed to Vo) with trapped hole states, 274,321 a high concentration trap state at 0.82 eV (likely related to the deep level state, e.g., Vo) below the CBM of Ga 2 O 3 detected by DLTS, 306 and depthresolved cathodoluminescence spectroscopy and surface photovoltage spectroscopy. 322

Hydrogen interstitials (H i ) and substitution (H O )
Alternatively, hydrogen impurities were proposed to act as shallow donors in Ga 2 O 3 and can be present both as an interstitial species (H i ) and as a substitutional donor at the oxygen vacancy site (H O ). 298,323 H i has low formation energy under both O-rich and O-poor conditions, indicating that it will easily be incorporated as an unintentional impurity, when hydrogen is present in the growth or annealing environment. However, H O has a low formation energy only under O-poor conditions. There is also experimental evidence that hydrogen may be a shallow donor in Ga 2 O 3 , 324 based on its implanted muonium counterpart whose properties mimic those of hydrogen form shallow donors and EPR of single-crystal samples. Hydrogen impurities are suggested as shallow donors, in general, in many wide bandgap oxide semiconductors such as ZnO, 325  However, the hydrogen shallow donor model has been questioned by Polyakov et al. 329 based on hydrogen plasma treatment of β-Ga 2 O 3 , after which they observed a pronounced decrease in the concentration of shallow donors that provide free electrons, which did not corroborate the theoretical prediction that hydrogen in β-Ga 2 O 3 should be an efficient shallow donor. There is a possibility that hydrogen forms electrically active complexes with deep native defects, such as V Ga , and gives rise to donor compensation.

Ga interstitials (Ga i )
Ga i are shallow donors and could act as an alternative source of n-type conductivity, but the recent calculation suggests that Ga i is highly mobile and it has a large formation energy (>2.5 eV) at extreme oxygen-poor growth conditions, which make them less likely to be present. 266,318

Other impurities
In addition to V O , hydrogen, and Ga i , residual impurities (Si, C, F, etc.) are present in bulk crystals, typically at a concentration of a few ppm by weight. 47 The sources of the residual impurities may come from starting precursors used for synthesis (all growth methods), containers and crucibles for growth, flux composition (solution methods), and thermal insulation and furnaces (all growth methods). Some of the residual impurities could be electrically active, e.g., Si, F, and others not, but they may affect the electrical properties (e.g., mobility) indirectly through structural quality. For example, it has been shown that Si is the main impurity present in high-purity Ga 2 O 3 powders 330 and single crystals. 275 The Si impurity concentrations are determined at 10-20 ppm (weight) for 4N (99.99%) purity Ga 2 O 3 and 0.05-1.8 ppm for 6N (99.9999%), which corresponds to a Si concentration of 1-3 × 10 18 cm −3 and 10 16 -10 17 cm −3 . These values would give comparable electron density observed in unintentional doped Ga 2 O 3 .

C. Intentional n -type doping
Controllable n-type conductivity can be realized by intentional doping with group IV elements (e.g., Si, Ge, and Sn) 13 334,335 ) and compatibility with epitaxial growth processes. Using Si, Sn, and Ge as dopants, a wide range of free carrier concentration (n) from 10 16 up to 10 19 cm −3 and a peak mobility of 152 cm 2 /V s have been achieved for bulk crystals, and n from 10 15 cm −3 to 10 20 cm −3 and a peak mobility of 184 cm 2 /V s have been achieved for epitaxial thin films. Table II  Si and Ge preferentially substitute the T d coordinated Ga1 site, while Sn prefers the O h coordinated Ga2 site because of its large cation size. Sn at Ga2 sites has been confirmed by x-ray absorption spectroscopy (XAS). 336 However, scanning tunneling microscopy/spectroscopy (STM/STS) on Si-doped EFG single crystals suggested an even distribution of Si between the Ga1 and Ga2 sites. 337 Si at different coordination may have different activation energies. Some authors suggest that Si at Ga2 sites may not be electrically active 268 or with an activation energy of 120 meV. 134 Figure 16(b) shows the total doped concentration determined by SIMS and carrier density determined by Hall effect measurements in van der Pauw geometry at room temperature. 238 It showed that free electron density systematically increases with dopants for dopants <10 19 cm −3 , indicating that most of the dopants are activated to give free carriers. At higher dopant concentration, the actual carrier concentration is limited by the solubility of the dopants, either through the formation of secondary phases of oxides (e.g., SiO 2 and GeO 2 ) or through low incorporation of Sn due to their high vapor pressure. On the other hand, it should be noted that the carrier concentration is also strongly influenced by other PERSPECTIVE scitation.org/journal/apm The electron mobility shows an inverse correlation with the free electron concentration. This is valid for both bulk crystals 25,27,46,139,335,[338][339][340][341][342][343] and high crystalline epitaxial thin films, 13,49,88,194,238,[344][345][346][347][348] as shown in Fig. 17. The electron mobility gradually decreases with the electron concentration, from >100 cm 2 /V s at n = 10 17 cm −3 to 30-50 cm 2 /V s at n = 10 19 cm −3 to 10 cm 2 /V s at n = 5 × 10 20 cm −3 . This indicates that the ionized dopants act as scattering centers. 134,170,174 In the case of layers of poor structural quality, e.g., thin films grown on Al 2 O 3 substrates with a large mismatch, the electron mobility is much lower as compared with bulk crystals or with high quality homoepitaxial layers because of the scattering at the grain boundaries or dislocations. 173,188,258 In general, a much higher conductivity and carrier concentration have been achieved in epitaxial thin films than in bulk crystals. Baldini et al. 238  The growth of highly conductive doped Ga 2 O 3 layers has important implications for device application. In particular, Ohmic contact formation to wide semiconductors has been a known problem in Ga 2 O 3 . The highly conductive Ga 2 O 3 layers can be used as electrodes to form Ohmic contacts with a low contact resistance. 173 Furthermore, because of the large bandgap, the doped Ga 2 O 3 is also highly transparent in the visible region, of particular interest as an alternative to Sn doped In 2 O 3 (ITO) transparent electrodes in optoelectronic applications.

Activation energies (Ea) of the shallow donors
Temperature dependent transport measurements, EPR, and theoretical calculation have also been performed to examine energy levels of the shallow donors in Ga 2 O 3 . These results, in general, revealed a low activation energy (Ea) of less than 70 meV. However, some discrepancies still remain regarding the values of Ea and the exact activation mechanisms; 298,272,318 Ea for Sn ranges from 7.4 meV to 60 meV, 331,332 for Si ranges from 16 meV to 50 meV, 237,278,299,305,333 and for Ge ranges from 17.5 meV to 30 meV. 334,335 The variation in Ea may be associated with differences in doping concentrations, other impurities and defects, growth methods, accuracy in the measurements, etc. Recent EPR studies by Son et al. 333 reported that Si may also behave as a negative-U center (often called a DX center) with the negative charge state DX − , similar to the Si donor in AlxGa 1−x N with a high Al content. 349 Ea for DX − is in the range of 44 meV-49 meV. After annealing at 1150 ○ C in nitrogen, the DX − donors are fully activated and become partly delocalized, forming impurity bands, which reduces the donor activation energy to Ea = 17 meV. The DX properties and the formation of impurity bands explain the large variation of the donor activation energies  (201) substrates was measured to be 110 meV using temperature dependent Hall effect measurements and 131 meV using admittance spectroscopy. Feng et al. 134 grew Si doped (010) β-Ga 2 O 3 homoepitaxial films using MOCVD with a record room temperature mobility of 184 cm 2 /V s; in their film, in addition to the primary shallow donor state with an activation energy of 34.9 meV and a concentration of 2.7 × 10 16 cm −3 , a secondary deep donor state with an activation energy of 120 meV and a concentration of 5 × 10 15 cm −3 was also found. Possible origins of the deep donor state at 120 meV could include antisites, interstitials, and impurities such as hydrogen or Si on the O h coordinated Ga2 site. The presence of such relatively deep donors and their ionization percentage at device operating temperatures could have an effect on the on-state resistance and breakdown voltage of rectifiers. 278 While the achievement of highly conductive doped Ga 2 O 3 is interesting on the one hand, the achievement of Ga 2 O 3 bulk crystals and particularly thin films with high carrier mobility and low defect density, on the other hand, is more crucial for FETs and RF rectifiers. 274,275 As reported by Ma et al., 237 the mobility in Ga 2 O 3 is limited at 220 cm 2 /V s by polar optical phonon (POP) scattering when the electron concentration is lower than 1 × 10 18 cm −3 and by ionized impurity scattering at high electron concentrations. Great efforts have been made to grow high crystalline quality and high mobility Ga 2 O 3 by minimizing the defect, dopant, and carrier concentration. Table II shows a summary of the room-temperature mobility vs carrier concentration for the state-of-the-art doped β-Ga 2 O 3 bulk single crystals and epitaxial thin films reported in the literature. It can be seen that the room temperature mobility for epitaxial thin films with lowest carrier concentration is close to the predicted theoretical limit of approximately 220 cm 2 /V s. Remarkably, Feng et al. 134 have recently grown high purity and high quality (010) β-Ga 2 O 3 homoepitaxial thin films with controllable scitation.org/journal/apm Si doping as low as 10 16 cm −3 using MOCVD. The films were found to exhibit record-high carrier mobilities of 184 cm 2 /V s at room temperature and 4984 cm 2 /V s at 45 K. The extracted compensation concentration was as low as 9.4 × 10 14 cm −3 , which is critical for controllable tuning of the doping concentration lower than mid-10 15 cm −3 . The Ga 2 O 3 films grown with high mobility and low compensation concentration are critical for developing highperformance lateral and vertical power devices with high critical fields. Another strategy to achieve high mobility is to use modulation doped β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 heterostructures to form a 2DEG at the interface. This is attributed to the spatial separation between ionized impurities and the 2DEG. The high mobility values allowed for the observations of the Shubnikov-de Haas (SdH) effect oscillations at cryogenic temperatures. 50 A record-high room-temperature channel mobility of 180 cm 2 /V s and a low temperature peak mobility of 2790 cm 2 /V s have recently been demonstrated. 50 Both the mobilities exceeded the highest experimental mobility values for bulk β-Ga 2 O 3 .
Doping of Ga 2 O 3 with transition metals (Nb, 269 Ta, 270 W, 350 Mo, 351 Fe, 352 Co, 353 and Cr 354 ) or rare-earth metals (Eu 355 and Er 354 ) has also received much interest. This is because, on the one hand, transition metals (e.g., Nb 5+ , Ta 5+ , W 6+ , and Mo 6+ ) have higher oxidization states and, in principle, each dopant donates more electrons than Si and Sn, minimizing scattering by ionized dopants in order to achieve the same level of carrier concentration. This has been demonstrated by the achievement of high mobility and conductivity of W 356,357 and Mo 358,359 doped In 2 O 3 and Ta 360 doped SnO 2 . One the other hand, transition metal doping (e.g., Co) may be of interest to achieve dilute magnetic semiconductors/oxides, and rare-earth metals (Eu) could improve the luminescence and electroluminescence properties. 355 Peelaers and Van de Walle 361 have performed DFT calculations on the viability of W, Mo, Re, and Nb as n-type dopants in Ga 2 O 3 . Their results show that Nb is the best candidate because it has a low formation energy (1.19 eV for T d Ga1 at the CBM and 0.31 eV for O h Ga2) and a small ionization energy (0.03 eV for T d Ga1 or 0.15 eV for O h Ga2 below the CBM), whereas W, Mo, and Re act as deep donors. Zhou et al. 269 have grown high quality β-Ga 2 O 3 bulk crystals with controllable Nb doping concentration by the OFZ method. It was proved that Nb is an effective n-type dopant for Ga 2 O 3 , and the carrier concentration can be controlled from 9.55 × 10 16 cm −3 to 1.8 × 10 19 cm −3 by tuning Nb doping concentration. Moderate electrical conductivity and mobility have also been achieved for Zr 270 and Ta 362 doping in Ga 2 O 3 bulk crystals. More experimental works should be done to explore the possibility of other transition metal dopants.

D. P -type doping in Ga 2 O 3
As mentioned earlier, p-type doping in wide bandgap oxide semiconductors including Ga 2 O 3 remains an outstanding challenge. 363,364 The challenge is due to the intrinsic electronic structure of oxide semiconductors; (i) the top of VB of most oxides mainly consists of strongly localized O 2p-derived orbitals, resulting in a large hole effective mass and, thus, low hole mobility; this means that most of the doped holes tend to be trapped by local lattices as small polarons, as opposed to the free holes that are delocalized in the valence band as in conventional semiconductors; (ii) the valence bands are deep in energy, and holes are easily compensated by defects such as Vo, leading to the low p-type dopability, and therefore, a shallow acceptor that can contribute to significant hole concentrations is still lacking. In simple chemical terms, p-type doping involves the introduction of holes into the O 2p states at VBM (i.e., oxidation of O anions), resulting in strongly localized, deep lying holes centered on single oxygen sites.
There are limited experimental works on the p-type doping of Ga 2 O 3 . Inspired by the success in GaN, Mg doping has received much attention, but the results are not conclusive. Chikoidze et al. 365 claimed the success of p-type conduction in Mg doped Ga 2 O 3 , as proved by combined Hall and Seebeck measurements, and photoemission and cathodoluminescence spectroscopies, but the ionization energy of the acceptor level was measured to be 1.1 eV above the VBM. Another study claimed p-type conductivity in Mg doped Ga 2 O 3 , but the as-grown materials were highly resistive, without hole carrier concentration and acceptor ionization energy being determined. 366 Other studies have found that Mg doping leads to semi-insulating Ga 2 O 3 367 and gave rise to sub-bandgap blue luminescence near 2.9 eV. 274 Zn is also a potential candidate for p-type doping in Ga 2 O 3 . Feng et al. 368 reported the fabrication of p-type Ga 2 O 3 nanowires doped with Zn, and the homojunction consisting of p-type doped nanowires and n-type Ga 2 O 3 substrates exhibited rectifying behavior. The cathodoluminescence spectra study suggests that the ionization energies for Zn doped Ga 2 O 3 are 0.25-0.5 eV which is relatively shallow and promising, but the films remained highly resistive. 182,369 Overall, achieving efficient p-type doping remains elusive. On the other hand, doping of acceptor impurities (e.g., Fe or Mg) has been used to reduce the background electron density in Ga 2 O 3 , e.g., to create insulating material. Semi-insulating Fe doped Ga 2 O 3 substrates are available commercially and are widely used for epitaxial thin film growth and device fabrication.
Extensive theoretical studies have also been done to understand the microscopic mechanism of p-type doping in Ga 2 O 3 . Early studies based on standard DFT calculations reported that Zn could lead to p-type conductivity. 370,371 However, it should be noted that DFT seriously underestimates the bandgaps and the extent of charge localization at defects, leading to difficulties in determining acceptor ionization energies. A later study by Kyrtsos et al. 271 using hybrid functional DFT (which provides a better bandgap description) suggested that Zn and other acceptors (Li and Mg) incorporated at the Ga sites have ionization energies in excess of 1 eV. The calculation by Varley et al. 372 also predicted that holes in Ga 2 O 3 can self-trap with a trapping energy of 0.53 eV, indicating that free holes are unstable and are spontaneously localized as small polarons. The localized hole states are consistent with the ultraviolet luminescence observed in undoped Ga 2 O 3 crystals. 274 EPR studies have also observed that the holes are trapped at nearest-neighbor oxygen sites of the Mg acceptors. 373 Nitrogen (N) has a similar atomic size as oxygen but has one less valence electron and a higher 2p orbital than oxygen. N has been explored as a dopant for other oxides such as ZnO but was theoretically found to have a large formation energy and ionization energies in excess of 2 eV 374,375 and cannot be an effective p-type dopant in Ga 2 O 3 . 376 The deep energies of N acceptors are caused by their defect states. It is found that N can form a variety of complexes with native defects, including Vo and Ga i , whose presence in N doped Ga 2 O 3 could compensate any p-type conduction. 372 This result suggests that the observed red-light emission originates from the recombination of an electron trapped on a donor due to Vo and a hole trapped on an acceptor due to N doping. 377 Very recently, Lyons 378 using hybrid DFT examined a large series of potential elements as acceptors in Ga 2 O 3 , including N, group 2 (Be, Mg, Ca, and Sr), and group 12 (Zn and Ca), as shown in Fig. 18. All the elements are found to exhibit acceptor transition levels above 1.3 eV. After examining formation energies as a function of chemical potential, Mg is determined to be the most stable acceptor species, followed closely by Be.
For summary, so far, there is no solid experimental evidence showing the achievement of high p-type doping in Ga 2 O 3 ; theoretical studies reach the consensus that the conventional acceptor doping approach gives rise to strongly localized hole states with larger ionization energies, prohibiting p-type conductivity. This is inherently caused by the localized nature of the O 2p-derived VB that leads to difficulty in introducing shallow acceptors and large hole effective mass. Learning from the design of p-type oxides, 379 a way to mitigate this problem is to use the hybridization of O 2p orbitals with closed-shell Cu 3d 10 orbitals and post-transition metal cations with filled lone pair states (ns 2 ), such as Sn 2+ (5s 2 ) and Bi 3+ (6s 2 ). 363,380,381 For example, because the s orbitals are generally spatially extended, it is, therefore, expected that their hybridization with O 2p states can result in lower effective mass. Sn in SnO 382,383 and Bi in Ba 2 BiTaO 6 384 have been proved to lead to a relatively high ptype mobility. Similarly, Sabino et al. 385 proposed based on hybrid DFT calculation that Bi doped Ga 2 O 3 , i.e., (Ga 1−x Bix) 2 O 3 solid solution, introduces a fully occupied intermediate VB that is significantly higher in energy than the original VB. This intermediate VB is composed mainly of Bi 6s and O 2p orbitals, providing the opportunity to achieve p-type doping in this system. It would be interesting to carry out experiments to prove this concept based on high-quality bulk crystal or thin films. Alternatively, Islam et al. 387 recently claimed that a remarkable hole density of 10 20 cm −3 can be achieved by incorporation of hydrogen at Ga vacancy position in the Ga 2 O 3 lattice. The hydrogen induced acceptor ionization energy is as low as 42 meV.
Very recently, Chikoidze et al. 386 reported an exciting result of the achievement of a hole mobility of 10 cm 2 V −1 s −1 and free hole concentrations of 10 17 cm −3 by annealing Ga 2 O 3 in oxygen atmosphere. The authors claimed that although p-type doping in Ga 2 O 3 has been considered impossible due to the flat VB resulting in a high hole effective mass, it has been also recently reported that the hole effective mass in Ga 2 O 3 is, indeed, fairly anisotropic and can be as low as 0.4 me for certain crystal orientations. It is particularly exciting to the research community that p-type Ga 2 O 3 is possible at least along some crystal directions. However, more research must be conducted to verify and determine its prospects for Ga 2 O 3 solar blind bipolar optoelectronics and high-power electronics based on p-n homojunctions.
On the other hand, as long as p-type Ga 2 O 3 remains elusive, combining n-type Ga 2 O 3 with existing wide bandgap p-type semiconductors such as p-GaN, SnO, NiO, Cu 2 O, Ir 2 O 3 , CuI, SiC, and diamond to form p-n heterojunctions would also be a compromising solution for vertical devices. Combining n-type Ga 2 O 3 with existing p-type GaN is promising for enabling next-generation highperformance transistors and optoelectronic devices. Attempts have been made to grow Ga 2 O 3 on GaN epi-layers 388,389 and directly grow GaN epitaxially on a Ga 2 O 3 single crystal substrate 10,39,40,390 for the fabrication of a high-responsivity UV photodetector. However, efforts need to be done to control the interface because of the incompatible growth of oxides and nitrides. 391,392 Diamond is also a particularly attractive candidate due to its range of highly desirable properties for power electronics including an ultra-wide bandgap of 5.5 eV, highest thermal conductivity, high electron and hole mobilities, and a high electric breakdown field. 393 P-type doping in diamond can be achieved either through conventional substitutional doping with boron (hole mobility of 2000 cm 2 /V s) 394 or by inducing on its surface through the so-called surface transfer doping process (hole mobility of 100-300 cm 2 /V s). 395  Over the past decades, tremendous progress has been made in the engineering of the bandgaps of semiconductors over a wide range by tuning the composition of semiconductor alloys that have the same crystal structure and similar lattice constants, as shown in Fig. 19. For example, the bandgaps of InxGa 1−x N and AlyGa 1−y N can be systematically tuned from 1.9 eV to 3.5 eV by varying the x value The thermodynamically stable phase of In 2 O 3 adopts a bodycentered cubic (bcc) bixbyite structure, with a lattice parameter of a = 10.117 Å. 407 The structure may be regarded as a 2 × 2 × 2 superstructure of fluorite with ordered removal of O from 1 / 4 of the anion sites, as shown in Fig. 20(b). In 3+ cations are O h coordinated by six O anions but with slightly different bonding lengths. The bixbyite In 2 O 3 has a fundamental bandgap of 2.9 eV but is optically forbidden; the optical bandgap with a strong absorption occurs at 3.75 eV. 284 In 2 O 3 is also a metastable polymorph of hexagonal corundum structure, with a lattice constant of a = 5.478 Å and c = 14.51 Å. The corundum phase In 2 O 3 has a direct bandgap of 3.0 eV. 408 Although the corundum In 2 O 3 is a metastable phase, it has been shown that it can be stabilized at the interface during the epitaxial growth of In 2 O 3 on Al 2 O 3 substrates. 409 As However, as mentioned above, different crystal structures and coordination bring frustration as for what is the preferred crystal structure as a function of x. For the bulk polycrystallines prepared by solid state synthesis 254 and thin films grown by PLD, 230,253 it was reported that (AlxGa 1−x ) 2 O 3 keep the monoclinic β-phase with Al contents up to x = 0.80. 410 With more Al content, the corundum structure is preferred. However, it should be noted that for the epitaxial thin films using MBE, the solubility of Al in (AlxGa 1−x ) 2 O 3 is restricted to x = 0.20. 51 The limited Al contents were attributed to the low growth temperature (<800 ○ C) during MBE growth, while incorporation of Al in Ga 2 O 3 lattice requires a temperature higher than 800 ○ C. 88,150 The lattice constants decrease linearly with an increase in the Al-content, consistent with the smaller atomic radius of Al compared to Ga. The linear decrease in lattice constant is in agreement with Vegard's law. The recent DFT calculations by Peelaers et al. 410 revealed more insights into the phase stabilities, lattice parameters, and electronic properties of (AlxGa 1−x ) 2 O 3 alloys. They found that the monoclinic phase remains energetically preferable for Al PERSPECTIVE scitation.org/journal/apm concentrations up to x = 0.71; for a higher Al content, a corundum structure is preferred, in close agreement with experimental phase diagrams. 230,253,254 More interestingly, it was found that the energetics strongly correlate with the preferred coordination environment of Al and Ga: Al atoms favor O h sites, which are the only coordination environments in corundum; in the monoclinic structure, half of the sites are O h coordinated and half of the sites are T d coordinated. Therefore, the x = 0.5 alloy (GaAlO 3 ) has a high stability with all Al atoms at the O h sites and all Ga atoms at T d sites.
As, expected, the bandgaps of (AlxGa 1−x ) 2 O 3 alloys can be tuned from the bandgap of β-Ga 2 O 3 (4.8 eV) to 6 eV with an increase in Al contents. Figure 21(b) shows the experimentally measured and DFT calculated bandgaps for the monoclinic and corundum (AlxGa 1−x ) 2 O 3 as a function of Al contents, adapted from Ref. 411. Good agreement is found between the calculated and experimental values. 410 The increased bandgaps would enable the realization of new applications in many devices such as FET, modulation-doped electron channels, and solar-blind photodetectors responsive to deeper UV bands. 412 For example, the larger bandgap of β-(AlxGa 1−x ) 2 O 3 would lead to an even higher BFOM than that of Ga 2 O 3 , which makes β-(AlxGa 1−x ) 2 O 3 a potential candidate for even higher power and higher frequency electronic devices. Kaun et al. 51 have grown (AlxGa 1−x ) 2 O 3 epitaxial thin films using MBE with composition up to x = 0.2. A preliminary report on β-(AlxGa 1−x ) 2 O 3 MESFETs shows a higher critical breakdown field than β-Ga 2 O 3 . 413 However, a low mobility of 4 cm 2 /V s in the grown β-(AlxGa 1−x ) 2 O 3 film results in a lower on-current in the device. Further work needs to be done to improve the crystal quality and mobility. Another very interesting use of β-(AlxGa 1−x ) 2 O 3 is as a barrier layer for β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 high electron mobility transistors (HEMTs). β-Ga 2 O 3 suffers from POP scattering which limits its maximum mobility to 220 cm 2 /V s. 237 Because of the larger bandgap of β-(AlxGa 1−x ) 2 O 3 , i.e., higher CBM, it is expected that electrons in (AlxGa 1−x ) 2 O 3 doped by Si would be transferred to the adjacent Ga 2 O 3 to form a 2DEG at the interface. The enhanced 2DEG sheet charge is predicted to screen out certain phonon modes, resulting in reduced scattering in the 2DEG channel. Theoretical studies predict that the 2DEG at the β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 interface has a mobility of about 500 cm 2 /V s, 414  While there is extensive research work in (AlxGa 1−x ) 2 O 3 alloys, the literature on (InxGa 1−x ) 2 O 3 ternary alloys is limited. In 2 O 3 (doped with 6% Sn, known as ITO) has been extensively investigated as a transparent electrode for flat panel displays, touch screens, and solar cells. The bandgap of In 2 O 3 has been widely quoted to be 3.75 eV, 415,416 which marks the onset of strong optical absorption. A weaker absorption onset at 2.62 eV has either been ignored or been attributed to indirect optical transitions. 417 In 2008, it was established based on XPS and DFT that In 2 O 3 has a direct but optically forbidden bandgap of around 2.9 eV. 284 The establishment of fundamental bandgap in turn leads to the identification of the surface electronic structure of In 2 O 3 , e.g., strong downward band bending and 2DEG at the surface of In 2 O 3 . 418-421 Alloying Ga 2 O 3 with In 2 O 3 offers the opportunity to tune the bandgaps from 4.8 eV to a lower value (2.9 eV) and also other material properties. However, similar to the (AlxGa 1−x ) 2 O 3 system, because Ga 2 O 3 and In 2 O 3 have quite different crystal structures, phase separation is expected. Shannon and Prewitt investigated the structural properties of (InxGa 1−x ) 2 O 3 powder and single crystalline samples for 0 < x ≤ 0.5 422 and found that a monoclinic β-phase structure was maintained. A complete phase diagram of (InxGa 1−x ) 2 O 3 alloys was established by Edwards et al., 423 using powder samples prepared by conventional solid state synthesis; they showed that the solubility of In 2 O 3 in Ga 2 O 3 maintaining a monoclinic structure is limited at x = 0.44, while on the In 2 O 3 side, the solubility limit for Ga in Most of the works also found that the lattice constants of (InxGa 1−x ) 2 O 3 increase linearly with an increase in the In content, [424][425][426] as expected from the larger cation size of In 3+ (0.79 Å) as compared to Ga 3+ (0.62 Å). As shown in Fig. 22(a), the increase in lattice parameters (a, b, c) is in agreement with Vegard's law. Epitaxial (InxGa 1−x ) 2 O 3 thin films have been prepared by a wide range of techniques including MBE, 425 MOCVD, 159 PLD, [427][428][429] and so on, but the reported solubility values are quite scattered depending on the growth techniques and growth conditions. Oshima 431 First-principle calculations were also performed to reveal more insights into the formation enthalpies, structural parameters, and electronic properties of the alloys. Maccioni and Fiorentini 432 showed that the solubility limit of In in Ga 2 O 3 was x = 0.1, significantly lower than the experimentally derived values of 0.43. Recently, Peelaers et al. 433 showed that a monoclinic phase is energetically favorable for x < 0.5. All In cations prefer occupying the O h sites because of their much larger size than that of Ga. In incorporation increases the local strain around the In cations, resulting in phase instability at higher In contents. A lower In content results in a partial occupation of the O h sites by Ga atoms. This effect may explain why the cation ordered GaInO 3 with all In at the O h sites and all Ga at T d sites similar to the case of GaAlO 3 were rarely synthesized and perhaps can only be synthesized at high pressures.
The incorporation of In in Ga 2 O 3 allows us to tailor the optical bandgap from 4.86 eV down to 4.1 eV in the range of x = 0-0.44. Thin films grown by the MBE, 425 MOCVD, 159 PLD, 427,428 and sol-gel method 430 have been measured using optical absorption spectroscopy. Figure 22(b) presents a few typical results from Refs. 13, 49, 170, 194, 238, 347, and 434. The bandgaps systematically decrease with an increase in the In content. 435 For x ≤ 0.3, the absorption edge depends linearly on x and can be fitted by Eg(x) = 4.90 eV − (2.42 × x) eV. Although the bandgaps have been deduced from optical absorption edges for higher x values (x > 0.44), bandgap bowing can be observed and can be fitted by Eg(x) = 4.87 eV − (2.16 × x) eV + (1 × x 2 ) eV for 0 < x < 1. However, it should be noted compositions for 0.44 < x < 0.90 produce mixed phases of β-GaInO 3 and bixbyite InGaO 3 . Furthermore, In 2 O 3 actually has a much smaller fundamental bandgap (2.9 eV) than the optical bandgap (3.7 eV). 284 Finally, it is interesting to note that the α-phase Ga 2 O 3 has the same corundum structure as Al 2 O 3 . All Ga cations are O h surrounded by six oxygen ions. The lattice parameters are a = 4.9825 Å and c = 13.433 Å. 82 Epitaxial thin films of α-Ga 2 O 3 can be stabilized by growing on α-Al 2 O 3 by mist-CVD at 430-470 ○ C. 83,172,245 The stabilization of the α-phase was attributed to the unique reaction path of this growth technique. The incorporation of Al contents up to 0.81 was reported by Ito et al. 171 The bandgap was increased from 5.3 eV to 7.8 eV. The thermal stability of the α phase is strongly enhanced due to alloying with α-Al 2 O 3 .
Moreover, the metastable corundum phase In 2 O 3 has the same corundum structure as α-phase Ga 2 O 3 . It has been shown that corundum In 2 O 3 could be stabilized by the Al 2 O 3 409 or Fe 2 O 3 buffer layer on Al 2 O 3 . 436 In the α-(InxGa 1−x ) 2 O 3 alloy system, a phase separation occurs for intermediate In admixtures. In Fig. 23, the bandgap energy of the experimentally realized solid solutions of Motivated by the successful epitaxial growth of ε-Ga 2 O 3 as well as κ-Ga 2 O 3 , Al and In alloying of these two unstable phases begins to come into the view of researchers. [438][439][440][441] Tahara et al. 438 first reported the Al 2 O 3 alloying in ε-Ga 2 O 3 using mist-CVD, with the Al content of ε-(AlxGa 1−x ) 2 O 3 reaching up to the value of x = 0.395 and bandgap tuned from 5.0 eV to 5.9 eV. In 2 O 3 alloying with ε-Ga 2 O 3 was also achieved by mist-CVD, and its bandgap could be controlled from 4.5 eV to 5.0 eV without phase separation. 439 Recently, alloying in κ-Ga 2 O 3 was reported by the researchers from Universität Leipzig. [440][441][442] A specially designed continuous composition spread (CCS)-PLD method was utilized to grow κ phase (AlxGa 1−x ) 2 O 3 and (InxGa 1−x ) 2 O 3 . For Al alloying, the Al content could be achieved to a remarkable value of x = 0.65 with a tunable bandgap value from 4.9 eV to 5.8 eV. 440 The In alloying was reported with a maximum content of x = 0.35 and the bandgap value varied from 4.3 eV to 4.9 eV. 442

VI. SUMMARY AND REMARKS
In this article, we provided a timely review on the semiconductor physics of Ga 2 O 3 in terms of electronic structures, optical properties, chemistry of defects and dopants, and bandgap engineering. Recent progress and fundamental understanding on the synthesis of bulk single crystals, epitaxial growth of thin films, chemical and physical properties of defects and impurities, deep level states, and origin of unintentional n-type doping, p-type doping, and ternary alloys with In 2 O 3 and Al 2 O 3 were reviewed.
In the past decade, a significant process has been made for the growth of high-quality bulk crystals and thin films of Ga 2 O 3 . 4-in. high quality β-Ga 2 O 3 (201) wafers grown by EFG with EPD on the order of 10 3 cm −2 were commercially available from Novel Crystal Technology, Inc. High quality β-Ga 2 O 3 homoepitaxial thin films, with record-high carrier mobilities of 184 cm 2 /V s and low carrier concentrations of 2.5 × 10 16 cm −3 , have been achieved by MOCVD. 134 This enables further scaling-up for mass production. Using Si, Sn, or Ge as dopants, electron carrier concentrations ranging from 10 16 up to 10 20 cm −3 can be controllably obtained. 13,49 Through modulation doped β-(AlxGa 1−x ) 2 O 3 /Ga 2 O 3 heterostructures to form a two-dimensional electron gas at the interface, a record-high room-temperature channel mobility of 180 cm 2 /V s and peak mobility of 2790 cm 2 /V s at 50 K have also been demonstrated. 50 The achievement in growing high quality bulk crystals and thin films has accelerated research progress in the fundamental understanding of semiconductor physics of Ga 2 O 3 and device optimizations. Similar to other oxide semiconductors such as ZnO, In 2 O 3 , and SnO 2 , Ga 2 O 3 exhibits unintentional n-type conductivity. The origin of the unintentional doping is still not clear. V O , H i , H O , Ga i , and impurities from the synthesis/growth processes have been proposed as possible sources. Based on more advanced hybrid DFT calculations and evidence from experiments, it appears that Vo is a deep level donor, unlikely contributing free electrons at room temperature, and Ga i has a high formation energy. Hydrogen and unintentional impurities such as Si are most likely the origins of unintentional n-type conductivity. Several studies reported the detection of Si residual (with ppm wt) even in 6N purity Ga 2 O 3 . Such a trace amount of Si can lead to a free electron density of ∼10 16 cm −3 . Furthermore, a trace amount of Fe impurity has also been detected in bulk crystals likely from the containers used for material growth. It is interesting to obtain Ga 2 O 3 precursors with an even higher purity, thus eliminating possible contaminations during the synthesis process to further reduce the background electron carriers. Several deep level states, including E 1 (E C -0.62 eV), E 2 (E C -0.82 eV), E 3 (E C -1.00 eV), E 4 (E C -2.16 eV), and E5 (E C -4.4 eV), have been detected in bulk single crystals and epitaxial thin films. These deep level states may be associated with the above-mentioned unintentional impurities (e.g., Fe) or defects (e.g., Vo and V Ga ) or may be the intrinsic properties of Ga 2 O 3 . The identification of their physical origins is an important task because these deep level states are associated with the breakdown voltage, specific on-resistance, and leakage in power electronic devices and may also be associated with the long delay times and persistent photoconductivity often observed in solar-blind photodetectors. It has been proved that Si, Sn, Ge, and Nb act as shallow dopants with activation energy in the range of 10-60 meV. The doping behaviors (conductivity, carrier PERSPECTIVE scitation.org/journal/apm concentration, mobility, activation, Fermi level, optical properties, etc.) can be understood by classic semiconductor physics. There are certain discrepancies regarding the electronic structure and substitution sites of the dopants, e.g., Si substitution at the Ga1 site may act as deep donors. More experiments based on temperature dependent transport measurement, EPR, photoluminescence, photoemission, x-ray absorption, and so on should be performed to clarify this point. It is a challenging task to achieve p-type doping in Ga 2 O 3 , which is inherently caused by the localized nature of the O 2p-derived VBM that leads to difficulty in introducing shallow acceptors but the ease of formation of localized polaron states. So far, there is a lack of strong experimental evidence proving the achievement of p-type doping in Ga 2 O 3 . Some new strategies have been proposed but remain to be further proved, such as to form a band using elements such as Bi 3+ and Sn 2+ containing ns 2 lone pair states or hydrogen substitution at the Ga position. One the other hand, integrating Ga 2 O 3 with other p-type semiconductors (p-GaN, SiC, and diamond) or oxides (NiO, Cu 2 O, and Ir 2 O 3 ) to form p-n heterojunctions would be a convenient solution. In particular, integration of Ga 2 O 3 with p-type diamond could open up new opportunities to develop high-performance and robust power devices. Being the best thermal conductor (thermal conductivity of diamond of 22 W cm −1 K −1 ), diamond can additionally help mitigate the low thermal conductivity of Ga 2 O 3 by dissipating heat from it, in a similar fashion as GaN-on-diamond power electronics in which diamond acts as a heat spreader. 443 However, there remain significant challenges in the direct growth of one on the other due to lattice mismatch and different crystal symmetries. Transfer of mechanically exfoliated Ga 2 O 3 nanomembranes on a diamond substrate provides an alternative approach to forming van der Waals-type heterojunctions, 444 but this procedure clearly poses limitation to practical applications. Despite Ga 2 O 3 having a small electron effective mass, the Hall mobility of Ga 2 O 3 is limited to 220 cm 2 /V s due to POP scattering and decreases with an increase in doping and defects due to ionized impurity scattering. 237 Besides the continuous efforts to further increase the quality of material growth, modulation doping using the β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 interface has been proved as a promising strategy to enhance the mobility. It is predicted that 2DEG at the interface can screen out certain phonon modes and a mobility of ∼500 cm 2 /V s can be achieved. 414 Bandgap engineering by alloying with Al and In results in an increase or reduction in the bandgap and offers new properties for the realization of enhanced device performance, such as increased bandgap for higher power electronic devices, forming heterostructures for high electron mobility devices and the design of wavelength selective photodetectors. However, because Al 2 O 3 , Ga 2 O 3 , and In 2 O 3 have quite different crystal structures, their ternary alloys adopt a variety of crystal structures with different solubility limits, which also leads to different optical and electronic properties. For bulk crystals, (AlxGa 1−x ) 2 O 3 keeps the monoclinic phase with x up to x = 0.80; a corundum structure is preferred with x > 0.80. The bandgap of (AlxGa 1−x ) 2 O 3 can be tuned from 4.8 eV to 6 eV. However, in the epitaxial thin films using MBE, the solubility of Al in (AlxGa 1−x ) 2 O 3 is restricted to x = 0.20 because the incorporation of Al in Ga 2 O 3 requires a higher temperature (>800 ○ C) than that required for the MBE growth. It was predicted that to avoid unwanted parallel conduction channels in MODFETs based on β-(AlxGa 1−x ) 2 O 3 /β-Ga 2 O 3 heterostructures and achieve a high performance modulation doping, a large CB offset of at least 0.47 eV is preferred, which requires a bandgap of 5.15 eV with an Al concentration of x > 0.2. 445 Increasing Al contents using other growth techniques (e.g., MOCVD and PLD) and demonstration of modulation doped devices remain to be explored. Furthermore, the as-grown β-(AlxGa 1−x ) 2 O 3 films still showed a low mobility of 4 cm 2 /V s, which results in a lower on-current in devices. Further work needs to be done to improve the crystal quality and carrier mobility. Alloying Ga 2 O 3 with In 2 O 3 has been less explored. In 2 O 3 in Ga 2 O 3 maintaining a monoclinic structure is limited at x = 0.44, which allows us to tailor the optical bandgap from 4.86 eV down to 4.1 eV. This would offer opportunity to realize selective optoelectronic devices from UV to deep-UV. Overall, the fundamental research on the alloys is still in its infancy and the realization of heterostructures and devices still awaits demonstration.
Finally, it is important to point out that although β-Ga 2 O 3 has been extensively studied, α-Ga 2 O 3 has the potential as the dark horse in Ga 2 O 3 research. Although it is a metastable phase, it can be stabilized by Al 2 O 3 substrates because of the same crystal structures and the small lattice mismatch. As a matter of fact, the only commercial Ga 2 O 3 device at present is the SBD fabricated using α-Ga 2 O 3 grown by mist-CVD and commercialized by FLOSFIA, Inc. In view of the material structure, α-Ga 2 O 3 with only O h coordinated Ga provides a more symmetric structure to achieve low defect density and possible higher mobility (300 cm 2 /V s). The corundum structure is more compatible with many other oxides and III-V semiconductors. α-Ga 2 O 3 can form solid solutions with Al 2 O 3 and corundum In 2 O 3 . FLOSFIA, Inc. and a group from Kyoto University recently reported that α-Ga 2 O 3 can form epitaxial p-n heterojunctions with corundum Ir 2 O 3 as an inversion layer. 122 Certainly, more attention should be paid to α-Ga 2 O 3 . 451