Review—Theory and Characterization of Doping and Defects in β -Ga 2 O 3

Gallium oxide ( β -Ga 2 O 3 ) is an emerging semiconductor with relevant properties for power electronics, solar-blind photodetectors, and some sensor applications due to its ultra-wide bandgap and developing technology base for high quality, melt-based substrate growth and thick, low-doped homoepitaxial layers. Of critical importance for the commercialization of this potentially important material is understanding of doping mechanisms in the monoclinic lattice, where two types of Ga sites and three types of O sites have been identiﬁed. A critical literature review of doping and defects of the monoclinic β -phase of gallium oxide is provided in this work. Theoretical fundamentals of both donor and acceptor doping in Ga 2 O 3 are reviewed. Advances in doping of epitaxial Ga 2 O 3 with a focus on molecular beam epitaxy and ion implantation are critically examined. As doping is fundamentally related to defects, particularly in this material, a review of defect characterization by optical and electrical spectroscopic methods is provided as well. P-type doping, one of the fundamental challenges for Ga 2 O 3 , is discussed in terms of ﬁrst-principles calculations and ion implantation of known acceptors such as Mg and N.

Gallium oxide is an ultra-wide bandgap semiconductor whose properties have been studied for almost seven decades, but only recently has Ga 2 O 3 gained significant attention as a material relevant for power electronics applications. [1][2][3][4][5][6][7] The monoclinic β phase is thermally stable with reported bandgap values in the 4.6-4.9 eV range, depending on the specific crystal orientation and measurement method. Its theoretically predicted critical field ranges from 6 to 8 MV/cm, i.e., more than twice that of other wide bandgap semiconductors such as gallium nitride and silicon carbide. Ga 2 O 3 can be doped n-type over nearly six orders of magnitude range (10 14 -10 20 cm −3 ). Phase purity of the In and Al ternary alloys has led to novel heterostructure devices with exceptional promise for future power switching devices. [8][9][10][11][12][13] Most of all, however, the low cost of high quality substrates grown from the melt has provided a rapidlygrowing technological foundation not seen since SiC substrate technology became commercially available almost 30 years ago. [14][15][16] This review article consists of several sections. First, we review the theoretical aspects of doping in Ga 2 O 3 based on density functional theory (DFT) electronic structure calculations. We then briefly review epitaxial layer doping, followed by ion implantation. Finally, a short review of the most relevant spectroscopic methods for Ga 2 O 3 characterization are discussed: photoluminescence, cathodoluminescence, and deep level transient and optical spectroscopy.

Theory of Doping Ga 2 O 3
Theoretical formalism.-In this section we review theoretical studies of dopant impurities and native defects in gallium oxide. Nearly all employed DFT, 17 which has for decades been the method of choice for describing the electronic structure of semiconductors. However, standard implementations of DFT seriously underestimate band gaps, which can make the quantitative prediction of dopant properties difficult, 18 especially in the case of an ultra-wide-band-gap semiconductor like Ga 2 O 3 . Moreover, these methods are not capable of correctly predicting charge localization at defects, which is of utmost importance when attempting to describe deep defect centers.
To overcome these issues, many theoretical studies of Ga 2 O 3 have employed hybrid density functional theory, such as the so-called HSE z E-mail: marko.tadjer@nrl.navy.mil functional. 19 Such methods mix exact exchange into the exchangecorrelation functional of DFT, resulting in a computationally feasible approach that is capable of quantitatively predicting semiconductor band gaps. 18 For Ga 2 O 3 HSE has been shown to provide an accurate band structure, 20 and to predict stable self-trapped holes 21 that have been verified by experiment. 22 Most studies discussed below employ the supercell method to study isolated defects within the periodic boundary conditions implemented in most commercially available DFT codes. Using this approach, defect formation energies are calculated. These energies can be used to determine the quantity of defects or impurities expected to incorporate under the appropriate growth conditions (temperature, pressure, etc.). 18 Since dopant formation energies explicitly depend on the chemical potentials of the involved species, these calculations can also provide information about how dopants will incorporate as growth conditions vary (e.g., going from O-rich to Ga-rich conditions). By determining the formation energies of relevant charge states, the thermodynamic transition levels of dopants can be calculated. These levels are equivalent to dopant ionization energies, and determine a dopant's effectiveness in producing free carrier concentrations. 18 In the following sections we discuss separately theoretical studies of n-type and p-type doping for Ga 2 O 3 . Gallium oxide features a dispersive conduction band comprised predominantly by Ga s states, and a number of efficient donor dopants are known. In contrast, the Ga 2 O 3 valence band is made up by O 2p states, and is virtually dispersionless. 20 This feature helps to explain the ineffectiveness of acceptors dopants in Ga 2 O 3 found in the studies discussed below.
n-type doping.-Using semi-empirical methods, early calculations of β-Ga 2 O 3 explored the role that oxygen vacancies (V O ) played in causing n-type conductivity. 23 Neutral vacancies gave rise to occupied defect states, which is usually a sign of deep defect behavior. Using the HSE hybrid functional, Varley et al. found that V O were deep donors, with ionization energies larger than 1 eV regardless of type of O site the vacancy occupies (Fig. 1). 24 These results indicate that oxygen vacancies will not be a source of conductivity, though they may still be present and act as sources of deep-level luminescence. Subsequent studies have reported that all native species, with the exception of gallium interstitials (Ga i ), are deep defects in Ga 2 O 3 . 25-27 Thus, native species will not be direct sources of electrical conductivity (although they could influence it indirectly, Figure 1. The conventional unit cell of monoclinic β-Ga 2 O 3 . The two inequivalent Ga sites (large spheres) and the three inequivalent O sites (smaller spheres) are indicated. The Ga sites are labeled as tetrahedral (Ga tetra ), corresponding to a Ga(I) site, and octahedral (Ga octa ), corresponding to a Ga(II) site. Reprinted Fig. 1 with permission from H. Peelaers and C.G. Van de Walle, Phys. Rev. B 94, 195203 (2016). Copyright 2016 by the American Physical Society. e.g., by acting as compensating centers). Although Ga i are shallow donors and could act as a source of n-type conductivity, recent calculations have reported these species are highly mobile, 28 in addition to having large formation energies under n-type conditions.
A number of different impurities have been predicted to be efficient n-type dopants in β-Ga 2 O 3 . 24 Hydrogen impurities were found to act as donors in gallium oxide, and can be present both as an interstitial species (H i ) and also as a substitutional donor on the oxygen site. The hydrogen substitutional (H O ) is most stable under O-rich conditions, as is the hydrogen interstitial (H i ), though its formation energy is moderate even under O-poor conditions. H i can also be trapped at and form stable complexes with acceptors such as gallium vacancies. 29 Since the hydrogen-vacancy complex has a lower formation energy than the bare vacancy, H can stabilize the presence of negatively charged cation vacancies, but also lowers their charge state through passivation.
Silicon, germanium, tin, chlorine and fluorine have also been investigated as potential donor dopants in β-Ga 2 O 3 . 24 Both fluorine and chlorine were found to be shallow donors when substituting on the oxygen site (F O and Cl O ), whereas silicon, germanium and tin were found to be shallow donors when incorporating on the gallium site. 24,30 Under both O-rich and Ga-rich conditions, F O had the lowest formation energy among all donors, indicating it should incorporate most easily into gallium oxide. Incorporation of cation-site impurities was found to be most favorable in Ga-rich conditions, and among those dopants considered the Si Ga donor had the lowest formation energy. 24 Transition metal impurities have also been explored as n-type dopants; 31 although W, Mo, and Re were found to be deep donors, Nb was found to be a promising shallow donor candidate.
Carbon impurities have also been predicted to be a source of n-type conductivity. 32 Although carbon could incorporate on the oxygen site and act as a deep acceptor, under more likely growth conditions the C Ga shallow donor was found to be most favorable. A subsequent study 33 disputed this finding, and found that C Ga was a deep donor that exhibited DX-like behavior. 34 However, it should be noted that in Ref. 33 a post hoc band-edge correction was employed, in contrast to the self-consistent hybrid functional approach employed in Ref. 32 First-principles calculations have also explored the vibrational and optical properties of n-type β-Ga 2 O 3 . Kang et al. have investigated electron-phonon scattering in donor-doped material, and reported that intrinsic anisotropic carrier mobility was small, and suggested that experimentally measured anisotropy 35 was due to other factors. 36 Furthermore, mobility reduction and high doping levels were attributed to compensating defects (such as gallium vacancies). Peelaers et al. also explored sub-band-gap absorption by free electrons in n-type doped β-Ga 2 O 3 . 37 Strong, polarized sub-band-gap free carrier absorption was reported, even for carrier concentrations as low as 10 19 cm −3 , which could lead to decreased transparency in heavily donor-doped gallium oxide.
p-type doping.-Holes have been predicted to self-trap in β-Ga 2 O 3 . 21 behavior that is well documented in wide-band-gap oxide semiconductors. 38 This means that holes are more stable localized as small polarons at a single O site, as opposed to being a free hole delocalized over a much larger region as in conventional semiconductors. The self-trapped hole was predicted to be 530 meV more stable than the free hole (the largest trapping energy among all oxides considered in Ref. 21), even in the absence of any defect or impurity. Negatively charged acceptors will bind strongly with positively charged free holes, and this result implies that no shallow acceptors will exist in gallium oxide (since with the added binding energy, the ionization energy of the acceptor will be even higher than 530 meV).
Recent calculations have explored the properties of a range of substitutional acceptor impurities in β-Ga 2 O 3 . 28,[39][40][41][42][43][44][45][46][47] Early studies reported that cation substitutional acceptors such as Zn could lead to p-type conductivity, 42,44,47 however these studies employed standard DFT that is known to underestimate charge localization at defects (and hence, acceptor ionization energies). Despite employing such methods, these calculations already found that impurities such as Cu and N lead to deep levels. 40,45,46 Kyrtsos et al. demonstrated that acceptor ionization energies increase significantly when employing a hybrid functional, and found that Li, Mg and Zn acceptors incorporating on the Ga site have ionization energies in excess of 1 eV. 41 Later work found that group-II cation-site acceptors had ionization energies larger than Mg (and all above 1.3 eV), and that they trapped localized holes at nearest-neighbor oxygen sites. 43 Very similar behavior for the Mg Ga acceptor has been observed in experiment. 48 Nitrogen impurities incorporating on the oxygen site (N O ) were calculated to have ionization energies in excess of 2 eV. The deeper nature of N O acceptors is caused by their defect states being derived from N 2p-like orbitals, as opposed to the cation-site acceptors whose properties derive from the polaronic O 2p-like orbitals. 43 The consensus among recent theoretical studies is that conventional doping approaches will not lead to p-type conductivity, since all acceptors are too deep to give rise to free holes. However, incorporating acceptor impurities can still be useful for controlling electrical conductivity (e.g., to create semi-insulating material). Varley et al. explored the properties of iron impurities, which are used explicitly for this purpose and are common impurities in Ga 2 O 3 . 39 They reported that iron incorporates readily on the gallium site, where it acts as an exceedingly deep acceptor with a level only 0.6 eV from the conduction band minimum. Moreover, Fe Ga has very low formation energy, especially under O-rich conditions. Peelaers et al. also considered deep acceptor doping, and considered N O (most stable under Ga-rich conditions) and Mg Ga (most stable under O-rich conditions). 28 Exploring diffusion mechanisms, Peelaers et al. found distinct migration behavior for N O and Mg Ga acceptors. Whereas Mg Ga diffuses easily via an interstitial mechanism, N O migrates via a N O -V O complex with a much larger migration barrier, making N O more immobile. 28 These results agree well with depth-resolved diffusion studies of Mg-and N-doped material. 49 Recent work has also demonstrated that Mg-H complexes are likely to form in Mg-doped gallium oxide containing hydrogen. 50

Doping in Epitaxial Gallium Oxide
As discussed in previous sections, β-Ga 2 O 3 has the distinct advantage being one of the few UWBGs that can compete with wide bandgap semiconductors such as GaN and SiC for power and radio frequency devices. For almost all applications, control of carrier concentration via doping with foreign impurities is essential. Either group Table I. n-type dopants, their donor level (E d ), carrier concentration (n), cell and growth temperatures and electron mobility (μ) for grown layer on (010) β-Ga 2 O 3 . Nb was doped using optical floating zone method.  24 Their calculation shows that Si and Ge prefer tetrahedral site (Ga(I)) while Sn prefers octahedral site of Ga (Ga(II)). While Si GaI has lower formation energy than Sn GaII for Ga-rich growth, they have almost same formation energy for O-rich growth. Among the previously mentioned discussed transition metals, Nb GaII has low formation energy and Nb doping control is demonstrated using optical floating zone. 31,51 Among different shallow donor impurities Si, Ge and Sn are most common n-type dopant in Ga 2 O 3 . Among them Si is predicted to be shallowest donor. 33 Table I summarizes most common shallow foreign impurity donors, their levels and MBE growth figure of merits. Gas phase oxidation in chemical vapor deposition growth and Si source oxidation in molecular beam epitaxy growth are the practical challenges for Si. Krishnamoorthy et al. demonstrated Si-delta doping by shuttering the Si source and controlled higher carrier concentration (6.8 × 10 19 to 1.7 × 10 20 cm −3 ). 11 Each donor dopant impurity has its own practical challenges. Recently, much research has been carried out on controlling electron concentration in the Ga 2 O 3 using these dopants. Sasaki et al. showed growth rate dependence on substrate orientation with maximum MBE growth rate along (010) directions. 52 Higashiwaki et al. demonstrated the first field effect transistors on (010) β-Ga 2 O 3 using Sn-doped epitaxial films. 1,53 Following these reports, most of the previous research on n-type doping were focused on (010) β-Ga 2 O 3 .
Han et al. investigated and compared Ge and Sn on (001) via MBE for the fixed Ga beam equivalent pressure (BEP) of 3.3 × 10 −8 Torr and Sn and Ge cell temperatures of 800 and 560°C, respectively. 54 It was shown that the Ge concentration decreases with increasing growth temperature above 675°C, however Sn concentration remains constant up to 800°C. This is important for the Al x Ga 1-x O 3 on β-Ga 2 O 3 heterostructures design for device applications as alloys of β-Ga 2 O 3 with Al 2 O 3 are generally grown at higher temperatures. It is also found that Ge incorporation saturates at Ge cell temperature over 700°C, however Sn doped layer can be grown at higher temperature (800°C) and was independent to the growth temperature. 54 At higher temperature formation of volatile Ge suboxides dominate and limits the incorporation into the film however it was not the case for Sn up to 800°C.
Defect free as grown β-Ga 2 O 3 is usually n-type, due to the presence of impurities. Thus, the insulating compensator doping of β-Ga 2 O 3 has been carried out using deep acceptor such as iron (Fe). Fe-doped semiinsulating substrates are available commercially. 55 Fe-derived levels are about 0.86 eV below the conduction band minimum. 13 Acceptor doping.-To have bipolar Ga 2 O 3 devices or effective field termination regions in power devices, the ability to dope p-type is required. Thus, exploring potential effective acceptors and the possibility of hole conductivity is very important. All probable acceptor dopants are at least 1.1-1.3 eV above conduction band maximum (CBM). Furthermore, the almost flat VBM results in high hole effective masses. Also, the formation of compensating donor oxygen vacancies and hole self-trapping are will impede p-type doping of β-Ga 2 O 3 . 13,28,43 Although claims of p-type conductivity on β-Ga 2 O 3 nano-wires by Zn doping, undoped and Mg-doped β-Ga 2 O 3 layers have been made, 61,62,63 p-type conduction appears to be very difficult.
In summary, n-type doping control in β-Ga 2 O 3 carried out using impurities such as Sn, Si and Ge has been studied most extensively to date. The choice of impurity dopant depends on the film growth system and device requirements. On the other hand, acceptor doping to get p-type carrier is very challenging, and it remains unclear whether it will be possible to demonstrate, either theoretically or experimentally. Rather, innovative heterostructure design appears to be a more fruitful approach for demonstrating Ga 2 O 3 -based bipolar devices.

Diffusion and Ion Implantation Doping in Gallium Oxide
Electronic device architectures depend on selective semiconductor doping. Early silicon technology at Bell Labs showed that diffusiondriven impurities can be used for emitter and base formation in bipolar transistors. 64 Ion implantation, on the other hand, relies on a high energy ion beam of a specified fluence, as opposed to the usual thermal diffusion kinetics of impurities in a material. This fundamental difference allows for much more precise control of impurity profiles, which in turn translates to smaller device footprint. Therefore, ion implantation has for decades been the standard method of selective doping control in semiconductor devices. In contrast, ion implantation in Ga 2 O 3 has been explored by a few groups primarily for the purpose of implanting Si to produce highly doped source and drain regions for low-contact-resistance ohmic contacts. To the authors' best knowledge, the first report of electrically active impurities in Ga 2 O 3 was by Peter and Schawlow in 1960, who showed Cr 3+ ions substituting Ga 3+ at the octahedral sites in the β-Ga 2 O 3 crystal. 65,66 In addition to the doping technology discussed in the previous section, here we review the progress made to-date in Ga 2 O 3 diffusion and ion implantation technology.

Donor diffusion and ion implantation: Si and Sn.-Doping by diffusion has been demonstrated by Zeng et al. using a spin-on-glass
with Sn concentration of 4 × 10 21 cm −3 and a 1200°C, 5 minute drive-in anneal. 67 The simulated and SIMS-measured profile of Sn were described by a simple exponential function D(T) = D 0 exp (−D E /kT) used to model interstitial diffusion of a single positively charged particle, 68 69 Annealing temperatures ranged from 700-1100°C in N 2 atmosphere, achieving activation efficiency (defined as the ratio of N D -N A measured by capacitance-voltage method near the Ga 2 O 3 surface to the total Si implantation dose) as high as 80 percent for the lowest implantation dose (10 19 cm −3 ) annealed at 1000°C. The implanted Ga 2 O 3 substrates were all of the (010) orientation and grown by the float-zone (FZ) method, with some samples having an additional 150 nm thick epilayer grown by molecular beam epitaxy. This early success in measuring low contact resistance using Ti/Au electrodes (4.6 × 10 −6 cm 2 ) resulted in a number of successful device demonstrations from the same group.
An important consideration for the viability of ion implantation in Ga 2 O 3 is the rate of diffusion of the different impurities, which can be where C is the impurity concentration and D is the diffusion coefficient. 70 Figure 3 compares the SIMS profiles of implanted Mg and N, showing that significant redistribution of Mg occurs even at 800°C, whereas N was relatively stable after and 1100°C anneal and could even be annealed at 1200°C. The significant thermal diffusivity of Mg required the use of N for the selective implantation required for a CAVET. 73,74 However, as pointed out previously, Mg is still a useful acceptor for achieving uniformly-doped semi-insulating Ga 2 O 3 .
It has also been observed that post-annealing treatments result in effective crystal lattice recovery caused by Mg and/or N ion implantation damage. 49,75 The availability of samples with intrinsically low free-electron concentrations and the development of ion implantation technology could therefore potentially create a unique opportunity to accomplish effective acceptor doping of Ga 2 O 3 . Figure 4 shows the low temperature CL spectra of (001) EFG β-Ga 2 O 3 samples implanted with 10 18 and 10 19 N/cm 2 dosages, and annealed at 900°C in oxygen atmosphere for 30 minutes. Note that the intensity of the CL spectrum of the sample implanted at lower dosage recovers quite well with the annealing procedure, consistent with considerable reduction of the implantation-induced defect concentration. A detailed study, including XRD and electrical characterization will be reported elsewhere. Despite the increase in resistivity and reduction of leakage current observed by Wong, no evidence of acceptor related emission bands were observed in the CL spectra of our samples. 49,75 These preliminary results are important for the potential high field management using guard rings or edge termination strategies. However, detailed research of various potential acceptors, as well as implantation and thermal annealing schedules must be investigated to find out if acceptor doping of Ga 2 O 3 can be achieved in practice.

Luminescence Studies of Gallium Oxide
Point defects (intrinsic, impurity related, and their complexes) and extended structural defects (dislocations, stacking faults, etc.) have long been associated with poor device performance. They are responsible for excess of dark current, noise, and reduced responsivity of detectors, and for reduced efficiency and operation lifetime in optical devices. Point defects and impurity complexes introduce parasitic current paths, decrease device gain, increase noise in electronic devices. At the same time they can increase threshold current, slope efficiency, and operation lifetime of laser diodes, and introduce instabilities in charge control in high-electrical-field devices. Therefore, to realize high performance devices, these defects must be detected and identified, and those correlated to specific poor device performance must be eliminated or reduced to the lowest possible concentrations. The effects related to extended defects are considerably reduced in bulk and  homoepitaxial films. Despite that, a handful of point defects have been detected in bulk β-Ga 2 O 3 by deep level spectroscopies. 76 Therefore, to achieve full control of the optical and electronic properties of homoand hetero-epitaxial device layers, these defects must be thoroughly investigated by employing various defect-sensitive techniques which can identify the defects responsible for device failure.
Luminescence is a well-established, highly-sensitive, noninvasive, and non-destructive technique to detect and identify native and impurity related point defects and their complexes in semiconductors. Characterization by luminescence involves the measurement and interpretation of the spectral distribution of recombination radiation emitted by the samples. Generated electrons and holes usually become localized or bound to an impurity or intrinsic defect before recombining. The identity of the localized center that they were bound can often be determined from the luminescence spectrum. Qualitative information about crystal quality can be inferred from the efficiency and line width of near-band-edge emission spectra, and impurities can sometimes be identified based on the binding energies inferred from the spectral positions and free-to-bound transitions. In general, due to the presence of various radiative and/or non-radiative recombination processes competing for the generated electron-hole pairs, luminescence processes alone cannot be conveniently used as a reliable quantitative technique.
If electrons and holes are generated by the absorption of photons, the process is called photoluminescence (PL). But, if these carriers are created by kinetic energy transfer from an electron-beam to the semiconductor lattice, the process is named cathodoluminescence (CL). While one absorbed photon creates one electron-hole pair, one impinging electron will create multiple electron-hole pairs depending on its kinetic energy. In case of wide bandgap semiconductors, because of the large activation energies, which are beyond the reach of common exciting light sources, CL has become the method of choice to investigate the defects that control the optical and optoelectronic properties of such materials. 77 Another advantage of CL spectroscopy is the depth-profiling capability, easily accessed by increasing the impinging electron-beam (E-beam) energy. 78 CL depth-profiling is extremely useful in the study of activation of implanted dopants, thermal annealing lattice recovery, and multi-layered structured materials.
Low temperature (4-6K) CL spectra of high crystalline quality bulk β-Ga 2 O 3 grown by edge-defined film-fed (EFG) method are depicted in Fig. 5. 8 These spectra were excited with a beam accelerating voltage and current of 3 keV and 3 μA, respectively. The light emitted by the samples, mounted on a continuous liquid-helium flow cold-finger cryostat placed in a UHV chamber, collected by a combination of f-number matching mirror and lens, was analyzed by a compact fiberoptical CCD spectrometer.
The spectra of as grown β-Ga 2 O 3 shown consistently lack of near band-edge emissions, but they show frequently a broad emission band made of three major emission bands, in the spectral range between 2.3 and 4.5 eV. Similar spectral intensity distributions are also observed in homoepitaxial films deposited by metal-organic chemical vapor deposition and hydride vapor phase epitaxial. 10,79 In nominally undoped EFG samples, similar to those discussed in this work, Onuma et al. 80 reported that the UV emission bands at 3.2, 3.4 and 3.6 eV dominate at low temperatures, while at room temperature the blue (2.8 and 3.0 eV) and green (2.4 eV) bands were more prominent. Si-doped EFG samples showed only the UV bands. 80 Yamaga et al. 81 suggested that the blue emission occurs through recombination of self-trapped holes 21 and electrons trapped at single oxygen vacancies. More recently, CL studies performed on neutron-irradiated or remote oxygen plasma treated bulk EFG samples and epitaxial Ga 2 O 3 films grown by various methods suggested that this broad band may be fit with four Gaussian lines with peaks around 2.5, 3.0, 3.5, and 3.8 eV. In this study, the 2.5 and 3.0 eV emission bands were tentatively attributed to V Ga -related defects, while the 3.5 eV emission band was assigned to V O -related defects. 82 The unambiguous identification of these defects are critical for achieving full material control, Luminescence studies of Mg-and Zn-doped β-Ga 2 O 3 leads to semi-insulating samples with sub-bandgap emission bands near 2.9 eV, and 2.4 and 2.8 eV, respectively. Both Mg and Zn were reported to contribute to the blue luminescence intensity consistent with deep acceptor levels (2.8-2.9 eV), whereas the ultraviolet emission intensity was independent of dopant concentration. 80,83,84 Finally, luminescence studies of rare earth ions (Er, Eu, Gd) implanted into nanowires and single crystals of Ga 2 O 3 have been performed in order to study the optical response of these materials for potential applications as optical devices in the ultraviolet regime. [85][86][87] Luminescence effects of implanted Cr and Mn were recently reported as well. 88 Finally, the amorphisation effects of implanted P, Ar, and Sn were quantified using Rutherford backscattering. 89

Deep Levels in Gallium Oxide
To characterize defect states within the entire ultra-wide bandgap of Ga 2 O 3 , a combination of both thermal and optical-based measurement techniques need to be employed. The use of deep level transient spectroscopy (DLTS), which relies on thermal emission rates of trapped charge, provides sensitivity only within ∼1 eV of the majority carrier band edge. 90 To measure defect states deeper inside the bandgap, optical techniques, such deep level optical spectroscopy (DLOS), which can interrogate deep levels all the way to the valence band of Ga 2 O 3 . 76 must be employed.
The ultra-wide bandgap, complex monoclinic structure, and the relatively immature material growth technology of Ga 2 O 3 translate to a large number of defect states that can potentially exist. Defects have been shown to degrade the performance of Ga 2 O 3 devices, and can be observed as threshold voltage instability and dynamic on-resistance in field effect transistors. 91,92 It is critical to understand the origin of these defect states that adversely affect device performance. Also, some defects are intentional dopants, and are incorporated into the crystal to serve a specific role, such as Si for low contact resistance 69 or Fe for forming semi-insulating material. 93 Deep level optical characterization can aid in understanding the effectiveness of dopant incorporation and activation. It is important to understand which defects depend on material growth method and crystal orientation and which defects are intrinsic or extrinsic, and so on.
An example of where DLOS and DTLS were performed on EFG UID (010) Ga 2 O 3 substrates resulted in five distinct defect states illustrated in Fig. 6 (left). 76 These five states states detected were located at E C -0.62 eV, 0.82 eV, 1.00 eV, 2.16 eV, and 4.40 eV, with the E C -0.82 eV and E C -4.40 eV states having the highest concentration. According to Zhang et al., the state located near E C -0.82 eV is assumed to be attributed to Sn Ga . 94 or V O . 24 However, it is also possible that the E C -0.8 eV level is due to Fe Ga . 39 Another EFG UID (010) Ga 2 O 3 sample showed similar defect signature as grown, but was then exposed to neutron irradiation. 95 Figure 6 (right) shows the E C -0.8 eV and E C -4.4 eV levels were not impacted by the irradiation, whereas there was an increase in the E C -1.03 eV and E C -2.00 eV state, as well as an introduction to a new state at E C -1.29 eV. Capacitance-voltage measurements showed that the irradiation created a reduction in carrier concentration, indicating the radiation induced defects contributed as compensation centers.
As discussed earlier, compensating defects formed by dopant incorporation were demonstrated by co-doping with Si and N in halide vapor phase epitaxy (HVPE) grown Ga 2 O 3 . 10 The N acceptors were determined to compensate Si donors, which resulted in low free carrier concentration films. Photoionization spectroscopy is a technique useful in characterizing traps in semi-insulating materials shows an acceptor-like state located at E C -0.23 eV (Fig. 7b) in the Si and N co-doped sample, which is not observed from measuring a reversebiased Schottky diode with an unintentionally Si-doped HVPE drift layer (Fig. 7a).

Summary
In this review, we have summarized advances in the theory and growth of doped monoclinic β-Ga 2 O 3 structures. Special attention was paid to focus on doping-related issues, as published reviews of this rapidly re-emerging material so far have not fully encompassed this critically important topic. The theoretical portion of this review considered donor and acceptor impurities, including commonly found impurities such as hydrogen and carbon. Defects such as the oxygen vacancy are not expected to contribute to conductivity even if present as deep energy levels in luminescence studies. Acceptors, even if not expected to produce room-temperature p-type Ga 2 O 3 , are still useful for producing semi-insulating material. Ion implantation of Ga 2 O 3 is still in early stages of development. Both donor (Si and Sn) and acceptor (Mg and N) implantation studies have been published. The large diffusion coefficients implanted species (Si and Sn) as well as Fe introduced in EFG Ga 2 O 3 substrates during growth, have been documented. Several studies of deep levels in Ga 2 O 3 have been performed. Photo and catodoluminescence studies, as well as deep level transient and optical methods, reveal a number of deep levels in Ga 2 O 3 . Even though the controllable doping range of Ga 2 O 3 already is remarkably wide (10 14 −10 20 cm −3 ), much more exploratory work remains to be done, particularly as material quality improves and new doping techniques are discovered. Of the possible applications for this material, photodetectors and high power devices are most sensitive to the quality of substrate and epitaxial material used in device fabrication. Thus, doping and defect science are indelibly linked for the foreseeable future, particularly in the emerging field of ultra-wide bandgap semiconductors.