Perspective on comparative radiation hardness of Ga₂O₃ polymorphs

Gallium oxide (Ga₂O₃) is currently attracting much interest for future generations of high-power electronics^1–6 as well as solar-blind UV photodetectors.^7–13 The four polymorphs of Ga₂O₃ most investigated are trigonal (α), monoclinic (β), cubic (γ), and orthorhombic (κ). Each of these polymorphic forms exhibit distinct structural and electronic characteristics^13–41 and they transform into the beta phase at specific temperature ranges. The order of decreasing stability under standard conditions is listed below:^{24,25,28,30,33,42–44}

1. β-Ga₂O₃: the most thermodynamically stable phase under normal conditions.

2. α-Ga₂O₃: this phase has a corundum structure like Al₂O₃ and is more stable under high-pressure conditions.

3. κ-Ga₂O₃ is a metastable phase with an orthorhombic structure. It is closely related to ɛ-Ga₂O₃, another metastable phase with a hexagonal structure.

4. γ-Ga₂O₃ is a metastable phase with a defective spinel structure.

The stability order can change under different conditions, such as high-pressure or specific growth conditions. Especially, the exact order of stability among ɛ, κ, and γ can sometimes vary depending on the specific study.^{34,36,39–41} A summary of their properties is shown in Table I, while Fig. 1 shows the lattice structures and high-resolution images of these four polymorphs. More is known about the response of the β phase to radiation than the other polymorphs.⁴² The ability to grow high-quality β-Ga₂O₃ bulk crystals using melt growth methods lowers the cost of production relative to SiC, AlN, or diamond.⁴² The metastable phases α, γ, and κ-Ga₂O₃ also present unique properties, such as strong polarization and ferroelectric characteristics for the latter polymorph.⁴⁴ The α phase has the largest bandgap and the highest critical electric field. γ-Ga₂O₃ is the least stable of the main polymorphs; however, it shows similar stability to the β phase under Ga-deficient conditions. This transition occurs under ion irradiation to produce high vacancy concentrations ([V₃−Ga] > 3%) at room temperature.^23,28–32 The β → γ transformation occurs via simultaneous migration of Ga atoms from tetrahedral lattice sites to octahedral interstitial positions.^30,36 The transformation barriers are large in undamaged Ga₂O₃ but are reduced by the presence of high concentrations of Ga vacancies.^{28,30,34,36,44}

The γ-phase contains these high Ga vacancy concentrations that maintain the stoichiometry of Ga₂O₃, through partial Ga occupancy at tetrahedral and octahedral sites.^28,30,34,36 These properties have led the γ-phase to be classified as the most radiation-hard of all semiconductors in terms of resistance to amorphization under ion irradiation conditions.⁴⁴  Figure 2 shows how the different polytypes transform back to the β-phase at different ion irradiation or annealing conditions.

One thrust of Ga₂O₃ research has been increasing the bandgap through alloying with Al₂O_3.^22,45–48 Such (Al_xGa_1−x)₂O₃ alloys are attractive since they have a range of tunable bandgaps from 4.6 to 8.6 eV. The differences in the crystal structure and the lattice constant from pure Ga₂O₃ to pure Al₂O₃ require careful strategies for alloying. One approach is to use the monoclinic β-(Al_xGa_1−x)₂O₃ polymorph, the stable phase for pure Ga₂O₃.^44–48 The widest composition range demonstrated in this approach is 0 ≤ x ≤ 0.61. This corresponds to a bandgap range of 4.6–5.9 eV.⁴⁶ The other option is the α-(Al_xGa_1−x)₂O₃ system, the stable phase for pure Al₂O₃. This has demonstrated alloying over the entire composition range,⁴⁶ corresponding to bandgaps of 5.4–8.6 eV. At the high-Al composition range, the bandgaps achievable are larger than both AlN (6.0 eV) and diamond (5.5 eV).

Of strong interest are the relative radiation hardnesses of the different polymorphs and heterojunctions with oxides like NiO. The latter is used to provide a p–n junction in the absence of facile p-type doping in Ga₂O₃.^49–58 It is important to note that device radiation hardness differs from semiconductor radiation hardness. The latter is generally considered to be the threshold ion dose at which amorphization occurs under ion irradiation and is based on the measured lattice damage. The device radiation hardness considers the degradation in electrical properties of the semiconductor after radiation exposure. If all the carriers in the active channel of the device are removed by trapping into the defects created by radiation damage, then obviously, the device is no longer operational. A key parameter to measure in this regard is the carrier removal rate, or number of carriers removed per incoming unit of radiation.⁵⁹ 

Another parameter of interest is the carrier diffusion length.^59–61 The minority carrier diffusion length (L) in a semiconductor is a crucial parameter that dictates how far, on average, a minority carrier can travel before it recombines with a majority carrier. The minority carrier diffusion length (L_D) is mathematically expressed as $L D= ( D τ )$⁠. D is the diffusion coefficient of the minority carriers. This coefficient is related to the mobility (μ) of the carriers by the Einstein relation: D = (k_BT/q)μ, where k_B is Boltzmann’s constant, T is the absolute temperature, and q is the elementary charge. So, higher mobility leads to a larger diffusion coefficient and, thus, a longer diffusion length. τ is the minority carrier lifetime. This represents the average time a minority carrier exists before recombining. A longer lifetime directly translates to a longer diffusion length.

Radiation, particularly high-energy particles of electrons, protons, or neutrons, can significantly degrade the minority carrier diffusion length. The primary mechanism for this degradation is the creation of defects and traps within the semiconductor lattice. This trap formation has been the subject of extensive study in the literature for Ga₂O₃.^63–88 Radiation displaces atoms from their lattice sites, creating vacancies and interstitials. These defects act as recombination centers, reducing the minority carrier lifetime. Radiation can also create traps, which are energy levels within the bandgap that can temporarily capture carriers. Trapping also effectively reduces the time a carrier is free to move, thus reducing the effective lifetime and diffusion length.⁸⁹ 

The reduction in minority carrier lifetime due to radiation-induced defects directly leads to a decrease in the diffusion length. The degradation of minority carrier diffusion length has significant implications for semiconductor devices, especially those operating in radiation-rich environments (like space or nuclear facilities). Understanding the relationship between minority carrier diffusion length and radiation-induced defects is crucial for designing radiation-hardened semiconductor devices.

In this paper, we discuss the comparative changes in carrier removal rate and minority carrier diffusion length in the different polymorphs of Ga₂O₃ because of exposure to different types of radiation. While it is difficult to precisely compare radiation hardness directly in the sense, many of the samples reported in the literature have different doping and growth methods,^41,59,86 and some conclusions can be drawn. In particular, rectifiers have generally been used as the device platform in these studies since they allow a fairly direct measurement of both carrier removal rate and minority carrier diffusion length. A schematic of a typical rectifier and the change of reverse breakdown voltage, which depends on carrier concentration changes and defect density induced by radiation damage, is shown in Fig. 3.

Another aspect we cover is the change radiation response when Ga₂O₃ is combined with p-type NiO in a heterojunction.^49–58 While these provide the basis for improved rectifiers with higher breakdown voltage and temperature stability relative to conventional Schottky rectifiers, the presence of NiO does raise issues as to differences in radiation response, since oxides typically are prone to more changes in radiation environments.^90,91

The common deep-level defects in epi and bulk β Ga₂O₃ include E1 (E_C – 0.60 eV) and E2 (E_C – 0.80 eV).⁶⁸ Trap E1, with ambiguous origins, is weakly influenced by irradiation, while E2, commonly associated with Fe impurities (Fe_Ga), is prevalent in both bulk and epitaxial materials. E2 likely comprises sublevels E2a and E2b, linked to Fe in tetrahedral or octahedral sites. Trap E2* (E_C – 0.75 eV) is attributed to intrinsic defects like V_Ga or Ga_O, with concentrations increasing under radiation damage.^67,71 Other notable traps include E3 (E_C – 1.0 eV), potentially linked to Ti_GaII, and E4 (E_C – 1.2 eV), associated with native defects and sensitive to proton irradiation.^67,70 High-energy traps like E6 (E_C – 2 eV) and E8 (E_C – 4.4 eV) are linked to vacancies or complex defects, while shallow donor traps like E10 (E_C – 0.20 eV) are attributed to Si_GaII substitution.^68,71

The study of deep-level defects in Ga₂O₃ is particularly focused on their behavior under high-energy irradiation, given the material’s radiation-hard properties.^92–113 However, the impact of other stress factors, such as high temperatures or electric fields, remains largely underexplored. Traps like E9 (E_C – 0.40 eV) and EN (E_C – 3.1 eV) are associated with intrinsic defects and nitrogen acceptors, respectively.^67,70 Minority carrier traps, such as H1, H2, and H3, have also been identified, with H3 tentatively linked to gallium vacancies. Despite significant progress, the origins and mechanisms of many deep-level defects remain unclear, necessitating further research to clarify their roles in device performance and radiation tolerance.^68,71

The relation between charge and electric field (Poisson’s equation) and transport (drift/diffusion) equations in devices such as rectifiers or transistors depends on carrier mobility and density. Radiation exposure creates traps that remove carriers from the conduction process and degrade mobility, i.e., n and μ are reduced.⁸⁹ 

It is important to note that, virtually, all quoted values for the carrier removal rate in the literature are approximate because it is usual to simply measure carrier loss at one dose condition. To get an accurate value, it would be necessary to demonstrate that the carrier loss scales linearly with the dose over the experimental range. In lightly doped layers, the doses needed to cause sufficient traps to remove most carriers are also low, whereas in heavily doped layers, such doses would not cause a significant change in conductivity. While the values in the literature are not precise, they still give an estimate of the true carrier loss that is valuable in determining the radiation doses that can be tolerated by a particular device.⁵⁹ In this review, we will show a compilation of all reported literature values for the different polymorphs and also a collection of values collected under conditions where a comparison between polymorphs is valid.

The carrier removal rates at low proton energies in β-Ga₂O₃ are usually lower than those predicted based on the Stopping and Range of Ions in Matter (SRIM) calculations of V_Ga density due to dynamic annealing. For energies, ∼10–20 MeV experimental values are close to the calculated values. At very high proton energies, the actual removal rates are higher than those predicted. The removal rates in β-Ga₂O₃ for protons and neutrons are on par with those reported for n-GaN and n-SiC.¹⁰² 

Protons account for above 80% of all space radiation particle species and, therefore, are a favored species for radiation damage studies. Point defects introduced by proton damage create trap states that reduce the carrier concentration in Ga₂O₃,^92–109 with a carrier removal rate of 236 cm⁻¹ for protons at 10 MeV.^92,93 Annealing at 300 °C produces a recovery of approximately half of the carriers in Ga₂O₃, while annealing at 450 °C almost restores the original reverse breakdown voltage. The minority carrier diffusion length decreased from ∼340 nm in the starting material to ∼315 nm after proton irradiation. The carrier mobility decreased by 73% with a fluence of 2 × 10¹⁵ p/cm².

Li et al.¹⁰⁵ studied the effect of 300 MeV proton irradiation on β-Ga₂O₃ Schottky barrier diodes. This irradiation caused reductions in forward current, breakdown voltage, and carrier concentration. Yue et al.¹⁰⁶ measured a carrier removal rate of 335 cm⁻¹ for 3 MeV proton irradiation of β-Ga₂O₃ p–n diodes without bias and the trap concentration also increased significantly.

Polyakov et al.^64,67,69 showed that proton irradiation caused the diffusion length of charge carriers to decrease from 350–380 to 190 μm for a fluence of 10¹⁴ cm⁻². This correlated with an increase in the density of hole traps with optical ionization threshold energy near 2.3 eV. These defects most likely determine the recombination lifetime in Hydride Vapor Phase Epitaxy (HVPE) β-Ga₂O₃ epilayers. The electron traps at E_c – 0.75 eV and E_c – 1.2 eV present in the as-grown samples increased in density after irradiation and indicate that these centers involve native point defects.

Wang et al.¹¹¹ reported degradation and trap evolution in NiO/β-Ga₂O₃ heterojunction pn diodes under on-state electrical stress. Reductions in turn-on voltage and forward current correlated with an increase in the density of compensating acceptorlike traps at E_V + 1.3 eV. These were attributed to Ga vacancy complexes with hydrogen (V_Ga–H).

Yue et al.⁹⁹ examined the synergistic effects of simultaneous reverse bias stress and 3 MeV proton irradiation on β-Ga₂O₃ p–n diodes. The forward current density decreased with proton fluence. The acceptorlike traps at E_c – 0.75 eV ascribed to Ga vacancy-related defects were the main reason for device degradation since these produce carrier concentration reduction. Biasing at −100 V during irradiation doubled the decrease in forward current density. The presence of the electric field caused the carrier removal rate to increase from 335 to 600 cm⁻¹.

Li et al.¹⁰¹ reported that 17 MeV proton irradiation at fluences from 3 to 7 × 10¹³ cm⁻² of NiO/β-Ga₂O₃ heterojunction rectifiers produced carrier removal rates of 120–150 cm⁻¹ in the drift region. The forward current density decreased by 100× for the highest fluence, while the reverse leakage current increased by a factor of ∼20.

Low-temperature annealing approaches for reducing radiation damage is of interest in such devices where thermal annealing is not feasible at the temperatures needed to remove defects. While thermal annealing has previously been shown to produce a limited recovery of damage under these conditions, athermal annealing by minority carrier injection from NiO into Ga₂O₃ produced an increase in forward current and partial recovery of the proton-induced damage. Since the minority carrier diffusion length is 150–200 nm in proton irradiated Ga₂O₃, it is not possible to cause recombination-enhanced annealing of point defects through a 10 μm thick drift region. Therefore, we suggest that electron wind force annealing occurs.

Manikanthababu et al.¹⁰³ reported on Ni/β-Ga₂O₃ Schottky barrier diodes measured in situ during the irradiation by 120 MeV Ag⁷⁺ ions over a fluence range of 10¹⁰−10¹² ions cm⁻². The Schottky barrier decreased from 1.11 to 0.93 eV with the ideality factor increasing from 1.16 to 2.06. The reverse leakage current increased by four orders of magnitude after irradiation.

Li et al.¹⁰⁵ showed that 15 MeV proton irradiation of NiO/β-Ga₂O₃ heterojunction rectifiers reduced the reverse breakdown voltage from 4.3 to 3.7 kV at a fluence of 10¹³ ions cm⁻² and 1.93 kV at 10¹⁴ ions cm⁻². The forward current density decreased by one to two orders of magnitude, with an increase in on-state resistance R_ON. The mechanism is a reduction in carrier density and mobility in the drift region. The reverse leakage current was increased by ∼2× for the highest fluence. Postirradiation annealing to 400 °C also increased reverse leakage due to deterioration of the contacts. The initial electron concentration of 2.2 × 10¹⁶ cm⁻³ was basically restored by this anneal for the lower fluence condition. In the higher fluence sample, approximately half of the carrier loss was restored by annealing. The carrier removal rates were 190–1200 cm⁻¹, independent of whether Schottky rectifiers or NiO/Ga₂O₃ heterojunctions were used.

Yue et al.¹⁰⁷ reported on the effect of neutron irradiation on β-Ga₂O₃ Schottky barrier diodes. After equivalent 1 MeV neutron irradiation at a fluence of 10¹⁴ n/cm², the devices exhibited a 20% lowering of forward current density, 75% lowering of reverse current density, and an increase of 300 V in breakdown voltage. The interface state density at the Pt interface with Ga₂O₃ increased from 2.6–6.4 × 10¹² to 2.9–7.0 × 10¹² cm⁻² eV⁻¹. Similarly, the trap activation energy increased after neutron irradiation from 0.09–0.122 to 0.096–0.134 eV. The carrier density in the drift region reduced from 1.80 × 10¹⁶ to 1.35 × 10¹⁶ cm⁻³.

Polyakov et al.⁶⁹ examined the effects of pulsed neutron irradiation on Si doped, n-type β-Ga₂O₃. This irradiation produced a linear increase with neutron fluence of the concentration of traps E2* (E_c−0.74 eV), E3 (E_c−1.05 eV), and E4 (E_c−1.2 eV). The introduction rate of these traps was 0.4–0.6 cm⁻¹. Neutron irradiation did not alter the density of the E2 traps (E_c−0.8 eV) due to Fe. Deep traps with an optical ionization threshold of 1.3, 2.3, and 3.1 eV were induced by neutron damage at the introduction rates of 0.8–2 cm⁻¹. The carrier removal rate was 28 cm⁻¹ and the carrier diffusion length got reduced.

Li et al.⁹⁴ found that NiO/Ga₂O₃ heterojunctions exposed to 1 Mrad fluences of Co-60 γ rays with or without reverse biases produced a three orders of magnitude reduction in forward current and a two orders of magnitude increase in reverse current, independent of whether bias was present during irradiation. The on–off ratio was lowered by five orders of magnitude by irradiation. The effective carrier removal rate was <4 cm⁻¹ in the drift region. All radiation-induced changes could be reversed by the application of short forward current pulses, showing there were no permanent total ionizing dose effects produced.

Polyakov et al.⁶⁷ showed that the irradiation of α-Ga₂O₃ with protons at energies of 330, 400, and 460 keV at a fluence 6 × 10¹⁵cm⁻² or with 7 MeV C⁴⁺ ions at a fluence of 1.3 × 10¹³ cm⁻² produced a conducting layer at the maximum of the ion distributions. Deep traps at E_c – 0.25, 0.8, and 1.4 eV were induced and ascribed to Ga vacancies, gallium–oxygen divacancies V_Ga–V_O, and oxygen vacancies V_O.

Polyakov⁶⁹ showed that α-Ga₂O₃ (Sn) doped in the range 5 × 10¹⁵–8.4 × 10¹⁹ cm⁻³ irradiated with 1.1 MeV protons at fluences of 10¹³–10¹⁶ cm⁻² showed carrier removal rates of ∼35 cm⁻¹ at 10¹⁴ cm⁻² and ∼1.3 cm⁻¹ for 10¹⁵ cm⁻². This shows how ostensibly the carrier rate can vary over a wide range depending on doping, unless it is a verified one operating in the linear region where carrier loss is proportional to fluence. These removal rates were produced by the introduction of deep acceptors with optical ionization energies of 2, 2.8, and 3.1 eV. Similarly, for samples with doping 4 × 10¹⁸ cm⁻³, the carrier removal rate was 5 × 10³ cm⁻¹ for 10¹⁵ cm⁻² fluence and ∼300 cm⁻¹ for 10¹⁶ cm⁻² fluence. In this case, the introduction rate of the deep acceptor was many times lower than the carrier removal rate. The radiation tolerance of lightly doped α-Ga₂O₃ is higher than that for similarly doped β-Ga₂O₃ layers.

Figure 4(a) shows a summary of the carrier removal rates for different types of radiation exposure of various polymorphs, while Fig. 4(b) shows a more detailed comparison of the carrier removal rates for protons only in different polymorphs under conditions where the carrier removal rate was obtained from the linear region where carrier loss is proportional to fluence. The most fruitful comparison is between samples of similar concentrations. For the best studied case of low net donor concentrations of ∼10¹⁶ cm⁻³, such a comparison can be done in Fig. 4(b) for β, α, and κ polymorphs for protons with energy 1.1 MeV. At that proton energy, the introduction rates for γ-Ga₂O₃ were also measured. Note the emphasis on the word introduction, since we observed an increase in carrier density and not a loss of carriers for this polymorph. For α-Ga₂O₃ and β-Ga₂O₃, we also measured the rates for different starting concentrations. For the admittedly limited data existing, the removal rates do not change strongly for net donor concentrations below ∼10¹⁸ cm⁻³. For the lowest net donor densities, the removal rate is not too different from the introduction rate of deep acceptors related to Ga vacancies. For higher starting concentrations, the removal rates are much higher than the aggregate concentration of deep acceptors. This suggests that, overall, the removal is due to complexing of V_Ga with shallow donors complemented, and for low fluences, by the actual compensation by deep V_Ga-related acceptors. In κ-Ga₂O₃, we have only one point, for γ-Ga₂O₃, the starting concentrations are low, and they slightly increase with irradiation with MeV protons. To summarize, for 1 MeV protons, the removal rates for β polymorph are the highest, followed by α, and then, κ polymorph. This reflects, on the one hand, the higher introduction rate of V_Ga vacancies in the best crystalline quality β-Ga₂O₃, possibly because some vacancies are trapped at the grain boundaries in α- or κ-Ga₂O₃. It seems to be corroborated by the results of Rutherford backscattering experiments for irradiation with high doses.

For other types of irradiations, one really needs, when comparing different polymorphs, to have samples with similar starting concentrations, but the majority of results in the literature refer to the lightly doped samples most relevant to rectifiers and transistors. It remains likely that the relative removal rates should not be too different from the 1 MeV protons case since the mechanism of damage is similar.

The changes in carrier diffusion length and deep-level traps as a result of irradiation translate into real-world device degradation through a reduction in forward and reverse currents in rectifiers and transistors and changes in breakdown voltage. Since there is no effective p-type doping available in any of the polymorphs, comparative studies of doping influences defect formation, migration, and charge compensation under irradiation do not exist.

The diffusion lengths were calculated from the dependence of the electron beam current (EBIC) I_c collection efficiency on the probing beam energy E_b of a scanning electron microscope (SEM) at beam current I_b, I_c/(I_b × E_b). This is the most accurate way to determine the diffusion length L_d in wide-bandgap semiconductors with short L_d values.^60,61 For Ga₂O₃ Schottky diodes, the theory was reported previously,^43–62 while for p–n heterojunctions, the analysis was presented previously.⁶⁵ The measurements performed for high-quality β-Ga₂O₃ epi grown by HVPE on native substrates and lightly doped bulk crystals showed that the diffusion lengths in samples with a net donor density of ∼10¹⁶ cm⁻³ varied between 0.6 and 0.15 μm depending on the concentrations of defect related centers E2*(E_c – 0.74 eV), E3 (E_c – 1.05 eV) and deep acceptors E2 (E_c – 0.8 eV) due to Fe on the Ga site.^62,65,66

In case of irradiation with 20 MeV protons, the starting diffusion length of 0.6 μm decreased to 0.33 μm after a fluence of 5 × 10¹³ cm⁻² and to 0.16 μm after 10¹⁴ cm⁻².⁶⁷ The changes in diffusion lengths correlate with the proton irradiation increase in the density of three major electron traps E2* (related to V_Ga–V_O⁶⁸), E3, and E4 (possibly related to V_O deep donors).^67,68 The damage constant for L_d is about 4.4 × 10⁻¹⁵ mm/cm⁻². As 1/L_d² is proportional to the density of recombination centers, one can also introduce the damage constant for 1/L_d² that is 3.6 × 10⁻¹³ mm⁻²/cm⁻². The changes in 1/L_d² are in line with the changes in the density of the E2*, E3, and E4 electron traps that all display introduction rates of ∼8 cm⁻¹ and the correlation between 1/L_d² and the density of these traps introduced by 20 MeV protons is reasonable. For samples irradiated with 10¹⁴ cm⁻² 10 MeV protons, the diffusion length decreased from 0.35 to 0.19 μm which corresponds to 1/L_d² damage rate 2 × 10⁻¹³ mm⁻²/cm⁻² similar to the damage rate for 20 MeV protons.⁶² The damage rate for 18 MeV a-particles is about an order of magnitude higher than for 20 MeV protons.⁶⁷ 

The irradiation of β-Ga₂O₃ epilayers with fast reactor neutrons with an average neutron energy of 1.25 MeV⁶⁹ to 3.6 × 10¹⁴ cm⁻² led to a decrease of the diffusion length from 0.16 to 0.12 μm. The lower starting value of the diffusion length in this epitaxial β-Ga₂O₃ samples is attributed to a much higher concentration of the E2 (Fe) acceptors and suggests them to contribute to nonradiative recombination in β-Ga₂O₃ as is the case with Fe acceptors in GaN.⁷⁰ The corresponding degradation constant for 1/L_d² was 8.4 × 10⁻¹³ mm⁻²/cm⁻².

Similarly, a high Fe concentration in bulk β-Ga₂O₃ crystals grown by Czochralski also resulted in a considerably shorter diffusion length of 90 nm⁶⁵ compared to the best epitaxial material. This higher concentration of residual E2 (Fe) acceptors led to lower starting diffusion lengths but to slower changes of this value with radiation.

It is interesting to measure the changes in L_d with proton irradiation in heterojunctions of epitaxial n-type β-Ga₂O₃ with p-NiO.^64,71 In these heterojunctions, there exists a layer with stoichiometry shifted toward oxygen excess that results in the presence of a high density of relatively shallow centers near E_c – 0.16 eV and a suppressed concentration of the E2* traps, while the E2(Fe) traps are also present.⁶⁴ This results in the diffusion length in the n-portion of this heterojunction being considerably higher than in the Schottky diode made on the same material (0.37 versus 0.24 μm) (the diffusion length in the p-NiO layer is only 20 nm). After irradiation with 2 × 10¹³ cm⁻² of 1.1 MeV protons, the density of shallow donors in the heterojunction decreases much faster than in the Schottky diode, but the density of E2* is unchanged as is the diffusion length.⁷¹ 

In these studies, the samples of α-Ga₂O₃ were grown by HVPE on sapphire. The films were either unintentionally doped, in which case they had low density of residual donors rendering them either semi-insulating or heavily compensated n-type due to the presence of a high density of deep acceptors in the lower half of the bandgap with levels close to E_c – 2.3 eV and E_c – 3.1 eV attributed to Ga vacancies acceptors of either split or normal types, similar to the case of b-Ga₂O₃.⁷² The n-type dopant was Sn: when lightly doped (10¹⁶–10¹⁷ cm⁻³), there were energy levels near E_c – 014 eV (E1) and E_c – 0.25 eV (D centers), and E_c – 0.35 eV(E2), with deeper electron traps near E_c – 0.6 eV (B centers), E_c – 0.8 eV (C centers), and E_c – 1 eV (D centers). The distribution of the centers in lightly doped (∼10¹⁶ cm⁻³) films was nonuniform with depth, with the near-surface region ∼1 μm thick dominated by the 0.35 eV centers, while in the deeper portion of the films, the dominant traps were the 0.25 eV centers.⁷⁴ In more heavily doped films (>10¹⁷ cm⁻³), the dominant centers were the 0.14 eV states, with the 0.25 eV states present deeper inside the films. The samples grown by HVPE on sapphire display a high density of edge dislocations on the order of 10⁹ cm⁻² and the density of screw and mixed dislocations of ∼10⁷ cm⁻².⁷³ The dislocation density can be decreased when growing the films using Cr₂O₃ buffers.

The diffusion lengths were measured for samples in which leakage current was low enough to allow EBIC collection efficiency dependence measurements on beam voltage. The values were 0.10–0.15 μm in lightly doped samples (1.1 × 10¹⁷ cm⁻³) and 0.07 μm for more heavily doped samples (4 × 10¹⁷ cm⁻³).^72,73 The samples with donor density ranging from <10¹⁶ to >10¹⁹ cm⁻³ were irradiated with 1.1 MeV protons. The carrier removal rate increased with increasing shallow donor density from about 35 cm⁻¹ for 10¹⁶ cm⁻³ donors to about 300 cm⁻¹ for concentrations over 10¹⁸ cm⁻³.^73,74 For lightly doped samples, this resulted in the emergence of a highly compensated layer near the surface that gradually becomes deeper as the fluence increases. Measurements of the diffusion length did not reveal strong changes in the apparent diffusion length. For heavier doped samples, the changes were qualitatively the same, with the emergence of a heavily compensated layer and its propagation deeper into the sample as the dose increases, but with the thickness of the compensated region much lower.

Effects caused in the undoped films of α-Ga₂O₃ were by implantation of protons with energies 330, 450, and 550 keV with a fluence of 6 × 10¹⁵ cm⁻².⁷⁶ The samples were highly compensated n-type with the Fermi level pinned near E_c – 0.14 eV and with deep electron traps near E_c – 0.5 eV and E_c – 0.6 eV.⁷⁵ Deeper hole traps with optical ionization energy near 3.1 eV were detected in photocapacitance and photocurrent spectra.

Irradiation shifted the Fermi level deeper inside the band to near E_c – 0.25 eV, enhanced the signal in Phoot-Induced Current Transient Spectroscopy (PICTS) due to E_c – 0.5 eV and E_c – 0.6 eV traps and introduced traps with the level near E_c – 0.8 eV attributed to V_Ga–V_O vacancies.^76,77 Diffusion lengths measured for the virgin sample and the samples irradiated with these low-energy protons gave the starting diffusion length as 0.11 μm, decreasing to 0.05 μm for irradiation with 330 keV protons, to 0.07 μm for 450 keV, and 0.08 μm for 550 keV. Such irradiations also produced a prominent narrow defect band that peaked near 3.3 eV in micro cathodoluminescence (MCL) spectra, in addition to the usual broad band characteristic of α-Ga₂O₃ samples. The relative intensity of this new band increased for decreasing probing beam energy in MCL suggesting that the effect is confined to the surface layer. The peak energy slightly changed with temperature varying from 3.317 eV at 80 K to 3.289 eV at 327 K. The temperature dependence of the new band suggests that activation involves a center with energy between 0.3 and 0.35 eV. The spectrum observed for high SEM beam energy corresponding to excitation deep in the sample was the usual broad band characteristic for MCL spectra of α-Ga₂O₃. It could be deconvoluted into Gaussian bands that peaked at 2.5, 2.84, and 3.04 eV whose position and intensity are virtually temperature independent, suggesting that these bands correspond to donor-acceptor pair recombination. The MCL feature similar to the narrow intense peak near 3.3 eV induced by proton irradiation has been previously reported for α-Ga₂O₃ samples treated in molecular hydrogen at high temperature.⁷⁷ 

We also looked at semi-insulating α-Ga₂O₃ subjected to treatment in H plasma and converted at the surface to n⁺ type with a shallow donor density of ∼10¹⁹ cm⁻³. The sample was then annealed at high temperature and for 450 °C, turned into low doped n-type with the donor density ∼10¹⁶ cm⁻³ and DLTS spectra, and AS spectra dominated by deep electron traps E_c – 0.65 eV, E_c – 0.82 eV, and E_c – 1.2 eV similar to the states observed in lightly doped α-Ga₂O₃. The diffusion length was 0.15 μm.⁷⁷ 

Deep trap spectra and diffusion length measurement results have not been reported until recently because of the predominance in κ (also marked as ɛ)-Ga₂O₃ films of rotational 120° nanodomains.^80–83 HVPE growth of thick (above ∼20 μm) k-Ga₂O₃ films on GaN substrates allows us to obtain films with low n-type doping and suppressed formation of rotational domains, making them suitable for deep-level transient spectroscopy with electrical and optical injection and admittance spectroscopy.^80,86

These experiments revealed relatively shallow donor states at E_c – 0.15 eV and E_c –  (0.25–0.35) eV, deep electron traps at E_c – 0.6 eV, E_c – 0.7 eV, and E_c – 1 eV and deep acceptors with optical ionization energy 2 and 2.8 eV, 3.4 eV as determined by photocapacitance spectra.^86,93 The upper 2 μm thick portion of the films was characterized by the predominance of the E_c – 0.25 eV centers, a high density of the E_c – 0.7 eV electron traps, and a high density of the deep acceptors near 2.8 and 3.4 eV. The diffusion length measurements showed the diffusion length to be 0.07 μm. After irradiation with 1.1 MeV protons with fluence 10¹⁴ cm⁻², the top 4.5 μm of the sample was totally depleted of the shallow donors, suggesting the electron removal rate to be ∼10 cm⁻¹ (taking into account both types of major donor centers), somewhat lower than for similarly doped α-Ga₂O₃, but much lower than for β-Ga₂O₃.

At the depth where the electrical properties and traps could be probed after irradiation, the deep electron trap spectra were dominated by the E_c – 0.7 eV and E_c – 1 eV states, but with a lower concentration. The apparent concentration of the deep acceptors were also reduced, with the 2 eV trap absent and the densities of 2.8 and 3.4 eV lower. The diffusion length was not changed. These results indicate that, even in thick k-Ga₂O₃, the electrical properties and deep traps spectra are nonuniform in depth, with the upper 2.5 mm portion dominated by the high density of 0.25 eV donors, high density of E_c – 0.7 eV donors, and high density of deep acceptors with 2.8 eV, 3.4 eV, while deeper inside the sample, where the properties are probed after irradiation, the densities are lower. No significant changes in diffusion length with proton irradiation of k-Ga₂O₃ occur, although the recombination mechanism must be understood better.

Figure 5 summarizes the percentage change in minority carrier diffusion length as a function of radiation type for the different polymorphs. A summary of the absolute values of L_D before and after different types of radiation exposures, as well as the carrier removal rates (CRR) and the deep traps observed are given in Table II. There is not a direct correlation between electrical changes such as the carrier removal rate and the changes in diffusion length. Some possible reasons for this discrepancy include that traps created by irradiation may have different energy levels and capture cross sections for electrons and holes. This selective trapping can lead to different impacts on carrier density and minority carrier diffusion length. Irradiation may create traps nonuniformly across the material, leading to localized regions with varying trap densities. This nonuniformity can affect minority carrier diffusion length more significantly than the overall carrier removal rate, as minority carriers are more sensitive to localized defects. Some irradiation-induced defects may act as recombination centers rather than simple carrier traps. These centers can reduce minority carrier lifetime and diffusion length without necessarily contributing proportionally to carrier removal. Carrier mobility is affected by scattering from defects, which may not directly correlate with the number of carriers removed. Certain defects may cause strong scattering, reducing mobility significantly even if they remove only a small number of carriers. Minority carrier diffusion length is strongly dependent on carrier lifetime, which can be affected by deep-level traps and recombination centers. These defects may not contribute significantly to carrier removal but can drastically reduce minority carrier lifetime and diffusion length. Irradiation can create complex defects that have different effects on carrier removal and minority carrier diffusion. These complexes may introduce additional energy levels or recombination pathways that disproportionately affect minority carriers. The initial defect density and material quality can influence how irradiation affects carrier removal and minority carrier diffusion. Higher initial defect densities may amplify the impact of irradiation on minority carrier diffusion length.

In summary, the lack of exact correlation between carrier removal rates and minority carrier diffusion length trends can be attributed to the complex nature of defect interactions, the specific properties of the traps created, and the differing sensitivities of majority and minority carriers to these defects.

NiO/Ga₂O₃ heterojunctions are being used in place of conventional Ni/Ga₂O₃ Schottky barrier diodes to achieve higher breakdown voltages, improved thermal stability, and better rectification performance due to the wider bandgap and higher p-type conductivity of NiO.^49–58 However, the introduction of an oxide to form a p–n junction with Ga₂O₃ raises questions about whether the radiation tolerance is affected.^89,90 As discussed earlier, gamma irradiation of such heterojunctions can produce a reversible change in the current–voltage characteristics, but little work has been done to measure changes in these heterojunctions using spectroscopic techniques after radiation exposure.

Figure 6 shows the initial data on the differences between deep traps in proton irradiated NiO/Ga₂O₃ rectifiers versus conventional Ni/Ga₂O₃ rectifiers. p-NiO/n-Ga₂O₃ heterojunction (HJ) diodes demonstrate significantly greater sensitivity to 1.1 MeV proton irradiation compared to Schottky diodes (SDs) fabricated on the same material.⁷¹ In HJ diodes, a narrow region near the heterojunction boundary exhibits a high density of deep-level defects with energy states near E_C – 0.17 eV, alongside a depleted zone adjacent to the interface. The series resistance of HJ diodes is marginally higher than that of SDs and exhibits a temperature-dependent behavior with an activation energy of ∼0.12 eV, consistent with the resistivity of the NiO film. Proton irradiation induces a notable reduction in hole concentration within NiO, with a carrier removal rate of ∼1.3 × 10⁵ cm⁻¹, and a strong compensation effect in the interfacial region, where the concentration of E_C – 0.17 eV centers decreases at a rate of ∼7 × 10³ cm⁻¹. These combined effects result in a more pronounced increase in the series resistance of HJ diodes relative to SDs. The observed disparity in radiation response between HJ and SD structures cannot be conclusively linked to the changes in the density of deep electron or hole traps identified in the study.²¹ 

Using NiO/Ga₂O₃, heterojunctions does affect the sensitivity to specific radiation. For Co-60 γ-ray irradiation, Schottky rectifiers display almost no change in forward or reverse currents, while in sharp contrast, heterojunctions show reversible 10²× increases in reverse current, and reversible 10³× decreases in forward current. The changes in I–Vs are reversible by short forward current pulses at 300 K, with the mechanism suggested to be irradiation assisted desorption of oxygen containing species from the surface. Exposure to O₂ partially restores the initial resistivity. This mechanism is also the origin of enhanced conductivity in low dose irradiated oxides. For proton irradiation, the interfacial region is more affected after irradiation in heterojunctions, with the heterojunctions displaying larger changes (2×) with irradiation than Schottkies. There is a reduced concentration of traps E2* in NiO/Ga₂O₃ heterojunctions, thought to be V_Ga–V_O. The presence of NiO modifies traps in the interfacial region between NiO and Ga₂O₃. NiO is less thermally stable than metal contacts. There was no injection-enhanced annealing detected in the heterojunctions. For electron irradiation, there was no difference in carrier removal in the drift region in both types of devices. For alpha particles, there was also no difference-carrier removal in the drift region in both devices, but heterojunctions have larger changes with irradiation. For neutron irradiation, carrier removal in the drift region competes with the damage induced in NiO, with the breakdown voltage increasing in Schottky rectifiers because of carrier loss in the drift region, while the breakdown decreases in heterojunctions because of the damage in NiO.

A summary of the differences in Schottky diodes versus heterojunction rectifiers is given in Table III.

This paper summarizes the radiation hardness of different Ga₂O₃ polymorphs (α, β, κ, and γ) by examining the changes in minority carrier diffusion length and defect introduction rates after various types of irradiations (protons, neutrons, alpha particles, and gamma rays). β-Ga₂O₃, the most thermodynamically stable polymorph, has been extensively studied, revealing that L_d values in high-quality epitaxial layers range from 0.15 to 0.6 μm depending on defect concentrations (E2*, E3, and E2). Irradiation with 20 MeV protons decreased L_d, correlating with an increase in electron trap densities (E2*, E3, and E4). The damage constant for 1/L_d² was approximately 3.6 × 10⁻¹³ mm⁻²/cm⁻². Neutron irradiation and alpha particle irradiation also reduced L_d, with varying damage rates. Studies on NiO/β-Ga₂O₃ heterojunctions showed different responses to irradiation compared to Schottky diodes. In comparison, α-Ga₂O₃ exhibits a higher radiation tolerance than the β-phase, with low-energy proton implantation in α-Ga₂O₃ also reducing L_d and inducing a new defect band MCL spectra while κ-Ga₂O₃ demonstrates minimal L_d changes after irradiation, though its properties are complicated by nonuniformity. It exhibited short L_d values (∼70 nm) with minimal changes after 1.1 MeV proton irradiation. γ-Ga₂O₃, being metastable, also exhibits unique defect dynamics. The study highlights the complex interplay among polymorph structure, doping, irradiation type, and the resulting changes in transport properties.

The literature provides several insights into why different polymorphs of Ga₂O₃ exhibit varying degrees of radiation hardness. The differences in radiation hardness can be attributed to several factors, including structural stability, defect dynamics, doping concentrations, and the nature of the defects introduced by irradiation.

In summary, different polymorphs exhibit varying degrees of radiation hardness with β-GaO₃ generally being the least radiation-tolerant and γ-Ga₂O₃ the most for proton irradiation. The differences are not large for these conditions and not significant enough to suggest that the other polymorphs are favored for radiation-hard applications. While γ-Ga₂O₃ is very resistant to damage, it has, as yet, not been successfully doped and has limited device applications.

• What are the underlying structural and electronic factors that contribute to the differences in radiation hardness among the polymorphs?

• How do the dominant recombination mechanisms differ between the polymorphs?

• How do changes in L_d correlate with the introduction of specific defects in each polymorph?

• Can athermal annealing methods, such as electron wind force annealing, effectively recover radiation-induced damage in Ga₂O₃, and how does this compare to thermal annealing?¹¹⁴ 

• How do different annealing atmospheres influence the recovery of radiation damage?^111,112

• How do surface and interface properties influence the radiation hardness of Ga₂O₃, particularly in heterojunctions like NiO/β-Ga₂O₃?

• How does alloying Ga₂O₃ with Al₂O₃ affect the radiation hardness of the material, particularly in α and β phases, and what is the optimal Al composition in alloys for maximizing radiation hardness while maintaining the desirable electronic properties?

• How do changes in optical properties correlate with changes in electrical properties after irradiation?^113–115 

• What is the role of hydrogen in passivating or activating defects in Ga₂O₃ polymorphs^112,113 and how does it interact with native defects to influence the material’s radiation hardness?

• How does the radiation hardness of Ga₂O₃ compare to diamond, AlN, or other oxides,^115–119 in terms of carrier removal rates and defect dynamics at similar doping levels?

These questions highlight the complexity of understanding the radiation hardness of Ga₂O₃ polymorphs and provide a roadmap for future experimental and theoretical investigations.

The work at UF and PSU was performed as part of Interaction of Ionizing Radiation with Matter University Research Alliance (IIRM-URA), sponsored by the Department of the Defense, Defense Threat Reduction Agency under Award No. HDTRA1-20-2-0002. The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred. A. Haque acknowledges the support from the Air Force Office of Scientific Research, Agreement No. FA9550-24-1-0341. The work at NUST MISIS was supported in part by a grant from the Ministry of Science and Higher Education of Russian Federation (Agreement No. 075-15-2022-1113). The work at IMT RAS was supported by the State Task (No. 075-00296-24-01). The authors at NUST MISIS and UF thank Andrej Kuznetsov for discussions on the gamma polymorph. The research at UCF was supported in part by the National Science Foundation (NSF) (Nos. ECCS2310285, ECCS2341747, and ECCS 2427262), US-Israel BSF (Award No. 2022056), and NATO (Award No. G6072; G6194).

The authors have no conflicts to disclose.

S. J. Pearton: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Fan Ren: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Alexander Y. Polyakov: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Eugene B. Yakimov: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Leonid Chernyak: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Aman Haque: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal).

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