Crystal orientation dependence of deep level spectra in proton irradiated bulk β-Ga₂O₃

Ga₂O₃ is currently attracting interest because of the promise of this ultra-wide-bandgap transparent semiconductor and related ternary and quaternary solutions for high-power electronics and solar-blind photodetectors.¹⁻⁴ Much attention has been focused on the properties of the stable monoclinic β-Ga₂O₃ polytype. The main advantages here are the availability of good crystalline quality bulk crystals grown by all versions of melt-growth techniques, the ability to grow high-quality epitaxial films by various techniques, the relative ease of n-type doping with group IV dopants, and of obtaining a semi-insulating material by the addition of transition metal impurities or dopants producing deep acceptors.^1−3,5 The material is expected to have a very high electric breakdown field of 5−8 MV/cm, a high saturation velocity of electrons of ∼2 × 10⁷ cm/s, and figures of merit for performance at high power far exceeding those of more mature wide-bandgap materials.¹⁻³ 

High-quality substrates prepared by the Edge-defined Film-fed Growth (EFG), thick epitaxial films grown on such substrates by Halide Vapor Phase Epitaxy (HVPE), and heterojunctions with ternary (Al_xGa_1−x)₂/Ga₂O₃ are commercially available.¹⁻³ Various prototype power devices and solar-blind photodetectors with promising performance have been demonstrated.¹⁻⁴ Studies of the electronic and structural properties of β-Ga₂O₃ have advanced both theoretically and experimentally. These show the important role of Si, Sn, and Ge as shallow donors substituting Ga,^1−4,6,7 of Fe as a substite for Ga and acting as deep compensating acceptors with the level near E_c−0.8 eV,^8,9 of triply negatively charged Ga vacancies V_Ga and split Ga vacancies (Ga vacancies complexes with off-center Ga interstitials) V_Gaⁱ as major deep native defects serving as compensating acceptors, and, finally, of doubly charged oxygen vacancies (V_O) forming deep donor levels.^6,9,10

The important aspect setting the β-Ga₂O₃ polytype apart from other important wide-bandgap semiconductors is its low monoclinic symmetry, resulting in the existence of two types of Ga vacancies, tetrahedrally coordinated V_Ga1 and octahedrally coordinated V_Ga2, and three different types of O vacancies, V_O1, V_O2, and V_O3. There is a propensity of defects in β-Ga₂O₃ to form complexes with each other and with impurities, particularly with hydrogen.^9,10,11−14 The low crystalline symmetry of β-Ga₂O₃ gives rise to considerable anisotropy of different properties.^1,15 Notably, it has been reported that the formation of some deep level defects was more pronounced for certain crystal orientations than for others.^16–18 Hydrogen has been shown to easily form complexes with split Ga vacancies, but this occurred more effectively for the (−201) orientation.^12,13 Hydrogen diffusion in β-Ga₂O₃ has been shown to proceed via the formation of complexes with structural defects and hopping from site to site,¹⁹⁻²³ with the diffusion coefficient much higher in the direction normal to the (010) surface compared to the direction normal to the (−201) surface.¹⁹⁻²³ This was attributed to the peculiarity of the β-Ga₂O₃ structure in which open channels going along the direction normal to the (010) surface exist and facilitate easy hopping of hydrogen along this direction.²³ The results of hydrogen plasma treatment have been reported to be radically different for the cases of (010)- and (−201)-oriented samples.²⁴ 

A better understanding of the consequences of anisotropy in β-Ga₂O₃ on the performance of crystals and films based on this material is clearly necessary. In this paper, we present results on the effects of proton irradiation on electrical properties and deep traps spectra of bulk n-type crystals with orientations (010) and (−201).

The samples used were bulk n-type β-Ga₂O₃ crystals grown by EFG from Tamura Corp. (Japan). One of the crystals had (−201) orientation, and the other was (010)-oriented. Both types were doped with Sn and had a shallow donor concentration of ∼3 × 10¹⁷ cm⁻³. The thickness of the samples was 650 μm. The backside was mechanically polished with the front side chemo-mechanically polished to epi-ready quality. For electrical characterization, circular Ni Schottky diodes with a diameter of 1 mm and a thickness of 20 nm were deposited on the front polished epi-ready surface with e-beam evaporation at room temperature through a shadow mask. Full area Ohmic contacts to the back mechanically polished surface were prepared by e-beam evaporation of Ti/Au (20/80 nm). Prior to the Ohmic contacts deposition, the samples were subjected to treatment in dense Ar plasma and to rapid thermal annealing at 500 °C. The Ohmic contact preparation preceded the Schottky diodes deposition.

The electrical properties and deep trap spectra of both types were studied before and after irradiation at room temperature with 20 MeV protons. Proton irradiation was performed on the injector-linear accelerator I-2 “Kamiks” at the Center of Collective Use, Institute of Theoretical and Experimental Physics, Moscow (Russia). The proton fluences used were 5 × 10¹⁴ and 10¹⁵ cm⁻² with a proton flux of 10¹¹ cm⁻² s⁻¹. Modeling with the Stopping-and-Range-of-Ions-in-Matter (SRIM) code^25,26 and the results of modeling²⁷ showed previously that the range of such protons exceeds 1.2 mm, and the distribution of primary radiation defects throughout the entire thickness of the samples should have been approximately uniform.

Characterization involved current–voltage (I–V) and capacitance–voltage (C–V) in the dark and under illumination with a set of high-power light-emitting diodes (LEDs) with peak photon wavelengths from 365 to 940 nm (most were done with optical power density 250 mW/cm²). Those were complemented by measurements under illumination from UV LEDs with wavelengths of 340 nm (optical power 250 mW/cm²) and 259 nm (the optical power density 1.2 mW/cm²).

Deep trap spectra characterization involved Deep Level Transient Spectroscopy (DLTS),²⁸ Current Deep Level Transient Spectroscopy (CDLTS),²⁹ Steady-State Photocapacitance (SSPC), C–V profiling with monochromatic excitation (LCV),³⁰ and Admittance Spectroscopy (AS).²⁸ The temperature in these experiments could be either stabilized with an accuracy of 0.1 K or ramped up or down with the controlled rate of 2 K/min in the temperature range 100−500 K using a liquid nitrogen cryostat (Cryotrade company, Russia). Detailed descriptions of experimental setups can be found elsewhere.^27,31–33

Both types of samples showed similar I–V characteristics with an ideality factor n = 1.1 and the saturation current density of 10¹⁵ A/cm² for (−201) and 2.7 × 10⁻¹⁷ A/cm² for (010), but a somewhat high series resistance because of the relatively low donor doping density handicapping the specific Ohmic contact resistance [Fig. 1(a)]. C–V characteristics were linear when plotted as 1/C² vs V and gave a net donor density of 2.8 × 10¹⁷ cm⁻³ for (−201) and 3.25 × 10¹⁷ cm⁻³ for the (010), with respective built-in voltages V_bi = 1.25 and 1.55 V [Fig. 1(b)].

DLTS spectra measured in the near surface region by applying the reverse bias of −1 V and a bias pulse of 1 V, and the spectra were measured deep inside the sample for the bias voltage of −10 V and a forward bias pulse of −1 V were very similar for both types and revealed the presence of electron traps with levels E_c−0.8 eV (electron capture cross section σ_n = 2.5 × 10⁻¹⁵ cm²), the so-called E2 traps,^8,9,34,35 and electron traps with levels E_c−0.95 (σ_n = 2 × 10⁻¹⁴ cm²) similar to the E3 traps^34,36 [Figs. 2(a), 2(b) and 3(a), 3(b)]. No other centers were detected in our DLTS measurements in the temperature range of 100−450 K. The ordinate axis in these DLTS figures shows the product of 2N_d × ΔC/C × F⁻¹, where N_d is the net donor density determined from C–V profiling; ΔC is the DLTS signal ΔC = C(t1) – C(t2), with C(t1) and C(t2) being the transient capacitance values at time windows t1 and t2 during the capacitance decay measurements; C is the steady-state capacitance; and F⁻¹ is the spectrometer function converting the ΔC DLTS value into the full amplitude of capacitance transient.²⁸ For temperatures corresponding to peaks in DLTS spectra, the amplitudes in these coordinates give the concentration of the trap without taking into account the so-called –correction.²⁸ According to the literature,^8,9,35 the E2 traps belong to the substitutional Fe acceptors. For the E3 traps, the attributions vary. In some papers, these traps are ascribed to Ti deep donors,³⁶ while other reports associate them with native point defects.^27,34 The data in Figs. 2 and 3 suggest that the densities of deep electron traps did not seriously differ between the two orientations and did not strongly vary with depth.

The type and concentration of deep hole traps present in the lower half of the bandgap and not accessible to DLTS probing were determined from C–V profiling with monochromatic illumination (LCV measurements^27,30,31 and from steady-state photocapacitance spectra (SSPC) measurements that produced similar results.^27,31 The dependences of the photoinduced concentration on the photon energy measured in the LCV experiment are shown for the two samples before irradiation in Fig. 4(a). For both orientations, the spectra consisted of the feature with an optical threshold near 1.3 eV and showing a plateau near 2 eV, a very pronounced signal with an optical threshold near 2.3 eV, reaching a plateau near 3.1 eV, and a distinct signal onset at 3.1 eV. Such spectra are often observed in bulk β-Ga₂O₃ crystals and films grown on native substrates.^27,30,31

Among the LCV features in Fig. 4, defects with the optical threshold ∼2.3 eV have been identified with the split Ga vacancy acceptor complexes with off-center interstitial Ga, the so-called V_Gaⁱ centers^37,38 predicted by theory.^6,9,10 Detailed Deep Level Optical Spectroscopy (DLOS) measurements and LCV/SSPC measurements show that these centers possess a high barrier for the capture of electrons (∼0.5 eV according to DLOS³⁰ and give rise to a strong persistent photocapacitance that cannot be removed by the application of the high forward bias, supplying electrons into the Space Charge Region (SCR) of the Schottky diode.^27,31 The two other deep traps in the LCV spectra have also often been observed in Ga₂O₃, but their identity is still not clear. The 1.3 eV centers were observed in Sn or Ge doped films grown by MBE³⁹ and in HVPE films irradiated with protons, α-particles, or neutrons.^27,31,40 They also, as the 2.3 eV V_Gaⁱ centers, show prominent persistent photocapacitance^27,31,39,40 that cannot be quenched by forward bias pulsing and, hence, is likely related to the presence of a measurable barrier for the capture of electrons indicating that strong lattice relaxations involved.

The centers with the optical threshold near 3.1 eV, on the contrary, do not possess a high barrier for the capture of electrons, which makes it possible to suppress the persistent photocapacitance related to them by applying forward bias pulsing.^27,31,40 We have suggested these centers to be related to Ga vacancy acceptors or their complexes²⁷ One of the problems that arise is that theory places the charge transfer levels of V_Ga much higher than expected if one attributes the 3.1 eV optical threshold to them.^6,9,10,23 On the other hand, experimental results unambiguously point to the center in question being related to a native-defect or a complex involving such defects.^27,40 Moreover, the p-type conductivity observed at high temperatures in Ga₂O₃ grown under oxygen-rich conditions was shown to be due to deep acceptors with levels near E_v + 1 eV.⁴¹ 

The density of V_Gaⁱ states/2.3 eV defects is virtually the same in the (010) orientation compared to the (−201), while the density of the 1.3 eV centers is considerably lower (and the threshold energy is slightly shifted towards 1.5 eV), and the concentration of the 3.1 eV centers is much higher in the (010) orientation compared to the (−201).

The changes induced in the room temperature C–V profiles by irradiation with fluences of 20 MeV are summarized for the two orientations in Figs. 5(a) and 5(b). They are similar for both orientations, with an effective carrier removal rate close to 200 cm⁻¹, similar to the value reported for HVPE-grown samples with a lower net donor concentration of 3 × 10¹⁶ cm⁻³.²⁷ 

DLTS spectra measurements after irradiation with the 5 × 10¹⁴ cm⁻² fluence revealed important differences for the (010) and (−201) orientations. For the (−201) sample, the spectra are qualitatively similar for the near surface (bias/pulsing sequence of −1/1 V) and bulk (bias pulsing −10/−1 V) regions. Irradiation introduces additional shallow electron traps EX1, EX2, EX3 with levels near E_c−0.45 eV (capture cross section σ_n = 5.5 × 10⁻¹⁵ cm²), E_c−0.25 eV (σ_n = 4 × 10⁻¹⁹ cm²), and E_c−0.2 eV (σ_n = 1.2 × 10⁻¹⁹ cm²) with low concentration, while the densities of the deeper E2 and E3 electron traps are not strongly altered [Figs. 3(a) and 3(b)].

By sharp contrast, the spectra for the (010) orientation were very different in the near surface and bulk regions. In the near surface region, a prominent electron trap EX2* similar to the EX2 center in irradiated (−201) was observed with level E_c−0.27 eV (σ_n = 4 × 10⁻²¹ cm²) and concentration higher than the dominant E2 trap [Fig. 4(a)]. In the bulk, the spectra [Fig. 4(b)] comprised the deeper electron traps E2 and E3, and a peak due to the E_c−0.45 eV trap similar to the EX1 in the (−201) orientation. The density of this latter trap exceeded the concentration of the similar peak in the sample (−201) but was much lower than the concentration of the near surface EX2* E_c−0.27 eV peak in Fig. 4(a). Some additional light on the nature and location of this new prominent EX2* peak was shed by C–V profiling experiments carried out at 110 K when cooling the sample at a high reverse voltage of −3 V (Fig. 6). There is a step in the space charge density with a height of 8 × 10¹⁶ cm⁻³. These centers are located in the 0.1 μm-thick layer near the surface. The higher charge concentration in the step could be removed by the application of a forward bias of +1 V for a period of ∼5 min. The result of Fig. 6 suggests the presence of a prominent acceptor with high concentration and a slow capture of electrons in the upper 0.1 μm of the sample.

Measurements of DLTS spectra with different biases and different pulse heights for the irradiated (010) sample showed that there is a competition in the spectra between the EX2* E_c−0.27 eV center and the EX1 E_c−0.45 eV trap, with the former consigned mostly to the near surface region and the latter distributed more or less uniformly across the thickness of the sample. Figure 7(a) shows the actual spectra, while Fig. 7(b) presents the trap concentration profiles. For high forward biases, DLTS spectra in Fig. 7(a) shows a broad structureless shoulder possibly coming from a continuum of relatively shallow states most likely located near the interface with the Schottky metal.

The presence of high densities of the EX2* traps was found to cause metastability in forward I–V characteristics measured at low temperatures. The turn-on voltage in the forward direction at 110 K was strongly dependent on conditions under which the sample was cooled and on biasing sequence at low temperature [Fig. 8(a)]. If the sample was cooled down at −3 V, the turn-on voltage was ∼0.7 V. If after this first measurement, a bias of +2 V was applied to the sample for a long period (5 min), the turn-on voltage was shifted to 1.2 V. Application of reverse bias of −3 V for a time sufficient to remove electrons from the EX2* trap returned the turn-on voltage to the starting value.

The close relation between the trapping and detrapping of electrons by the EX2* center and the hysteresis in forward I–V characteristics is confirmed by the results of CDLTS measurements on the irradiated (010) orientation. In this experiment, the sample was biased at −1 V and pulsed to +2 V for 5 s, and respective current transients were monitored in the temperature range of 100–400 K. Figure 8(b) presents the temperature dependence of the CDLTS signal ΔI = I(t1) − I(t2) for several time windows t1 and t2 [I(t1) and I(t2) are the transient current values at the respective time windows]. The spectra show a prominent peak corresponding to the trap with an ionization energy of E_a = 0.25 eV and an electron capture cross section of σ_n = 10⁻²¹ cm², similar to the signature of the EX2* trap in DLTS (0.27 eV and 1.8 × 10⁻²¹ cm²). The spectra also show a broad shoulder at low temperatures, similar to the broad shoulder in DLTS spectra taken with high forward bias in Fig. 7 and probably related to the presence of a high density of interfacial traps near the Schottky diode boundary. The peak at high temperatures in Fig. 8(b) is due to the E2 electron trap also prominent in DLTS spectra.

For the (−201) orientation, no well-defined hysteretic behavior of the kind shown in Fig. 8(a) was detected. The reason for the observed low temperature hysteresis in I–V characteristics of the irradiated (010) orientation has yet to be understood, but it seems plausible the depletion of electrons on the high density EX2* compensating acceptors in the near surface region of the sample by reverse bias leads to increased space charge density and lowers the effective height of the Schottky barrier, which causes the decrease of the turn-on voltage. Application of the forward bias refills the EX2* centers with electrons and increases the effective Schottky barrier height and hence the turn-on voltage. However, this process requires a long filling time, suggesting the presence of a barrier for the capture of electrons. The cycle can be reversed by applying the reverse bias for a long time sufficient for the emission of electrons from the EX2* acceptors.

The parameters of the center giving rise to the peak near the E3 peak in the irradiated (010) sample were slightly different from those before irradiation: the level was somewhat deeper, 1.1 eV instead of 0.95 eV, and the capture cross section somewhat higher, 2 × 10⁻¹³ cm² instead of 2 × 10⁻¹⁴ cm². This needs further study, but, given the controversy in reported behavior of the E3 trap with irradiation,^27,36 it seems the explanation could be similar to the case of E2 and E2* centers, of which E2 is related to the substitutional Fe acceptor, and the other (E2*) to a native defect,^8,9 likely a V_Ga–V_O divacancy, possibly complexed with hydrogen.^23,42 Detailed measurements of high resolution Laplace DLTS spectra on bulk and epitaxial Ga₂O₃ samples before and after irradiation combined with Secondary Ions Mass Spectrometry (SIMS) might be informative since this approach has been used previously in distinguishing the nature of the E2 and E2* traps.^8,35

Regarding the major radiation defects, EX1 (0.45 eV) prominent in the bulk region of the (010) and (−201) orientations and EX2* (0.27 eV) dominant in the near surface region of the (010) orientation, additional experiments are also necessary. The position of the EX1 trap is not that different from the E1 traps³⁴ found in Czochralski, EFG, HVPE, and MBE materials in the range E_c−(0.46−0.54) eV.^9,23,36 These are never the dominant electron traps in the bulk material. The centers of that type can be introduced by irradiation¹⁶⁻¹⁸ and should be related to native defects or their complexes. Theoretical calculations²³ indicate that a complex of a split Ga vacancy with oxygen vacancy and hydrogen, V_GaⁱH–V_O1, could be responsible for such states. On the other hand, theoretical analysis⁷ indicates that Sn atoms normally should occupy octahedral Ga2 sites (as opposed to Si donors preferring the tetrahedral Ga1 sites) where they preferentially behave as simple shallow donors, although a less energetically favorable DX-like configuration with a relatively deep (+/−) charge transfer state at E_c−0.19 eV is also possible under nonequilibrium conditions. However, if Sn is displaced to the Ga1 site, it can form a deep DX-like state with the charge transition level near E_c−0.4 eV.

The centers reminiscent of the EX2/EX2* electron traps have been previously observed in irradiated Ga₂O₃ epilayers.²⁷ However, in irradiated HVPE-grown samples, these are always minor radiation centers, in contrast to our irradiated (010) bulk EFG-grown crystal where it is a dominant electron trap in the near surface region. Again, theoretical analysis suggests that the V_GaⁱH–V_O1 complexes can form a charge transition (0/2−) level near E_c−0.22 eV²³ close enough to the EX2* state. The EX2* level position is not far from the predicted DX-like (+/−) charge transition state of Sn in the Ga2 site. The slow filling of the center with the application of forward bias at low temperature supports such a possibility.

The concentrations of deep acceptors with optical ionization thresholds near 1.3, 2.3, and 3.1 eV were greatly increased after irradiation, more strongly in the case of the (010) orientation [Figs. 5(b) and 5(c)]. The changes in the concentrations of respective deep acceptors induced by proton irradiation are compared for the two orientations in Fig. 9. The strongest changes occur for the 2.3 eV V_Gaⁱ acceptors, and the amount of the density increase with irradiation is higher for the (010) orientation. This trend is similar to that observed in Positron Annihilation Spectroscopy (PAS) experiments.^37,38 One concern, however, is that the concentrations of the V_Gaⁱ acceptors calculated from PAS (∼10¹⁸ cm⁻³) are much higher than seen for the 2.3 eV centers in our LCV measurements (<10¹⁷ cm⁻³). In electrical measurements, the very high compensation ratios expected from PAS experiments have never been seen.^43–45 It could be that PAS spectra were mostly obtained for heavily n-type doped crystals where the concentration of defects could be higher than in moderately doped crystals for which electrical compensation measurements were performed.

Irradiation of our bulk samples with a higher proton fluence of 10¹⁵ p/cm² led to strong depletion of the near surface region of about 0.15 μm in the (010) sample and of about 0.4 μm in the (−201) orientation (Fig. 5). The appearance of this depleted region led to a strong increase of the series resistance in I–V characteristics of both samples with the series resistance estimated as 1.5 × 10⁶ Ω for the (010) and 4 × 10⁶ Ω for the (−201) orientation (Fig. 10). Measurements of the current density vs temperature at a forward voltage of 2 V where the current is limited by the series resistance gave an activation energy of 0.35 eV for the (010) and 0.45 eV for the (−201) orientation. DLTS spectra measurements were problematic with these high series resistances even for measurements at a reduced probing frequency of 10 kHz.⁴³ However, admittance spectra could be taken, as well as the LCV and SSPC measurements at a low frequency of 1 kHz. Figures 11(a) and 11(b) shows the temperature dependences of capacitance C and AC conductance G normalized by the angular frequency ω = 2πf (f here is the probing frequency), G/ω, for several measurement frequencies for the irradiated (010) orientation (these admittance spectra were collected at −0.2 V). A well-defined peak in admittance and step in capacitance yielded the ionization energy of the responsible center as 0.35 eV with the capture cross section of 4.8 × 10⁻¹⁹ cm², which is close to the parameters of the EX2, EX2* centers and to the activation energy of the series resistance in the current vs temperature measurements.

For the (−201) orientation, similar data gave the parameters of the center as 0.45 eV and σ_n = 5.5 × 10⁻¹⁶ cm², close to the DLTS signature of the EX1 centers introduced by irradiation and again close to the current vs temperature results. Thus, it seems reasonable to assume that in the near surface region of the (010) orientation, the Fermi level is pinned by the dominant EX2* centers introduced by protons, while in the (−201) orientation, it is pinned by the EX1 centers.

The results of measurements of the deep acceptor spectra after the irradiation with 10¹⁵ p/cm² protons are summarized in Figs. 4(b), 4(c) and 9(a), 9(b). For the (010) orientation, the densities of the 2.3 and 3.1 eV acceptors tend to saturate but remain much higher than for the (−201) orientation. The density of the 1.3 eV centers increases with fluence for both types, with the introduction rate much higher for the (010) orientation.

We have shown that 20 MeV protons irradiation of bulk (010) and (−201) crystals lightly doped with Sn results in the decrease of the net donor density with the removal rate of ∼200 cm⁻¹ for both orientations and similar to the removal rate observed earlier for proton irradiated, lightly Si doped HVPE Ga₂O₃ films.²⁷ There are important differences between the types, concentrations, and locations of the deep electron and hole traps observed. Deep inside the Sn doped (010) and (−201) orientation samples, the main electron traps introduced by protons are EX1 traps near E_c−0.45 eV, with the density higher for the (010) orientation. These traps are similar to the E1 (E_c−0.6 eV) traps in HVPE samples,²⁷ but in the latter, the dominant proton-induced electron traps were the E2* (E_c−0.75 eV) and E3 (E_c−1.1 eV) centers. Moreover, near the surface of the (010) Sn doped crystal, irradiation introduces a high concentration of the EX2* traps at E_c−0.27 eV that give rise to hysteresis in low temperature I–V and C–V characteristics depending on the voltage at which the sample was cooled down and the length of time and order in which positive or negative voltage was applied at low temperature before the voltage sweep. In the (−201) orientation, traps EX2 with signatures similar to the EX2* traps are seen, but in a much lower concentration, virtually similar in the bulk and near the surface. Traps of that kind are not dominant in irradiated Si doped HVPE films.

The types of deep traps detected in LCV/SSPC spectra of the (010) and (−201) orientation were virtually the same in both types, with the centers with optical ionization threshold near 2.3 eV dominating these spectra. The concentration of these traps attributed to the split vacancies V_Ga^i23,38 grows much faster with proton irradiation fluence in the (010) orientation than for the (−201). The trend seems to agree with that observed in PAS experiments³⁸ and attributed to the presence of open channels going in the direction normal to the (010) surface in β-Ga₂O₃. However, the absolute concentrations of V_Gaⁱ acceptors estimated from PAS spectra are an order of magnitude higher than those calculated from LCV measurements. Moreover, as in the case of proton irradiated HVPE low Si doped β-Ga₂O₃ films,²⁷ the total number of compensating deep acceptors in proton irradiated samples is considerably lower than the observed decrease in the net donor density in proton irradiated (010) and (−201), while in orientations, the experimental removal rates are close to the calculated introduction rate of Ga vacancies.²⁷ 

Regarding the possible origin of the very high density of the EX2* E_c−0.27 eV acceptors near the surface of the (010) orientation, but not the (−201) orientation, additional studies are necessary. The key facts to be considered in constructing a model are as follows.

1. The effect is more pronounced for the (010) orientation for which the diffusion rate of interstitial hydrogen H_i donors is higher;²³ 

2. the width of the affected region is close to the thickness of the space charge region at 0 V bias in the (010) orientation;

3. the density of the split Ga vacancies V_Gaⁱ is much higher in the irradiated (010) than in the (−201) orientation; and

4. the Schottky barrier height in the (010) orientation is considerably higher than in the (−201) orientation, which has been related to a higher density of oxygen vacancies V_O1.⁴⁶ 

All these factors would favor the preferential formation of the V_GaⁱH–V_O1 complexes with the charge transfer (0/−2) level near E_c−0.22 eV predicted in Ref. 23.

One remaining thing to be addressed is that the dominant EX2* near surface acceptors have not been reported in lightly Si doped HVPE β-Ga₂O₃ films irradiated with protons. If it indeed proves to be true that no such effect is observed for Si doping, another option could be to assume and experimentally check the presence of a higher density of Ga vacancies near the surface of (010) oriented samples, causing an easier transformation of normal Sn donors in the octahedral Ga₂ sites into the high energy DX-like states with a (+/−) charge transfer level in the vicinity of E_c−0.2 eV.⁷ 

It is clear that the observed anisotropy of radiation effects in β-Ga₂O₃ has to be taken into account when designing devices.

The work at NUST MISiS was supported, in part, by the Russian Science Foundation, Grant No. 19-19-00409. The work at UF was sponsored by the Department of the Defense, Defense Threat Reduction Agency, Interaction of Ionizing Radiation with Matter University Research Alliance (Award No. HDTRA1-20-2-0002) monitored by J. Calkins and also by NSF No. DMR 1856662 (James Edgar).

All data that support the findings of this study are available within the article.