Non-linear effects in α-Ga₂O₃ radiation phenomena

Gallium oxide (Ga₂O₃) is an ultra-wide bandgap semiconductor attracting a lot of attention because of its promising applications for new generation high-power electronics, UV optoelectronics, and solar-blind sensors.^1–4 Ga₂O₃ exists in several crystalline lattice forms, called polymorphs, specifically α-, β-, γ-, δ-, and κ(ε)-phases .^5,6 The monoclinic β-Ga₂O₃ polymorph having the bandgap of ∼4.8 eV is the most thermodynamically stable under normal conditions and is readily grown in the form of single crystals by the edge-defined film-fed growth (EFG) or zone melting techniques .⁷ In its turn, the rhombohedral α-Ga₂O₃ is a metastable polymorph, however, exhibiting the highest bandgap (∼5.3 eV) among the rest of Ga₂O₃ polymorphs,⁸ providing potential technological advantages.⁹ Importantly, α-Ga₂O₃ is stable for up to 550 °C at atmospheric pressure and can be epitaxially grown on sapphire substrates using multiple deposition methods, e.g., chemical vapor deposition (CVD), chloride-hydride gas-phase epitaxy [halide vapor phase epitaxy (HVPE)], and mist-CVD.^10,11 Furthermore, the lattice structure of this polymorph allows its hetero-integration with a number of p-type semiconductors, such as Cr₂O₃, Rh₂O₃, Ir₂O₃, and AlN.¹² 

Ion implantation is one of the well-established technological tools for selective area modification of materials and is widely used in modern semiconductor technology to introduce dopants and create insulating regions.^13,14 However, ion implants are accompanied with the radiation-induced lattice disorder and the efficiency of the defect accumulation is a complex function of irradiation parameters, such as ion mass and energy, ion beam flux, and target temperature.^15,16 Notably, for the keV ion irradiation range, the lattice disorder formation in semiconductors occurs predominantly via elastic energy transfer to the target atoms, often referred to as the nuclear energy loss in the literature. Ions colliding with target atoms knock them out of the lattice sites; further on, the displaced atoms, gained enough energy, can collide with other atoms, displacing them from regular positions too, forming so-called collision cascade. The density of such individual collision cascades is one of the prime parameters affecting the efficiency of the keV-ion-irradiation-induced damage accumulation in semiconductors.^17,18

Importantly, to study the impacts of the collision cascade density in radiation phenomena, there is a proven methodology based on comparison of data for monoatomic and cluster ion implants keeping other parameters constant.^19,20 The core of this methodology is in a controllable enhancement of the collision cascade density for cluster ions with increasing their size occurring due to a spatial overlap of cascades produced by the individual atoms comprising cluster ions. This methodology was successfully applied for investigations of the disorder formation kinetics in various materials, including readily amorphizable semiconductors, e.g., Si^19,20 or SiC,²¹ and radiation tolerant materials, e.g., ZnO,²² GaN,²³ or β-Ga₂O₃.²⁴ Notably, for the Ga₂O₃ system, the majority of ion implantation related studies were performed for β-Ga₂O₃, where the roles of the ion dose,^25–27 implanted species,²⁸ irradiation temperatures,²⁹ and implantation-induced polymorph transformation^30–32 were investigated. In contrast, there are only a few initial studies of the radiation phenomena in other polymorphs, including that in α-Ga₂O₃.^33–37 Thus, the aim of the present work is to investigate radiation disorder dynamics in α-Ga₂O₃ in detail applying the controllable collision cascade density methodology.^19,20 As a result, we show that the collision cascade density governs the surface amorphization rates, also affected by the ion flux variations. These trends are discussed in terms of the non-linear in-cascade and inter-cascade defect interactions occurring during ballistic and dynamic defect annealing stages, respectively. As such, these data reveal new physics of the radiation phenomena in α-Ga₂O₃ and may be applicable for more predictive ion beam processing of α-Ga₂O₃-based devices.

We used ∼2 μm thick (0001) rhombohedral α-Ga₂O₃ layers grown on the c-plane sapphire substrate by HVPE at Perfect Crystals LLC.¹¹ The samples were irradiated with monatomic (P⁺) and cluster (PF₄⁺) ions at room temperature (RT) in a wide range of ion fluences and fluxes. Two series of implants with ion energies per atomic mass unit (amu) of 1.3 and 2.1 were performed. All implants were performed 7° off the normal to the sample surface to minimize the channeling effects. To make the data comparable, the samples were intended to have the same number of displacements per atom (dpa), as estimated according to the binary collision approximation. The dpa values were calculated as Φ_dpa = n_vΦ/n₀, where n_v is the number of generated vacancies per ion and depth unit at the position of the nuclear energy loss distribution maximum, Ф is the ion fluence in cm^–2, and n₀ is the atomic concentration of α-Ga₂O₃ (n₀ = 1.03 × 10²³ atoms/cm³). The n_v values were obtained using the SRIM code³⁸ simulations, with displacement energies of 25 and 28 eV for Ga and O sublattices, respectively. For PF₄ ion bombardment, the vacancy concentration was calculated as an algebraic sum of the vacancy concentrations produced by the atomic constituents of the cluster, i.e., n_v(PF₄) = n_v(P) + 4 × n_v(F). The dose-rate defined as F_dpa = dΦ_dpa/dt was kept constant in units of dpa/s for both types of ions. Thus, the irradiation conditions for both ions were chosen in such a way to keep constant (i) ion energy per atomic mass unit, (ii) ion dose in dpa, and (iii) ion flux in dpa/s. Therefore, the difference in the defect accumulation between monoatomic and cluster ion implants was attributed entirely to the fact that the atoms comprising a cluster ion impinge the surface at the same point, whereas monatomic ions hit the surface at randomly distributed locations. For convenience, the irradiation parameters used in the present study are listed in Table I. It should be noted that in order to ensure efficient heat transfer, we mounted samples on a massive metal holder. Thus, considering for relatively low ion fluxes used in the experiment (as presented in Table I), the irradiation-induced temperature increase on the samples was considered as negligible.

Lattice disorder produced by monoatomic and cluster implants was measured by Rutherford backscattering in channeling mode (RBS/C) using a 0.7 MeV He⁺⁺ beam. The incoming He⁺⁺ beam was aligned along the [0001] direction, placing a backscattering detector at a glancing angle of 103° relative to the incident beam direction to increase the depth resolution. The damage-depth distribution profiles were deduced from the raw RBS/C spectra using one of the conventional algorithms³⁹ and are referred to as relative disorder vs depth profiles in the rest of this paper.

Figure 1 shows the depth distributions of relative disorder in α-Ga₂O₃ after irradiation with 1.3 keV/amu P [Fig. 1(a)] and PF₄ [Fig. 1(b)] ions, as extracted from the RBS/C data [it should be noted that the surface topography data as well as the RBS/C data for the virgin (unimplanted) and irradiated samples together with the spectrum corresponding to the random direction of the probing He beam are available from the supplementary material]. Depth profiles of the primary displacements and implanted atom distribution, as calculated with SRIM code³⁸ simulations, are also shown on an arbitrary vertical scale. It is clearly seen that for both types of implants, the damage profiles exhibit bimodal depth distribution, featuring strong surface disordering [labeled as the surface amorphous layer (SAL), in accordance with the literature³² in the rest of this paper] and the peak located in the crystal bulk [labeled as the bulk damage peak (BDP)]. Notably, the BDP position is located slightly deeper than the depth of the implanted ion distribution (R_p) and the nuclear energy loss (R_pd) maxima. This observation corroborates with the results of other implants in α-Ga₂O₃³⁴ and can be attributed to the out-diffusion of generated mobile point defects (MPD) and their strong interaction with the surface and/or SAL interface.⁴⁰ 

The SAL thickness was calculated from the RBS/C spectra and its magnitude together with the BDP amplitude obtained in different implants are shown in Figs. 1(c) and 1(d) as a function of dpa. It is seen that for low dpa (<3), the surface amorphization is more efficient for the PF₄ ions compared to that for P, as shown in Fig. 1(c). In contrast, the BDP values are practically identical—compare the trends for the blue and red lines shown in Fig. 1(d). However, for higher dpa (>3), the BDP for P ions starts to grow and reaches the full amorphization level at the highest dose used. Concurrently, the BDP for PF₄ ions saturates at 0.2 and becomes practically independent of the dpa value, as shown in Fig. 1(d).

Accounting that both P and PF₄ ions generate similar number of primary “ballistic” collisions, as explained in Sec. II, the only different condition for the data shown in Fig. 1 is the collision cascades densities. At least the SAL thickness variations may be unambiguously attributed to this effect, as will be discussed in Sec. IV. Notably, the BDP trends may also be influenced by chemical effects, since the dose of P ions is significantly higher than that of PF₄ for the same dpa value; however, more detailed investigation of this possibility is out of the present paper’s scope.

Figure 2 shows the relative disorder vs depth profiles in α-Ga₂O₃ samples irradiated by 2.1 keV/amu P and PF₄ ions to the same dpa value of 0.44 using different ion fluxes (f). Notably, the dose corresponding to dpa = 0.44 is relatively low, so that the dose-related disorder saturation is not a dominating effect here and the SAL thickness variation trends may be unambiguously attributed to the impacts of the flux changes; see Fig. 2. Despite that SAL dominates for both ions, the damage profiles produced by P and PF₄ ions are different. Interestingly, at the level of relatively low BDP-related signal, an additional damage peak located at ∼13 nm below the surface is observed for P ion bombardment; see Fig. 2(a). This intermediate peak is located between the SAL and BDP, and its magnitude depends on the ion flux. Previously, a similar peak was observed in ZnO irradiated by heavy and cluster ions generating dense collision cascades; see, e.g., Refs. 22 and 41. However, this peak is not observed for PF₄ ions [Fig. 2(b)], so that another mechanism should be put forward. For example, its formation can be related to the strain effects attributed to the SAL and BDP interface regions similarly to that observed for implanted SiC.⁴² Consistently with this hypothesis, Azarov et al. have observed strain accumulation in the low dose ion implanted α-Ga₂O₃ concurrently detecting its release with increasing SAL thickness.³⁶ 

Figures 2(a) and 2(b) also show an increase in the SAL with increasing flux for both monatomic and cluster ion implants. Thus, the dose-rate effect on SAL formation is observed for RT implants consistently with the literature.³⁴ Meanwhile, the disorder enhancement for cluster ion irradiation as compared to that of atomic ones is also so-called molecular effect (ME). In short, the ME magnitude (Δ) can be determined as Δ = n_{d_mol}/n_{d_at}, where n_{d_mol} and n_{d_at} are the relative disorder produced by cluster and monatomic ions, respectively. The inset in Fig. 2(b) plots the Δ(f) dependence, and it is seen that for low f values, the PF₄ ions produce more defects as compared to that of P ions by a factor of 5 for the same dpa value. This inset also shows that the Δ(f) dependence exhibits a non-linear behavior, specifically the Δ magnitude decreases with increasing f.

It is well established that disorder formation in materials irradiated with ion beams is a result of two sequential stages occurring on different time scales.⁴³ In particular, formation of primary defects and collision cascades take place during the ballistic stage on a ps-time scale. In contrast, the second stage is characterized by the interaction and annihilation of the MPDs survived the collision cascade thermalization. This stage, so-called dynamic defect annealing, has a much longer characteristic time scale compared to that of the ballistic stage.⁴⁴ Both stages can lead to strong non-linear effects of the disorder accumulation under ion bombardment. For example, a concept of non-linear energy spikes was put forward to explain experimental observations for amorphizable semiconductors bombarded with keV heavy ions, which produce dense collision cascades.⁴⁵ In its turn, defect clustering was proved to be the dominating mechanism for keV light ions generating dilute collision cascades.²⁰ 

It should be noted that both stages or even a combination of the two can potentially lead to disorder enhancement in α-Ga₂O₃ samples for the PF₄ ions compared to the monoatomic P implants, as experimentally observed in Figs. 1 and 2. Thus, in order to reveal the relative contribution of the disorder formation mechanisms at the different stages, in the following, we discuss non-linear processes occurring within individual collision cascade as well as inter-cascade interactions for atomic and cluster ion bombardments.

In this section, we discuss the impact of the collision cascade density on the efficiency of disorder accumulation in α-Ga₂O₃ in order to reveal the defect interaction processes occurring within individual collision cascade, i.e., in-cascade processes. Even though, for estimation of the density of collision cascades produced by the atomic and cluster ions, we used the methodology described previously,²³ some clarifications are still needed. Indeed, for reliable estimation of the cascade density, modeling of the volumetric distribution of the primary defects is crucial. For example, Fig. 3(a) shows the 3D depth projection of randomly chosen individual cascades for one P and four F ions, corresponding to a single PF₄ cluster, as simulated by SRIM code. It is seen that the cascades consist of multiple subcascades heavily overlapping in the near surface region. Indeed, Figs. 3(b) and 3(c) show the lateral defect distributions at the depth of 0–15 and 20–30 nm, respectively, as derived from the data in panel (a). It is seen that in the near surface region, there is an efficient overlapping of sub-cascades produced by different ions [Fig. 3(b)], while the cascades become well-separated deeper in the sample [Fig. 3(c)]. This effect results in an increase in the average collision cascade density (ρ_aν) produced in α-Ga₂O₃ by PF₄ ions as well as the probability of subcascade formation (η) near the surface region as plotted in panels (d) and (e), respectively.

Thus, a region with a high density of atomic displacements is formed near the surface, while cluster cascade becomes more dilute with increasing depth. Indeed, the average distance between the cascades produced by the atoms comprising molecule ion increases with increasing depth, so that the cascade overlapping becomes less efficient as clearly shown in Figs. 3(b) and 3(c). Therefore, starting from a specific depth, the density of molecule-generated cascades will be identical to those of monatomic ions having corresponding masses and energies. This also implies that at the depth where the cascades produced by the atoms comprising PF₄ ion are fully separated, the density of the cascade created by heavier monatomic ion, i.e., P, would be higher than that of the PF₄ ion, as evident from Fig. 3(d).

The experimentally observed trends (Fig. 1), i.e., the enhanced surface amorphization and less efficient disorder formation in the BDP region for PF₄ ions compared to P ions, correlate well with the cascade density analysis shown in Fig. 3. Therefore, it can be concluded that the collision cascade density plays a profound role in the ion-beam induced radiation disorder formation in α-Ga₂O₃. This could be attributed to non-linear effects of the defect interaction at the ballistic stage of the disorder formation. In this case, the nonlinearity could be described either within the framework of a non-linear energy spike model (such as displacement and/or thermal spikes),^46–48 decreasing the threshold atom displacement energy caused by strong local lattice distortions⁴⁹ or local stoichiometric imbalance.⁵⁰ It should be noted that determination of the relative contribution of the above-mentioned effects is challenging; however, it should be noted that the energy spike nonlinearity is the most accepted concept to explain the non-linear phenomena in semiconductors for the irradiation regimes when dense collision cascades are generated. In addition, even if the defect concentration in the overlapping regions is not high enough to ignite energy spikes, non-linear effects can potentially appear due to enhanced defect interaction during cascade thermalization and subsequent dynamic annealing stage.

In order to estimate the interaction of defects generated in different collision cascades and their contribution to the residual disorder, we consider the Δ(f) variations. It should be noted that if only in-cascade energy spike mechanisms take place (discussed in Sec. IV A), there should be no Δ(F) dependence. Indeed, energy spike processes can occur only in dense collision cascades, so that it is practically impossible to experimentally reach a high enough dose-rate of monatomic ions to hit at the same surface point within a very short period of time that is needed to mimic a cluster cascade. On the other hand, the residual disorder could be affected by secondary defect formation processes occurring during dynamic annealing stage, for example, due to an MPD clustering.²⁰ In addition, MPDs could disappear on various sinks in the material, such as dislocations and stacking faults. However, the complexity of dynamic annealing processes is due to different possible routes for MPDs interaction as well as a variety of the intrinsic defects in Ga₂O₃, which include interstitials and vacancies from both Ga and O sublattices as well as nonequivalent sites.

Figure 4 illustrates the trends for the ME magnitudes and corresponding cascade overlapping as a function of the defect generation rate for monoatomic P and cluster PF₄ ion irradiations. Immediately after thermalization, cascades generated by monatomic ions are spatially separated, whereas the individual cascades, produced by atoms comprising a cluster, overlap. The survived MPDs out-diffuse forming a diffusional zone of the larger size compared to the initial cascade area (see the bottom panels in Fig. 4). It should be noted that the impact of the ion flux on disorder formation is a function of two characteristic time scales determining the defect balance. Indeed, a time period when the MPDs can diffuse and interact with other defects before annihilation or trapping is characterized by the cascade stabilization time (t_st). In its turn, the average time interval between ion impacts occurring in a close vicinity of each other, so the defects from these collision cascades can interact, can be characterized by a cascade overlapping time (t_ov). Obviously, t_st should be a function of irradiation temperature, while t_ov directly depends on the ion flux, so in the following, we consider the defect interaction scenarios as a function of the t_ov/t_st ratio.

For low ion fluxes (region I shown in Fig. 4), when t_st ≪ t_ov, MPDs generated in different cascades do not have a possibility to interact, so that the Δ(f) value in this regime should be maximal and is determined by in-cascade processes only. In its turn, for very high defect generation rate (region III shown in Fig. 4), when t_st ≫ t_ov, the interaction of MPDs from different collision cascades is so efficient that there is practically no difference between cluster and monoatomic irradiation regimes. In this regime, an inter-cascade MPDs interaction dominates for both monatomic and cluster ion irradiations, minimizing the ME magnitude, so that Δ(f) = 1 for negligible spike effects during ballistic stage or Δ(f) > 1 if non-linear energy spikes dominate the disorder formation for cluster ions. The central part of the schematics (region II shown in Fig. 4) illustrates the intermediate dose-rate region, where t_st ≈ t_ov, is of a particular interest. Indeed, in this regime, even minor variations of the ion flux can lead to dramatic changes of the disorder formation and ME magnitude.

Thus, the experimentally measured Δ(f) and its asymptotics at high dose rates may potentially reveal relative contributions of different mechanisms for radiation damage formation in α-Ga₂O₃. In addition, variation of the sample temperature may facilitate discrimination of the deferent mechanisms too. Indeed, it was demonstrated that irradiations at low or even cryogenic temperatures allows us to suppress dynamic annealing processes to a large extent, so energy spike contribution can be readily revealed.⁴⁷ Nevertheless, a comparison of the defect interaction scenario described above with the experimentally observed trends (Fig. 2) indicates that the inter-cascade defect interaction can lead to a strong non-linear effects of disorder accumulation for a limited range of the defect generation rates.

In conclusion, the impact of the cascade density on the disorder accumulation in α-Ga₂O₃ was investigated using irradiations with monoatomic P and cluster PF₄ ions. The corresponding disorder depth profiles exhibit bimodal distributions with two distinct peaks observed at the sample surface and in the crystal bulk. Importantly, we showed that the collision cascade density governs the surface amorphization rates, also affected by the ion flux variations. These trends are explained in terms of the non-linear in-cascade and inter-cascade defect interactions occurring during ballistic and dynamic defect annealing stages. As such, these data reveal new physics of the radiation phenomena in α-Ga₂O₃ and may be applicable for more predictive ion beam processing of α-Ga₂O₃-based devices.

The raw RBS/C spectra and the surface topography of the as-grown α-Ga2O3 films are provided in the supplementary material.

The work was supported by the Russian Science Foundation (Grant No. 22-19-00166). The authors acknowledge the M-ERA.NET GOFIB project (Research Council of Norway Project No. 337627) and the project in the frame of the FRIPRO Program (Research Council of Norway Project No. 351033) for financial support. The international collaboration was enabled by the INTPART Program funded by the Research Council of Norway (Project No. 322382).

The authors have no conflicts to disclose.

Anton Klevtsov: Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Platon Karaseov: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Alexander Azarov: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Visualization (equal); Writing – review & editing (lead). Konstantin Karabeshkin: Formal analysis (equal); Investigation (equal); Methodology (equal). Elizaveta Fedorenko: Formal analysis (equal); Investigation (equal); Visualization (equal). Andrei Titov: Conceptualization (lead); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Writing – original draft (lead). Andrej Kuznetsov: Formal analysis (supporting); Funding acquisition (equal); Project administration (equal); Resources (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.