Monoclinic gallium sesquioxide ( β-Ga₂O₃) has drawn a lot of attention due to its ultra-wide bandgap (~4.9 eV) and ultra-high breakdown electrical fields, which make it promising in the application of power electronics and deep-ultraviolet optoelectronics^[1,2]. In particular, it owns a high Baliga’s figure of merit more than four times that of GaN and SiC^[1], making it to be an excellent candidate for power semiconductor devices operating in high-frequency circuits^[1,2]. Besides, the β-Ga₂O₃ devices have the advantages of high radiation hardness, high-temperature stability, potentially low cost due to the earth-abundant material, and ease to manufacture massively due to its compatibility with Si microelectronic technology. In the application of semiconductors, defects can significantly influence the performance of devices. For example, they may bring in deep levels inside the bandgap to trap the carriers or even become the nonradiative recombination centers to kill the free carriers, deteriorating the performance of devices^[3].

In β-Ga₂O₃, three signature levels (E_1,E_2, andE₃) have been frequently observed in the deep-level transient spectroscopy (DLTS) measurements irrespective of different types of measured β-Ga₂O₃ samples, including bulk crystals grown by the Czochralski method (CZ)^[4] and edge-defined film-fed growth (EFG)^[5], and epitaxial thin films fabricated by metalorganic chemical vapor deposition (MOCVD)^[6] and hydride vapor phase epitaxy (HVPE)^[7]. Specifically,E₁ is 0.55–0.63 eV,E₂ is 0.74–0.81 eV, andE₃ is 1.01–1.10 eV below the conduction band minimum (CBM) of β-Ga₂O₃^[4–7]. The DLTS measurements also obtained the electron capture cross-sections, which are 10^–14–10^–13, 10^–16–10^–15, and 10^–14–10^–13 cm^2[4,5,7], respectively, for these three signature levels.Table 1 summarizes these experimentally measured defect signature levels and corresponding electron capture cross-sections. These signature levels have been assigned to different types of defects, such as intrinsic defects or extrinsic impurities^[8]. For instance, (i) the origin of theE₁ andE₃ centers used to be regarded as the transition metal impurities presenting at the Ga lattice sites^[9], including Fe_Ga and Co_Ga^[4]. (ii) TheE₂ center was initially suggested to be the Fe_Ga defects by Ingebrigtsenet al.^[8]. Zimmermanet al.^[10] further distinguished that there are two overlapping DTLS peaks, labeled asE_2a (0.66 eV) andE_2b (0.73 eV) instead of a singleE₂. These two signatures have then been assigned to the Fe substituting Ga on a tetrahedral site (Fe_GaI) and an octahedral site (Fe_GaII), respectively, based on the energy levels and the concentration ratio^[10]. Recently, Zimmermannet al.^[11] provided additional evidence to support the above conclusion regarding the good agreement of absorption cross-section between first-principles calculations of the Fe_Ga defect and the experimental results from steady-state photo-capacitance spectra measurements. (iii) TheE₃ trapping center has been suggested as oxygen vacancy (V_O)^[12], or substitutional transition-metal defects (e.g., Fe_Ga or Ti_Ga)^[9]. However, the calculated V_O defect level is located at 1.67–2.46 eV (below the CBM)^[13], which is much deeper thanE₃ at 1.01–1.10 eV and thus can be ruled out. Zimmermanet al.^[10] then assigned theE₃ center as a defect of Ti substituting Ga on an octahedral site (denoted as Ti_GaII) based on a strong correlation in concentration between theE₃defect and the Ti ions present in the samples and a good agreement in energy position between theE₃ level and the Ti_GaII defect, which is obtained by the hybrid functional calculations. So far, Fe- and Ti-related defects are considered as the most possible candidates forE₁,E₂, andE₃ centers not only due to the above arguments but also because they can be introduced to β-Ga₂O₃ unintentionally in fabrications. For example, Fe is the most common contaminant in manufacturing. Ti is often used as Ohmic contact for β-Ga₂O₃ devices^[1,14]. However, most identifications are made based purely on matching the energy levels, which could be accidental.

Generally, the DLTS is a highly sensitive analytical technique that is used to measure the energy positions of defects and obtain the carrier capture cross-sections, but without the capability to obtain information about the configuration and elements of the defects^[4]. The first-principles calculations are therefore used to explore the atomic origin of these defect levels by examining their defect levels. One challenge in previous theoretical studies of the defect levels is that only the predicted transition energies can be compared with experimental data. Therefore, the identification of the atomic origin for a special defect level is still a difficult task. Fortunately, the newly developed first-principles approach for carrier capture cross-sections enables us to examine the defect candidates utilizing a combination of both the energy level and carrier capture cross-section for each center. In this work, we use this approach to verify the well-established defect candidates of Ti_Ga and Fe_Ga for the three signatures in β-Ga₂O₃ by performing the first-principles calculations for both defect transition level and electronic capture cross-section. The calculated transition levels of Ti_GaI and Ti_GaII from a charge stateq= +1 to a charge stateq= 0 are 0.59 and 1.08 eV below the CBM within the ranges of DLTS measuredE₁ (0.55–0.63 eV) andE₃ (1.01–1.10 eV), respectively. This excellent agreement is consistent with previous first-principles calculations^[10]. In particular, the calculated electron capture cross-sections of Ti_GaI and Ti_GaII defects are both around 10^–14–10^–13 cm² and thus are also in excellent agreement with experimental results ofE₁ andE₃ centers^{[4,5,7,10,15]}. Subsequently, we can safely conclude that the Ti_GaI and Ti_GaII defects are responsible for DTLS observed E₁ andE₃ centers, respectively. However, the calculated electron capture cross-section of Fe_Ga defects is around 10^–13 cm², which is about two orders of magnitude larger than that of DLTS measuredE₂ center. Such large disagreement indicates thatE₂ has other origins than Fe_Ga, although the defect levels of Fe_Gaare in good agreement with theE₂ (orE_2a, andE_2b) center.

In this work, all the first-principles calculations were performed using the PWMAT^[16,17] package with the SG15 collection of the optimized norm-conserving Vanderbilt pseudopotentials (ONCV)^[18] with an energy cutoff of 70 Ryd. Heyd-Scuseria-Ernzerhof (HSE)^[19] screened hybrid functional was applied for all the calculations except the calculations of electron-phonon coupling constants which used the Perdew-Burke-Ernzerhof functional of the generalized gradient approximation (GGA-PBE). The Ga-4s, -4p, Ti-3s, 3p, -3d, -4s, and Fe-3s, -3p, -3d, -4s electrons were included as valence electrons. The fraction of the screened Hartree-Fock exchange was adjusted to α = 0.33 to reproduce the experimental band gap of 4.9 eV. The lattice parameters of the pure β-Ga₂O₃ were predicted to be a = 12.20 Å,b = 3.03 Å, andc = 5.78 Å with β = 103.8 °, as shown inTable 2. A 160-atom ( 1×4×2) supercell is adopted to calculate defects with a Gamma-onlyk-point mesh for integration over the Brillouin zone.Fig. 1 shows the atomic configuration of one Ti substituting one Ga atom on the tetrahedral site (Ti_GaI) and the octahedral site (Ti_GaII), respectively, in β-Ga₂O₃. The defect of Fe substitution of Ga (Fe_Ga) has the same configurations as Ti_Ga except for the replacement of Ti by Fe. We have considered spin polarization for the incorporation of Fe ions in the first-principles calculations. Fe substituting Ga atom in +3 (S=52) and +2 (S = 2) states^[8,20] are labeled as FeGa0 and FeGa−.

We use a well-established set of approaches^[27,28] to calculate the formation energies and transition levels εi/f of the defects based on the first-principles calculations of total energy. Specifically, for charged defects, we utilize the image charge interaction correction with the approximation method (C-AP) proposed in Ref. [29] to obtain the defect formation energy as follows,

ΔHf(α,q)={E(α,q)+EC(α,q)}−E(host)−∑iniμi+q(εF+εVBM).

Here, E(α,q) is the total energy of a supercell containing the defect α in a charge stateq, EC(α,q) is the C-AP correction term,E(host) is the total energy of the bulk host supercell without defect, andn_i is the number of atoms with chemical potentialμ_i added (n_i \gt 0) to or removed (n_i \lt 0) from the supercell to create the defect. The chemical potential of Ga(μ_Ga) is in a range with its upper and lower bound setting by bulk elemental Ga (Ga-rich) and the stability condition of Ga₂O₃ (Ga-poor), respectively. The chemical potential of Fe(μ_Fe) is in a range determined by Ga₃Fe and Fe₂O₃^[8] andμ_Ti is determined by TiO₂. The Fermi level εF is referenced to εVBMthe valence band maximum (VBM) of the host (here is Ga₂O₃) with its potential aligned with the potential of defect supercell at the corner (farthest away from the defect). The transition level from the initial statei in a charge state q to the final statef in a charge state q′ is the difference of their formation energy per charge when their Fermi levels equal,

εi/f=ΔH(α,q,EF=0)−ΔH(α,q',EF=0)q'−q.

For the transition levels εi/f close to the CBM, we transform them to referring to the CBM in terms of εi/f(CBM)=Eg−εi/f(VBM).

To calculate the nonradiative carrier capture cross-sections of defects, we then utilize the recently developedab initio multi-phonon method for nonradiative decay rates^[30–33] based on the multi-phonon recombination theory from Kun Huang^[34–36], which has been implemented in the PWMAT^[16,17] package. Specifically, the nonradiative decay probability from the initial electronic statei to the final electronic statef is^[30]

Wif=1ℏ(πλkBT)1/2∑kkBTωk2(∑R〈i|∂H∂R|f〉μk(R))2e−(εi/f−λ)24λkBT,

where εi/f is the defect transition level measured from CBM, λ the reorganization energy induced by the electron transfer fromi tof states, and μk(R) the eigenvector of the phonon modes. The corresponding coordinate difference ΔQ can be obtained in terms of ΔQ=∑αMαΔRα2, where α is atom index in the supercell, Mα is the nuclear mass, and ΔRα=Rf;α−Ri;α the atomic displacement. The summation term in Eq. (3) is defined as an electron-phonon coupling constant |VC|2=∑kkBTωk2(∑R〈i|∂H∂R|f〉μk(R))2, which indicates that the perturbation ΔH caused by atomic displacement due to random thermal vibrations can induce coupling between electronic statesi andj^[30]. Once we get the nonradiative recombination probability Wif according to Eq. (3), we can further compute the carrier capture rate coefficient B=WifV (where V is the volume of the supercell), which is divided by the average thermal velocity vth=3kBT/m* (where kB is Boltzmann constant,T is temperature, andm^* is the carrier effective mass) to finally obtain the carrier capture cross-section σ=B/vth. In β-Ga₂O₃, the electron effective mass is m*≈0.23m0^[37] and thus, at temperature T = 300 K, vth is 2.44 × 10⁷ cm/s, which is very close to the reported electron velocity of ~2 × 10⁷ cm/s in Ref. [38].

We have considered the substitutions of Ga atom on both tetrahedral (Ti_GaI and Fe_GaI) and octahedral sites (Ti_GaII and Fe_GaII). To investigate the capture of electrons by defect levels, we study the +/0 charge transition for Ti_Ga and 0/– transition for Fe_Ga. Our first-principles calculated transition levels and electron capture cross-sections of Ti_Ga and Fe_Ga defects are given inTable 3, in comparison with available results reported in the literature. Our calculated defect levels ε+/0 of Ti_GaI and Ti_GaII are 0.59 and 1.08 eV (below the CBM of β-Ga₂O₃), within the range of ~0.05 eV of previously reported first-principles calculations (0.60 and 1.13 eV for Ti_GaI and Ti_GaII, respectively)^[10]. For Fe_GaI and Fe_GaII, our predicted transition levels ε0/− are 0.61 and 0.74 eV below the CBM, respectively. They are in excellent agreement with previously reported first-principles results, 0.62 and 0.72 eV^[17], respectively. It is ready to learn that both the Ti_Ga and Fe_Ga defects presenting at the Ga octahedral site (GaII) have deeper energy levels than those at the Ga tetrahedral site (GaI). To assess the trapping center assignment based on defect levels, we align our calculated Ti_Ga and Fe_Ga defect transition levels with the DLTS measured defect signaturesE₁,E₂,E₃, as shown inFig. 2. From the alignment of energy levels alone, we indeed see that Ti_GaI, Fe_GaII, and Ti_GaII can be correlated withE₁,E₂, andE₃ trapping centers, respectively, which is consistent with previous assignments^[8,10].

Based on the calculated transition levels εi/f given inTable 3, we then predicted the electron capture cross-sections σn of Ti_GaI and Ti_GaII defects at 300 K by performing the first-principles calculations according to Eq. (3).Table 3 shows that σn of Ti_GaI is 8.56 × 10^–14 cm² and of Ti_GaII is 2.97 × 10^–13 cm². These two data are well within the range 10^–14–10^–13 cm² of experimental data ofE₁ andE₃ centers (compiled inTable 1)^[4,5,7]. Note that these are cross-sections for electron trapping from the original positive defect and hence could have a correction factor due to the long-range Coulomb interaction between defect and electron^[39], which makes the concentration of the electron carriers near the defect larger than the average carrier density. The exact value of this correction factor depends on many factors, including the static dielectric function, the carrier concentration, the carrier effective mass, and temperature. In previous studies^[39], this factor was found to be within 1 and 10 for oxides. After considering this correction factor, these calculated decay cross-sections for Ti_GaI and Ti_GaII are still within the experimental range ofE₁ andE₃ centers. Based on this, we thus conclude that the atomic origin of theE₁ trapping center is Ti_GaI and theE₃ trapping center is Ti_GaII. WhereasTable 3 shows that the electron capture cross-sections σn of Fe_GaI and Fe_GaII at 300 K are 4.23 × 10^–13 and 6.42 × 10^–13 cm², respectively. Note, for the initial neutral defect, the above-mentioned correction factor is close to 1. Therefore, the electron capture cross-sections of Fe_GaI and Fe_GaII defects are at least two orders of magnitude larger than the experimental value of 10^–16–10^–15 cm² forE₂ center^[4,5,7]. Such substantial disagreement in the electron capture cross-section rules out the Fe_Ga defect as theE₂ center, although from the energy level comparison we can assign Fe_GaII as theE₂ center or Fe_GaI and Fe_GaII as theE_2a andE_2b levels, respectively.

Nevertheless, before overturning the previous assignment for theE₂ center^[8,10], it is necessary to examine whether the computational uncertainties in the transition level and the coupling term can cause such a big disagreement in the electron capture cross-section between theE₂ center and its candidate Fe_Ga. First, the calculated coordinate difference ΔQ in the charge transitions are 2.06 (Ti_GaI), 1.42 (Ti_GaII), 1.61 (Fe_GaI), and 1.32 (Fe_GaII) amu^1/2/Å respectively, which are consistent with the previous first-principles calculations presented in Refs. [10,11]. This confirms that our supercell configurations and energy level calculations are aligned with the literature.

We then inspect the effect of energy level uncertainty on the electron capture cross-sections of defect candidates.Fig. 3 shows the calculated electron capture cross-sections σn of Ti_Ga and Fe_Ga as a function of the defect transition level εi/f at 300 K, which is an artificially rigid shift inside the host Ga₂O₃ bandgap from VBM to CBM. σn of Ti_Ga and Fe_Ga changes from ~10^–19 to ~10^–12 when εi/f varies from ~2.4 eV below CBM to CBM. Note that the peak position corresponding to the reorganization energy λ can also be written down as Sℏω¯k^[30] with the Huang-Rhys’ factorS^[35,36]. At the peak position, Wif and σn will get the maximum value because the defect level εi/f equals the reorganization energy λ and then exp(−(εi/f−λ)24λkBT)=1. As we can see, the maximum σn for these defects are almost at the same magnitude, so σn for each defect is finally determined by the exponential term, more specifically the energy difference between εi/f and λ.Table 3 shows the transition level εi/f of defects is very close to its reorganization energy, except for Ti_GaI whose εi/f is ~0.5 eV lower than λ. Thus, the carrier capture cross-sections σn are relatively high for the Ti_GaII, Fe_GaI, and Fe_GaII defects, mostly in the magnitude of 10^–13 at 300 K, while σn of Ti_GaI is a little smaller. These are relatively strong trappings of electrons and indicate the importance of these defects for carrier dynamics. In comparison, the defects in another typical wide-bandgap semiconductor SiC have much smaller trapping rates; for example, the electron capture cross-sections of defects such as V_C, V_Si, V_C–V_Si, and N_C–V_Si in 4H-SiC are all less than the order of 10^–15[3].Fig. 3 shows the dependence of σn on εi/f for each defect shares the same variation tendency and shape, indicating that the differences induced by the transition metal atoms Ti and Fe can be small. Thus, σn of Ti_Ga and Fe_Ga are in a similar order of magnitude.

We finally examine the effect of the electron-phonon coupling term |VC|2 for the capture cross-sections via comparing Fe_Ga and Ti_Ga defects.Table 3 shows that |VC|2 for Ti_GaI and Ti_GaII defects are 0.58 and 0.56 eV², respectively, and for Fe_GaI and Fe_GaII defects are 0.43 and 0.48 eV², respectively. The difference between two nonequivalent sites is tiny for each defect and the difference between Ti_Ga and Fe_Ga is also small. To gain insight into their similarity in the magnitude of |VC|2, we further evaluate the phonon mode and wavefunction of the defects, which govern the electron-phonon coupling constant |VC|2.Fig. 4(a) shows the phonon density of states (ph-DOS) for the system containing Ti_GaI and Ti_GaII, respectively. One can find that the different substituting sites will not induce a sizable change in the ph-DOS. This is also true for the Fe_Ga defect as shown inFig. 4(b). It is even more interesting to note that the Fe_Ga defects resemble their ph-DOS with Ti_Ga defects, indicating the change in the impurity atom seldom affects the ph-DOS of the system. One main factor is that they have similar ionic radius due to Fe and Ti. In the 6-fold coordination configuration, the ionic radius of the Ti impurity changes from 0.68 to 0.76 Å from Ti⁴⁺ to Ti³⁺, and the ionic radius of the Fe impurity changes from 0.64 to 0.74 Å from Fe³⁺ to Fe^2+[40]. As for the electronic property,Fig. 1 shows that the partial charge densities of the Ti_GaI and Ti_GaII defect states are very similar because they both originate from the Ti 3d orbitals. It is also expected to be the same in the Fe_Ga defects where the defect states stem from the Fe 3d orbitals. Subsequently, the effective phonon modes involving the electron-phonon coupling are also similar, even though there may have small differences in strength among these four defects, as shown inFigs. 4(c)–4(f). These above features result in the close |VC|2 for Ti_GaI and Ti_GaII, as well as for Fe_GaI and Fe_GaII. The change from Ti to Fe is unlike to remarkably alter the |VC|2.

Although the reorganization energy λ of these defects varies from 0.7 to 1.06 eV as listed inTable 3,Fig. 3 shows that, for all the defects, the maximum of Wif at εi/f=λ are in the same order of magnitude, which are 0.94 × 10¹⁶, 1.04 × 10¹⁶, 0.83 × 10¹⁶, and 0.97 × 10¹⁶ s^–1 for Ti_GaI, Ti_GaII, Fe_GaI, and Fe_GaII, respectively. The similarities in the ph-DOS, the defect charge density from the 3d orbital, and the similar impurity ion radius all contribute to the above similarity for the maximum capture rate. The similarity of the maximum Wif and the fact that their transition level energy is close to the reorganization energy λ result in a similar magnitude of σn around 10^–13 cm² for Fe_Ga and Ti_Ga defects. Based on this analysis, it is clear that Fe_Ga and Ti_Ga cannot have dramatically different σn. Even if there are some computational uncertainties, these uncertainties should equally apply to both Fe_Ga and Ti_Ga. We have concluded Ti_GaI and Ti_GaII are responsible forE₁ andE₃, respectively. Thus, the apparent difference (two orders of magnitude) in experimentally measured σn betweenE₁ (orE₃) andE₂ might be used as evidence for excluding Fe_Ga from the assignment toE₂.

From the perspective of the defect formation energy, we can also argue that the Fe_Ga defects are relatively unlike to form due to their high formation energy. Note that β-Ga₂O₃ is generally an n-type semiconductor.Fig. 5 exhibits that, to form the Ti_Ga (E₁ andE₃) defects clearly, the system must be in an O-poor condition (otherwise, the Ti_Ga formation energy can be as high as 2–3 eV). Under this O-poor condition, the literature has reported that the formation energies of both Fe_GaI and Fe_GaII are always higher than both Ti_GaI and Ti_GaII^[8,10]. Our calculations also show that the formation energy of Fe_Ga is higher than that of Ti_Ga if the Fermi level is ~0.8 eV below the CBM. The difference occurs only in the case of high n-type doping.Fig. 5(a) shows that the formation energy of Ti_GaI will raise over those of both Fe_GaI and Fe_GaII, while Ti_GaII remains smaller than the formation energy as the Fermi level increases towards CBM due to heavier n-type doping, which argues for the unfavorable formation of Fe_Ga. Experimental measurements have observed^[41] that electron trapping centersE₂ andE₃ have a comparable concentration of (2–4) × 10¹⁶ cm⁻³, butE₁ has one order of magnitude lower concentration (3 × 10¹⁴–6 × 10¹⁵ cm⁻³)^[41]. Our predicted higher formation energy of Ti_GaI (E₁) than that of Ti_GaII (E₃), as shown inFig. 5(a), clearly explains the concentration difference betweenE₁ andE₃ centers. However, the high formation energy of Fe_Ga (E₂) renders it impossible to have a comparable high concentration as Ti_GaII (E₃). Subsequently, we can safely rule out the Fe_Ga defects as the atomic origin of theE₂ center, which is the dominant electron trapping center and presents in all β-Ga₂O₃ samples.

Since we have ruled out the assignment of Fe_Ga as theE₂ center, it must have other defects responding to it. For instance, Irmscheret al.^[4] postulated thatE₂ may be associated with Sn_Ga and V_O; Farzanaet al.^[5] proposed C-related origins. From our understanding, we can suggest the possibleE₂ candidates. We have mentioned above that the electron capture cross-sections of deep level defects in β-Ga₂O₃ are at least an order of magnitude larger than those in SiC. Because SiC is more covalent than β-Ga₂O₃, thus results in a weaker lattice vibration-induced local dipolar field and electron-phonon coupling. Hence, we expect the change of foreign atoms is unlikely to substantially change the maximum value of σn at εi/f=λ. However, we can horizontally shift the downward “parabola” of the σn(εi/f) by modifying the reorganization energy λ, as shown inFig. 6, to remarkably reduce the σn value at εi/f=E2.Fig. 6 shows the schematic diagram for σn(εi/f) ofE₂ candidates with proper reorganization energy λ. Here, an experimental defect level ofE₂ (0.74 eV^[4]) is adopted, and the experimental electron capture cross-section σn is (0.3–3) × 10^–15 cm^2[4] . These two conditions require the candidates to have the reorganization energy at ~1.4 or ~0.1 eV. This means the large atom size difference between substituting atom and the host lattice atom or even complex defects can induce strong local distortion, resulting in a large reorganization energy of ~1.4 eV. Meanwhile, a defect with very small reorganization energy as ~0.1 eV, meaning the less atom size difference and weak local distortion, may also make sense. The first-principles calculation predicted transition level of the C_Ga defect is 0.81 eV below CBM^[42] which is very close to theE₂ level of 0.74 eV. The large difference in atom size between C and Ga is expected to induce strong distortion, which may give rise to larger reorganization energy (as large as ~1.4 eV) than 0.70 eV of Fe_GaII and have σn(εi/f) curve like the blue one shown inFig. 6. Therefore, C_Ga is very likely responsible forE₂. However, the defect level of V_O is 1.67–2.46 eV below CBM^[13], rather deeper than 0.74 eV; Sn_Ga has the defect level of 0.19 eV below CBM^[42] which is too shallow. Both V_O and Sn_Ga are unlikely responsible for theE₂ center. Beyond these defects suggested in the literature, we find that Ga_i and Ga_OII^[7], V_Ga–V_O divacancies such as V_GaII–V_OI or V_GaI–V_OII^[21] all have the defect levels at 0.7–0.9 eV below CBM and may also induce strong distortion and have large reorganization energy. Subsequently, the C_Ga, Ga_i, Ga_OII, and V_Ga–V_O defects can be candidates forE₂ and need to be studied further in the future.

We use first-principles methods to calculate the defect levels and the electron capture cross-sections of Ti_Ga and Fe_Ga in β-Ga₂O₃ which have been assigned to the experimental signaturesE₁,E₃, andE₂centers in the literature. Using both transition level position and electron capture cross-sections as criteria, we proposed that Ti substituting for Ga on a tetrahedral site (Ti_GaI) and an octahedral site (Ti_GaII) are indeed associated withE₁ andE₃ states respectively. However, for the signature levelE₂, the Fe substituting for Ga on a tetrahedral and an octahedral site have calculated transition level energies in good agreement with the experiment, but the calculated electron capture cross-sections are two orders of magnitude larger than the experimental results. A comparative analysis between the Ti_Ga and Fe_Ga defects and a computational sensitivity study of electron capture cross-sections indicate that the computational uncertainty is unlikely to cause a two order of magnitude difference in the electron capture cross-sections between Ti_Ga and Fe_Ga. Besides, the calculated formation energy shows it is unfavorable for the Fe_Ga formation. All of these lead us tentatively exclude Fe_Ga as the experimentally observedE₂ signature. Thus, the exact nature ofE₂ awaits future experimental and theoretical discovery.