Magnesium-doped gallium oxide may be utilized as a semi-insulating material for future generations of power devices. Spectroscopy and hybrid functional calculations were used to investigate defect levels in Czochralski-grown β-Ga2O3. Substitutional Mg dopants act as deep acceptors, while substitutional Ir impurities are deep donors. Hydrogen-annealed Ga2O3:Mg shows an IR peak at 3492 cm−1, assigned to an O-H bond-stretching mode of a neutral MgH complex. Despite compensation by Ir and Si and hydrogen passivation, high concentrations of Mg (1019 cm−3) can push the Fermi level to mid-gap or lower.

Gallium oxide (Ga2O3) is a wide bandgap, transparent oxide semiconductor with properties favorable for utilization in power electronic devices. It has a high breakdown field, estimated to be three times larger than that of SiC or GaN, other wide bandgap semiconductors used for power devices.1,2 β-Ga2O3, the most stable phase of Ga2O3, has a high electron mobility and large bandgap between 4.5 and 4.8 eV.3–5 β-Ga2O3 also benefits from being relatively cheap to produce and easy to grow in single crystals.6,7 Recently, there has been interest in the production of p-type β-Ga2O3, a more challenging prospect.8,9

One promising acceptor dopant is magnesium. There have been several reports of Mg doping yielding insulating β-Ga2O3.10–12 The positions of defect levels in the gap, however, are largely unknown. In this work, single-crystal undoped and Mg-doped β-Ga2O3 crystals were grown. The crucial roles of H and Ir impurities in passivating/compensating Mg acceptors were revealed by spectroscopy and hybrid functional calculations.

Infrared (IR) transmission spectra were collected using a Bomem DA8 vacuum Fourier transform infrared (FTIR) spectrometer. The system uses a silicon carbide light source, a KBr beamsplitter, and an InSb detector. Measurements for this work were taken with a 1 cm−1 resolution at 10 K. UV/visible transmission spectra were collected using a Perkin Elmer Lambda 900 Series UV/VIS/NIR Spectrometer with a deuterium lamp source. All UV/visible transmission spectra were taken at room temperature.

β-Ga2O3 boules were grown using the Czochralski (CZ) method. The raw material used was high purity gallium oxide powder (99.999%) from GFI Advanced Technologies, Inc. The raw material and dopants were weighed with 10 mg precision (adjusting for the inherent moisture content within the powders) to a target weight of 500 g and then ball milled using high purity (99.8%) alumina milling balls for 18 h. After mixing, the powder was compressed in an isostatic press to ∼20 kpsi to make the final charge.

Crystals were grown using an iridium crucible (86 mm diameter × 60 mm tall) with a radio-frequency induction coil operated at 20 kHz. First, the 500 g charge was melted over the course of ∼15 h and then cooled. After this, a second charge of 500 g was added to the crucible to increase the melt volume to 1 kg for improved heat flow and to maintain stable flow patterns during growth. The undoped crystal was difficult to grow by traditional CZ so a Kyropoulos style growth was used instead.13 The grown boules were all polycrystalline due to an inadequate seed; however, the bottom of the boules all had larger size crystals, allowing for single crystal samples to be obtained and tested. For optical measurements, light was incident normal to the (100) surface (a plane). Additional details are given in the supplementary material.

Hydrogen diffusion was performed by sealing the sample in a silica ampoule filled with ½ atm of hydrogen gas. The ampoule was then annealed in a furnace and water-quenched to room temperature. Similar annealing conditions were used for undoped (820 °C, 2 h) and Mg-doped (860 °C, 3.5 h) samples. Two-point resistance measurements with pressed indium contacts gave a resistance of ∼10 KΩ for our undoped samples, consistent with n-type conductivity from Si donor impurities. Measurements for H-annealed Ga2O3:Mg yielded a resistance of ∼300 GΩ, and the as-grown Ga2O3:Mg samples were too resistive to acquire a reading, confirming that Mg incorporation makes Ga2O3 insulating.

Secondary ion mass spectrometry (SIMS) was performed by Evans Analytical Group (EAG) on deuterated Ga2O3 and deuterated Ga2O3:Mg to a depth of 3 μm. Profiles were obtained for concentrations of deuterium, silicon, magnesium, and iridium. D and Si were calibrated from an implant standard and accurate within 30%. Ir and Mg were uncalibrated and only estimated to be accurate to within a factor of 3, according to EAG. O2+ ions were the primary ions for Mg and Ir detection, and Cs+ ions were the primary ions for D and Si measurements.

Calculations were performed using the HSE06 screened hybrid functional14,15 and projector-augmented wave (PAW) approach16 as implemented in the VASP code.17,18 The Ga 3d and Mg 1p and 2s electrons were chosen as explicit valence states and the fraction of screened Hartree-Fock exchange was set to 32%. This choice yields a bandgap of 4.85 eV and optimal lattice constants in excellent agreement with experimental values as detailed by Ingebrigtsen et al.19 Formation energies were computed for each defect using 120-atom supercells adopting the same formalism.19 The chemical potential of Mg was limited by the formation of competing phases that included MgGa2O4, MgO, and Mg2Ga5, with MgGa2O4 limiting the solubility of Mg in both the Ga-rich and O-rich limits (ΔΗ[MgGa2O4] = −16.3 eV). The chemical potential of Ir was bounded by the limiting phases of Ga9Ir2 in the Ga-rich limit (ΔΗ[Ga9Ir2] = −4.79 eV) and IrO2 in the O-rich limit (ΔΗ[IrO2] = −2.84 eV). The chemical potential of H was limited by the formation of water in the O-rich limit. Spin-orbit interactions were included explicitly for the formation energies of Ir impurities but neglected for all other defects.

Finite-size corrections were performed using the method of Freysoldt et al.20 with the low-frequency anisotropic dielectric constant measured by Schubert et al.21 Anharmonically corrected vibrational frequencies were calculated from a fourth-order polynomial fit as detailed in previous works.22,23 This procedure tends to overestimate O-H bond-stretching frequencies, as previously identified in SnO2 with the same hybrid functional parameters.22,23

As an experimental baseline, hydrogen diffusion was performed on an undoped Ga2O3 crystal (1–2 mm thick). Using IR spectroscopy, we observed absorption peaks at 3314, 3437, 3450, and 3500 cm−1 [Fig. 1(b)]. These peaks are assigned to O-H bond-stretching vibrational modes. The corresponding deuterium peaks were observed using the same annealing procedure with ½ atm D2 [Fig. 1(a)]. The observed isotopic frequency ratio between the H and D complexes is ∼1.35, in good agreement with O-H and O-D in other semiconductors.24,25 This ratio is slightly less than the square root of the isotopic mass ratio, 2, due to anharmonicity and the finite mass of the oxygen host atom. The peak at 3437 cm−1 was observed by Weiser et al.26 and attributed to a gallium vacancy decorated with two hydrogen atoms. The other peaks (3314, 3450, and 3500 cm−1) have not been identified. They may be due to hydrogen complexed with native defects or impurities.

FIG. 1.

IR absorption spectra of (a) deuterium and (b) hydrogen annealed Ga2O3. Both spectra have been baselined with polynomial fits.

FIG. 1.

IR absorption spectra of (a) deuterium and (b) hydrogen annealed Ga2O3. Both spectra have been baselined with polynomial fits.

Close modal

To assess the effects of Ir contamination and Mg incorporation, we include the calculated formation energy diagrams for substitutional Ir and Mg-related defects in Fig. 2 for the O-rich and Ga-rich limits. Our results identify that Ir and Mg most favorably incorporate on the octahedral Ga(II) site. Similar to previous studies,27 we find that MgGa(II) acts as a deep acceptor, with a calculated (0/–) charge-state transition level 1.06 eV above the valence-band maximum (VBM). Consistent with the work of Kananen et al.,12 we find that the hole most favorably localizes on an adjacent O(I) atom, while a hole localized on the O(II) atom is 0.16 eV higher in energy. Mg on the tetrahedral Ga(I) site is less favorable by 0.5 eV for both the neutral and negative configurations, yielding a slightly deeper acceptor level of 1.27 eV. Mg interstitials (Mgi) are shallow donors that can be favorable for Fermi levels below mid-gap. However, O-rich conditions suppress the formation of this self-compensating species.

FIG. 2.

Formation energy diagrams for Mg-related defects in Ga2O3 shown for (a) Ga-rich and (b) O-rich limits. The results identify Mgi as a shallow donor, while MgGa is a deep acceptor most favorable in n-type conditions. MgGa acceptors can also form complexes with Hi donors leading to their electrical passivation.

FIG. 2.

Formation energy diagrams for Mg-related defects in Ga2O3 shown for (a) Ga-rich and (b) O-rich limits. The results identify Mgi as a shallow donor, while MgGa is a deep acceptor most favorable in n-type conditions. MgGa acceptors can also form complexes with Hi donors leading to their electrical passivation.

Close modal

Conversely, IrGa(II) acts as a deep donor with two levels in the bandgap, indicating that IrGa defects are electrically inactive in n-type Ga2O3. The (+/0) charge-state transition level corresponding to the Ir4+/Ir3+ oxidation states is calculated to be close to mid-gap, 2.60 eV above the VBM (2.25 eV below the conduction-band minimum, CBM). An additional (2+/+) charge-state transition level is calculated to be 1.01 eV above the VBM.

Experimentally, the Mg-doped Ga2O3 samples exhibit a strong IR absorption peak at 5148 cm−1 [Fig. 3(a)]. Based on its similarity to absorption peaks from Ir4+ in other oxides,28,29 we attribute it to Ir4+ impurities introduced by the iridium crucible.30 The peak is assigned to a transition from the ground state to an excited d-orbital. Iridium present in the undoped sample is probably in the form of Ir3+, which is not visible in the IR. The added magnesium accepts an electron from the iridium, creating Ir4+ and the associated absorption peak.

FIG. 3.

IR absorption spectrum of Ir4+ in Mg doped Ga2O3 (a) before and (b) after hydrogen annealing.

FIG. 3.

IR absorption spectrum of Ir4+ in Mg doped Ga2O3 (a) before and (b) after hydrogen annealing.

Close modal

UV/visible transmission spectra of the Mg-doped samples show an absorption threshold at 2.8 eV (Fig. 4). This absorption threshold is not observed in the spectra of undoped Ga2O3, nor in Ga2O3:Mg produced by float-zone crystal growth.11 Because of this, we attribute the absorption to the excitation of a valence-band (VB) electron to the Ir4+/3+ level, rather than an excitation to/from the Mg level. Note that there is a second threshold at 3.2 eV. This feature could be due to the transition of a VB electron to an Ir3+ excited state, similar to the case of Fe in GaAs.31 

FIG. 4.

UV/visible transmission spectra of undoped Ga2O3, Mg-doped Ga2O3, and H2 annealed Mg-doped Ga2O3. Only the Ga2O3:Mg sample shows an absorption threshold at 2.8 eV. Band-gap absorption is observed near 4.5 eV.

FIG. 4.

UV/visible transmission spectra of undoped Ga2O3, Mg-doped Ga2O3, and H2 annealed Mg-doped Ga2O3. Only the Ga2O3:Mg sample shows an absorption threshold at 2.8 eV. Band-gap absorption is observed near 4.5 eV.

Close modal

To assess optical transitions between IrGa(II) and the valence and conduction bands, we calculated the excitation energies in a configuration coordinate diagram analysis (Fig. 5). For the process of electron capture from the VBM to the IrGa(II)+ donor state, the calculations predict a zero-phonon line of 2.6 eV and an absorption peak of 3 eV, which closely match the features in the measured spectra (Fig. 4). We additionally predict transitions to the CBM from the filled state of the neutral IrGa(II) (Ir3+/Ir4+) with a similar absorption peak of 2.8 eV and an onset of 2.25 eV. However, these features are not observed in undoped Ga2O3 (Fig. 4). This is similar to GaAs:Fe, where the lack of an Fe-to-CBM absorption feature was attributed to a very low optical cross section for that particular transition.31 

FIG. 5.

Calculated configuration coordinate diagram for optical excitations with IrGa(II) exchanging electrons with the VBM (left panel) and the CBM (right panel). The calculated absorption onset of 2.6–3 eV associated with an electron capture from the VBM by the IrGa(II)+ donor state agrees well with the measured absorption in Fig. 4.

FIG. 5.

Calculated configuration coordinate diagram for optical excitations with IrGa(II) exchanging electrons with the VBM (left panel) and the CBM (right panel). The calculated absorption onset of 2.6–3 eV associated with an electron capture from the VBM by the IrGa(II)+ donor state agrees well with the measured absorption in Fig. 4.

Close modal

The hydrogen complexes present in the undoped sample (Fig. 1) were not observed in H-annealed Ga2O3:Mg. Instead, a new hydrogen-related peak appears in the IR spectrum at 3492 cm−1 (Fig. 6), attributed to the O-H bond-stretching mode of a MgH complex. In Fig. 2, we also included the formation energy of hydrogen complexes with MgGa (MgGa(II)-H), which we find to be favorable defects that render MgGa acceptors electrically neutral. Relative to the isolated Hi+ donors and MgGa(II) acceptors, we find that the neutral complex is 0.6 eV more preferable, indicating a modest binding energy. Thus, hydrogen passivation of magnesium acceptors would no longer require them to be compensated by donors and lead to a Fermi level higher in the bandgap. This greatly weakens the Ir4+ peak at 5148 cm−1 [Fig. 3(b)]. The 2.8 eV absorption threshold in the transmission spectrum, which we attributed to Ir4+, is also suppressed (Fig. 4).

FIG. 6.

IR absorption spectra of Ga2O3:Mg annealed in D2, H2, and D2:H2 mixtures.

FIG. 6.

IR absorption spectra of Ga2O3:Mg annealed in D2, H2, and D2:H2 mixtures.

Close modal

To confirm that the 3492 cm−1 feature is a hydrogen-related defect, Ga2O3:Mg was annealed in deuterium. The resulting peak was appropriately shifted to 2586 cm−1 (Fig. 6). To establish the number of passivating hydrogen atoms involved in the complex, we annealed a sample in a mixture of H2 and D2. If the O-H and O-D peaks were the result of a two hydrogen center, “H-D” peaks would be expected to appear from centers that contained one H and one D.32 As shown in Fig. 6, varying ratios of hydrogen and deuterium changes the relative intensity of the O-H and O-D peaks but no H-D peaks were observed. From the lack of H-D peaks, we conclude that the magnesium-hydrogen center in Ga2O3 is a MgGa acceptor passivated by one H atom. A weaker O-H (O-D) line was observed at 3545 cm−1 (2622 cm−1), but its intensity varied from sample to sample. This line may be due to a different acceptor-hydrogen complex.

IR spectra of the H-annealed Ga2O3:Mg sample were taken at various angles with a linear polarizer to observe the relative strength of the 3492 cm−1 O-H peak (Fig. 7). The resulting spectra show the hydrogen related peak to be the strongest when E//c and not observable when E//b. From this, we conclude that the O-H dipole is oriented in the a-c plane.

FIG. 7.

IR absorption spectra of the primary hydrogen peak in H-annealed Ga2O3:Mg. θ = 0 corresponds to polarization along the b axis. Spectra are displaced vertically for clarity. Inset: Calculated model of the Mg-H complex.

FIG. 7.

IR absorption spectra of the primary hydrogen peak in H-annealed Ga2O3:Mg. θ = 0 corresponds to polarization along the b axis. Spectra are displaced vertically for clarity. Inset: Calculated model of the Mg-H complex.

Close modal

To additionally confirm this assignment, we calculated anharmonically corrected vibrational frequencies associated with the MgGa(II)-H complex (ω = ω0 − Δω). Owing to the energetically preferable configuration of H bonded to an O(I) atom, the complex consists of the O-H bond oriented largely along the a-axis within the a-c plane adjacent to the MgGa(II) (Fig. 7). Our calculated frequency is ω = 3617 cm−10 = 3889 cm−1 and Δω = 272 cm−1), which is 125 cm−1 higher than the experimental frequency. A similar overestimate (181 cm−1) was found for O-H complexes in SnO2.22,23 From the good agreement of this peak with the experimentally identified IR peak and the associated polarization dependence, the MgGa(II)-H complex is a plausible candidate for the 3492 cm−1 peak. We additionally compute wag modes of 1203 cm−1 (within the a-c plane) and 717 cm−1 (within the a-b plane) within the harmonic approximation using linear response theory, but these were not measured due to strong two-phonon absorption in that spectral region.

Finally, SIMS analysis shows an average concentration of 1.4 × 1018 cm−3 for D in the Mg-doped sample but only 2 × 1015 cm−3 in the sample without Mg (Table I). This three order-of-magnitude difference is consistent with the low formation energy of interstitial hydrogen in p-type or semi-insulating Ga2O3 as compared to the n-type material.22 In the Mg-doped sample, the D concentration is slightly lower than the Mg concentration. Given the margin for error, however, it is possible that the Mg acceptors may be fully passivated in hydrogen-annealed Ga2O3. In both samples, the combined concentration of Si and Ir donors is significantly less than that of the Mg. This bodes well for using Mg doping to lower the Fermi level. While it is possible that oxygen vacancies may act as compensating donors,4,33 oxygen-rich growth conditions may suppress their formation.

TABLE I.

Detection limits and elemental concentration from SIMS analysis on Mg-doped and undoped Ga2O3. The absolute concentrations of D and Si are accurate to within 30%, while Ir and Mg are estimated to be accurate to within a factor of 3.

DSiIrMg
Detection limit (cm−38.0 × 1014 1.0 × 1015 1.0 × 1015 5.0 × 1014 
Concentration in Mg-doped Ga2O3 (cm−31.4 × 1018 1.7 × 1017 7.1 × 1016 7.4 × 1018 
Concentration in undoped Ga2O3 (cm−31.8 × 1015 5.1 × 1016 4.4 × 1016 1.9 × 1015 
DSiIrMg
Detection limit (cm−38.0 × 1014 1.0 × 1015 1.0 × 1015 5.0 × 1014 
Concentration in Mg-doped Ga2O3 (cm−31.4 × 1018 1.7 × 1017 7.1 × 1016 7.4 × 1018 
Concentration in undoped Ga2O3 (cm−31.8 × 1015 5.1 × 1016 4.4 × 1016 1.9 × 1015 

In conclusion, we have observed H and Ir defects in β-Ga2O3. Ga2O3:Mg annealed in hydrogen forms neutral MgH complexes with an O-H vibrational mode at 3492 cm−1. SIMS shows that hydrogen is much more readily incorporated into the magnesium doped β-Ga2O3 than the undoped (lightly n-type) material. This observation, along with resistance measurements, supports the idea that Mg doping lowers the Fermi level significantly. Ir from the crucible compensates the magnesium acceptors, along with Si impurities. However, the concentration of Mg is much higher than that of compensating donors. While oxygen vacancies and Mgi may compensate acceptors, O-rich growth conditions can suppress the formation of these defects and allow the Fermi level to be pushed below mid-gap.

See supplementary material for SIMS plots and crystal orientation measurements.

The authors acknowledge helpful discussions with M. Scarpulla and thank D. Fields and C. Merriman for performing EBSD. This research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-FG02-07ER46386.

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