Identification and characterization of deep nitrogen acceptors in β-Ga₂O₃ using defect spectroscopies

Beta-phase gallium oxide (β-Ga₂O₃) possesses an ultra-wide bandgap (UWBG) of 4.6–4.8 eV,^1–3 inherent n-type conductivity with donor impurities,^4,5 and projected high radiation hardness.^6,7 The advantageous material properties of β-Ga₂O₃ lead to outstanding device figures of merit projections that can revolutionize high voltage and RF devices. As a result of these anticipated performance specifications, a large body of research has focused on advancing the quality of gallium oxide materials, heterostructures, and a wide variety of devices. To date, high breakdown β-Ga₂O₃ metal-semiconductor field-effect transistors (MESFETs),⁸ high 2DEG charge densities in (Al_xGa_1−x)₂O₃/Ga₂O₃ modulation-doped field-effect transistors (MODFETS),⁹ and enhancement mode β-Ga₂O₃ transistors¹⁰ have been epitaxially grown on Fe-doped β-Ga₂O₃ semi-insulating substrates. For these lateral devices, it is necessary to have semi-insulating or highly resistive buffers or substrates acting as a blocking layer to prevent buffer leakage. Regardless of the growth method, the unintentional n-type conductivity can be compensated by introducing deep acceptor-like impurities. Density functional theory (DFT) calculations have identified several impurities that are predicted to form deep acceptor-like bandgap states, such as iron (Fe), nitrogen (N), cobalt (Co), and magnesium (Mg).^11–14 These deep acceptors can be used as dopants to compensate for excess electrons and create highly resistive layers. Of these, Fe has been adopted in most cases for achieving highly resistive and semi-insulating bulk β-Ga₂O₃ substrates and epitaxial layers.^12,15,16

Due to this popularity, much work has been published regarding the properties of Fe in β-Ga₂O₃. Computational results validated by deep-level (thermal) transient spectroscopy (DLTS), electron paramagnetic resonance (EPR), and cathodoluminescence (CL) experiments have demonstrated that Fe incorporates into n-type β-Ga₂O₃ as an acceptor-like defect.^12,17–26 It is predicted to preferentially substitute on the Ga sites in the β-Ga₂O₃ lattice, creating a bandgap state at E_C-0.8 eV (commonly referred to as E2).^12,27 However, with an activation energy of only 0.8 eV below the conduction band, Fe has shown to be a source of device instabilities. For example, Mcglone et al. showed a clear link between the thermal emission of electrons from the E_C-0.8 eV Fe state during device biasing and significant threshold voltage instabilities for β-Ga₂O₃ delta doped MESFETs.²⁰ This results from Fe incorporation from the Fe-doped substrates tailing into the unintentionally doped (UID) epitaxial buffer layer between the substrate and the 2DEG device channel. Hence, while this degradation mode can be mitigated by using thicker UID buffers,¹⁹ this highlights the concern that the E_C-0.8 eV position of Fe acceptors in the 4.6–4.8 eV bandgap of β-Ga₂O₃ may not be ideal since its charge state can be modulated during device biasing and trapped electrons can be thermally emitted. An impurity with a deeper acceptor level could therefore be advantageous in reducing the chance of modulating its charge state during biasing and becoming thermally ionized, even at the high operating temperatures envisioned for β-Ga₂O₃ power electronics.

As a result, there is interest in alternative acceptor-like dopants to Fe. A recent study published by Seyidov et al. demonstrated cobalt doping in Czochralski (CZ) growth, resulting in semi-insulating β-Ga₂O₃ substrates with the Fermi level pinned at E_C-2.1 eV.¹³ Similarly, Mg doping has resulted in high-quality semi-insulating β-Ga₂O₃ materials with a predicted acceptor level at E_C-3.4 eV by DFT.^11,14,28 Nitrogen has been identified as a deep acceptor candidate by Peelaers et al. through DFT calculations.¹¹ N substituting on oxygen I, II, and III sites in the β-Ga₂O₃ lattice forms acceptor-like levels with (0/−1) charge-state transition levels at E_C-1.61 eV, E_C-1.46 eV, and E_C-2.84 eV, respectively.¹¹ In recent experimental measurements after ion implantation, N was found to diffuse only at temperatures greater than 1100 °C, while Mg diffusion was observed at temperatures as low as 800 °C.^29,30 Using these results and evaluating them with transition state theory, a barrier diffusion activation energy of 3.87 eV for N and 2.84 eV for Mg was obtained.^11,29 Large activation energies indicate high thermal stability in extreme environments and are desirable for deep acceptor dopants. In addition, the ion implantation study reported that a high acceptor doping efficiency was achieved using N.²⁹ Nitrogen has been successfully incorporated in epitaxial layers grown by metal-organic chemical vapor deposition (MOCVD) using an N₂O precursor, resulting in a room-temperature electron mobility of 153 cm²/Vs and a low net ionized doping concentration of 10¹⁴ cm⁻³.^26,31 With these promising preliminary work as motivation and given the lack of experimental knowledge regarding the nature of nitrogen-related defects within β-Ga₂O₃, we have undertaken a study to investigate the electronic properties associated with nitrogen-related deep-level defects within β-Ga₂O₃. A combination of both deep-level transient (thermal) spectroscopy (DLTS) and deep-level optical spectroscopy (DLOS) measurements was applied to a systematic sample set of Si and N co-doped β-Ga₂O₃ materials designed to allow for precise and quantitative identification of nitrogen-related defect states in β-Ga₂O₃, which were confirmed by DFT calculations. This study suggests very efficient incorporation of nitrogen into a preferred configuration in the β-Ga₂O₃ lattice, having an energy level of E_C-2.9 eV, implying significant promise for future applications of nitrogen doping to create ideal, highly resistive β-Ga₂O₃ materials for implementation into future device technologies.

A systematic set of experiments was performed using several N-implant conditions on thick, Si-doped hydride vapor phase epitaxy (HVPE) grown β-Ga₂O₃ materials with (001) orientation to investigate the introduction of deep levels associated with nitrogen. The reference sample was a 10 μm thick Si-doped HVPE grown epilayer on a highly conductive (n = 3–5 × 10¹⁸ cm⁻³) Sn-doped β-Ga₂O₃ substrate procured from Novel Crystal Technology.^32,33 The HVPE-grown epilayer was doped with Si to achieve a net ionized doping concentration of 1.2 × 10¹⁷ cm⁻³. This value was chosen so that subsequent nitrogen co-doping via ion implantation could be used to achieve nitrogen concentrations high enough to be measured using secondary ion mass spectrometry (SIMS), i.e., above the SIMS detection limit of ∼1 × 10¹⁶ cm⁻³, while simultaneously producing an appropriate degree of carrier compensation to be within ideal measurement conditions for capacitance-based DLTS and DLOS characterization. Using Stopping and Range of Ions in Matter (SRIM) simulations,³⁴ a uniform implantation profile was created by combining nitrogen implant energies from 10 to 680 keV, each with different dose; an example of the individual implant profiles is shown in Fig. 1(a) in the light gray curves. The cumulative nitrogen implant profile from the individual energy implants results in the desired uniform nitrogen concentration profiles. Two sets of samples were created, one with a uniform nitrogen doping of 2 × 10¹⁶ and another at 5 × 10¹⁶ cm⁻³, within the top ∼0.8 µm of the HVPE layer, depicted in Fig. 1(a). The implantation was performed using a commercial implanter (Cutting Edge Ions). Post-implantation annealing was performed at 1100 °C in nitrogen ambient for 10 min using a rapid thermal annealing (RTA) system to remove implantation damage and activate the dopants as reported elsewhere.²⁹ The annealing was performed on a ULVAC technology MILA 3000 rapid thermal annealing (RTA) system.

Multiple Schottky diodes were fabricated on each of the three samples: a baseline HVPE sample without implantation and annealing and the two implanted and annealed samples with nitrogen concentrations of 2 × 10¹⁶ and 5 × 10¹⁶ cm⁻³ confirmed by SIMS (discussed later). The Schottky diode fabrication process in all cases is now described. All samples were solvent cleaned with acetone and isopropyl alcohol (IPA), followed by a rinse in deionized (DI) water. Semi-transparent 8 nm Ni Schottky contacts (290 × 290 μm²) were then deposited using electron (e)-beam evaporation, followed by an e-beam deposited ohmic contact stack of Ti/Al/Ni/Au (20/200/30/200 nm) on the back side of the conducting substrate. A thick Ni/Au (30/200 nm) contact stack of 25 × 25 μm² was deposited on a small area of the thin 8 nm semi-transparent Ni-Schottky for probing the device and making stable contacts during measurements. A cross-sectional diagram depicting the fabricated diodes on the baseline HVPE and the post-implant annealed samples are shown in Figs. 1(b) and 1(c), respectively. The fabricated samples yielded dozens of high-quality Schottky diodes across each sample, with nearly identical I–V characteristics having ideality factors of 1.1 ± 0.05 and leakage current densities below 10⁻⁹ A/cm². Typical Schottky barrier heights were found to be ∼1.4 V as measured using internal photoemission (IPE) spectroscopy, with negligible changes after N-implantation.^35,36

DLTS measurements on the fabricated diodes were carried out over a temperature range from 77 to 400 K, enabling the determination of concentrations and activation energies for trap states within ∼1 eV of the conduction band. Briefly, the DLTS conditions used here consisted of a “fill pulse” of 0 V for 10 ms to fill traps, followed by a “quiescent state” reverse bias at −2 V for 2 s, during which any capacitance transients due to thermally stimulated electron emission from traps are recorded at each temperature from 77 to 400 K in steps of 0.1 K and subsequently analyzed using a conventional double boxcar method. The full details of the measurement can be found in previous publications.^37–40 The remaining distribution of trap states in the bandgap was obtained using DLOS measurements. DLOS is based on direct photoemission of trapped carriers from states too deep to be seen by thermally stimulated carrier emission measurements like DLTS. The trap-filling in the depletion region is achieved with a fill pulse voltage of 0.7 V for 10 s, followed by a thermal settling time of 100 s. Trapped carriers, if any, are then optically emitted by a monochromatized light source providing photons with energies between 1.2 and 5.0 eV, scanning the bandgap in 0.02 eV steps for 300 s each, and photocapacitance transients are recorded. These are subsequently analyzed to extract optical cross sections of any traps present as a function of photon energy. The extracted optical cross sections are then fitted to the Pässler model, which enables the determination of the equilibrium trap energy level and the Frank–Condon energy (D_FC).^41,42 The concentration of each DLOS-detected state is determined from the steady-state photocapacitance (SSPC) associated with each state. The lighted C–V (LCV) method was also used to assure complete saturation of the SSPC for accurate trap concentration extraction since we have reported that for cases where a defect state possesses a small optical cross section, SSPC saturation can be difficult.^35,36,43,44

As noted above, the Si:N co-doping concentrations were chosen to allow correlations between the nitrogen concentration, carrier compensation, and deep-level concentration by being within the measurement limits of both SIMS and DLTS/DLOS. The nitrogen concentration profiles obtained by SIMS for both target concentrations after the post-implant anneals are shown in Fig. 2(a), revealing uniform implant profiles in close agreement with the targeted design discussed earlier. Capacitance–voltage (C–V) measurements reveal systematically increased carrier compensation (lower net doping) as a function of increased nitrogen doping, as shown in Fig. 2(b) (it should be noted that without post-implant annealing, the implanted samples are fully depleted, presumably due to implantation damage). Based on the simple assumption that each nitrogen defect is activated and removes a single conduction band electron, nitrogen doping should remove ∼17% and 42% of the free electron concentration in the lower and higher nitrogen co-doped samples, respectively, for each N concentration. However, the results indicate that while almost all the implant damage was removed by the post-implant anneal, the slightly higher amount of carrier removal actually observed at 27% and 67%, respectively, suggests that some damage in the form of additional compensating defects is likely to remain, in addition to the nitrogen acceptors. This work, however, is not focused on anneal optimization. The next section presents comprehensive DLTS and DLOS investigations, which focus on identifying nitrogen-related states but can also reveal residual defect states that could contribute to the slightly higher degree of observed carrier compensation for the implant and anneal conditions used here.

The DLTS spectra for the baseline and two N co-doped (post-implant and annealed) HVPE samples are shown in Figs. 3(a)–3(c), with the Arrhenius characteristic for each DLTS trap shown in Fig. 3(d). The DLTS spectra reveal states at E_C-0.25 eV, E_C-0.34 eV, E_C-0.4 eV, E_C-0.6 eV, E_C-0.7 eV, and E_C-0.8 eV. The levels at E_C-0.7 eV and E_C-0.8 eV are also present in the baseline Si-doped HVPE sample, while the other four levels were only observed in the N co-doped samples. The trap concentrations for each state were calculated using the “lambda” correction to account for the volume of the depletion region in which the occupancy of the specific trap level is modulated by the DLTS biasing.³⁹ This is critical for the most accurate concentration values, shown for each trap in Figs. 3(a)–3(c).

Several observations are important from the DLTS data. First, none of these energy levels match anywhere close to the predicted nitrogen states previously reported for β-Ga₂O₃. Hence, the sources of these states are likely due to pre-existing defects in the baseline Si-doped HVPE material or result from implantation damage that was not fully removed by the post-implant anneal process used here and is not related to nitrogen.^7,12,21,45 Second, regardless of their source, the individual and total concentrations of DLTS-detected traps are on the order of 10¹³–10¹⁴ cm⁻³. This is far lower than what can account for the large carrier removal observed in the C–V data. However, the total is large enough to account for some of the differences between the anticipated and measured amount of carrier removal discussed above. While this work is not focused on optimizing the implant and annealing conditions for nitrogen doping by implantation, it is still helpful to consider possible sources for these defect states to provide insights into the HVPE material and the implant process used here.

To that end, we have included other sets of well-known and commonly observed DLTS data with the Arrhenius plot shown in Fig. 3(d), which are associated with Fe impurities and point defects due to high-energy particle irradiation, as labeled in the same figure. Comparisons with the data here are revealing. First, the radiation-induced defect data closely matches three trap states observed here at E_C-0.34, E_C-0.6, and E_C-0.7 eV.^6,7 Since the proton radiation damage produces intrinsic point defects, these are all likely due to residual damage from the nitrogen implantation process. The state at E_C-0.7 eV has received significant focus in prior work and has been connected with gallium vacancies; recent work has proposed the Ga–O divacancy as the most likely origin.^6,7,12,17 Additionally, the state detected at the E_C-0.8 eV closely matches the well-known trap associated with Fe_Ga defects, suggesting that residual Fe is present in the HVPE material.^12,15,21 As noted above, both the E_C-0.7 and E_C-0.8 eV traps are present in the control baseline HVPE sample, and the concentration of the E_C-0.8 eV trap did not change, consistent with its source being residual Fe. Finally, the sources of the remaining two DLTS states at E_C-0.25 eV and E_C-0.4 eV could be introduced by the implant damage and/or by the annealing process. Regardless, none of the DLTS traps have high enough concentrations of consequence to explain the strong carrier compensation observed in the co-doped samples. Thus, the section titled "DLOS results" focuses on the rest of the bandgap using DLOS measurements.

The individual DLTS measured trap concentrations (∼10¹³–10¹⁴ cm⁻³) were several orders of magnitude lower than the targeted N concentrations shown in Fig. 1(a) or the measured carrier compensation in Fig. 2(b). Furthermore, the N on oxygen substitutional sites in β-Ga₂O₃ form acceptor levels predicted by DFT to be significantly deeper than anything observed by DLTS. Therefore, DLOS and LCV measurements were used to interrogate the rest of the bandgap to investigate the possible presence of other state(s) responsible for the carrier compensation. The SSPC data in Fig. 4(a) reveal three SSPC onsets at E_C-2.0 eV, E_C-2.9 eV, and E_C-4.4 eV, associated with very deep levels in the bandgap. The concentrations from the SSPC onsets indicate trap concentrations on the order of 10¹⁶ cm⁻³, far higher than the DLTS trap concentrations. In order to ensure complete saturation of the DLOS-detected states to compare concentrations with SIMS, LCV measurements were applied to each state. Considering the E_C-2.9 eV state first, Fig. 4(b) compares independently measured E_C-2.9 eV trap concentrations with SIMS-measured N concentration as a function of the targeted N implant concentration. There is a clear correlation and quantitative match between the concentration of this trap and the total N concentration. The LCV measured trap concentrations for the E_C-2.9 eV state were found to be 1.8 × 10¹⁶ cm⁻³ and 4.5 × 10¹⁶ cm⁻³ for the 2 × 10¹⁶ cm⁻³ and 5 × 10¹⁶ cm⁻³ N co-doped samples.

The overall quantitative trends for all detected states as a function of N implant concentrations are depicted in Fig. 5, confirming that the primary influence of N doping is on the E_C-2.9 eV state. Before considering the physical defect configuration associated with the E_C-2.9 eV state, the two DLOS detected states at E_C-2.0 eV and E_C-4.4 eV warrant some discussion since both display small but measurable increases in their concentrations with nitrogen implantation, as seen in Fig. 5. Previous work on gallium oxide subjected to high energy particle irradiation by both protons and neutrons has connected the E_C-2.0 eV state with a $2VGa1−Gai$ defect “split-vacancy” complex,⁴⁶ and gallium vacancies will likely form due to the implantation damage (though largely annealed out). The commonly reported E_C-4.4. eV state is not well understood, and its physical source is still being explored, with prior reports showing inconsistent dependencies on variables such as growth method and high energy particle irradiation conditions.^{6,7,36,44,47,48}

The above experimental studies strongly indicate that the E_C-2.9 eV state is due to a nitrogen acceptor. To provide further verification and confirm the charge state and the possible physical defect configuration causing the emission process, we performed DFT studies. The calculations used projector augmented wave potentials^49,50 as implemented in the Vienna Ab initio Simulation Package (VASP) code.⁵¹ Ga 3d electrons were treated as valence states. We used the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional,⁵² with the screening parameter fixed at the standard value and the fraction of screened Hartree–Fock exchange set to 0.33, resulting in a direct bandgap of 4.9 eV. For nitrogen impurity calculations, we employed 160-atom supercells, a plane-wave energy cutoff of 500 eV, and a single special k-point at (0.25, 0.25, 0.25). Energies of various configurations and charge states were calculated using the formalism defined by Freysoldt et al.,⁵³ including charge-state corrections.^54–56 

As noted in the work of Peelaers et al.,¹¹ the N_O(III) configuration has the lowest energy among the three possible substitutional oxygen sites when the Fermi level is above 3 eV, a condition that is fulfilled in these Si-doped samples. As noted in the Introduction, the (0/−) charge-state transition levels for the nitrogen impurity were found to strongly depend on the site on which the nitrogen atom substitutes; again, it is the level for N_O(III), at E_C-2.84 eV, that closely matches the trap energy extracted from optical cross section shown in Fig. 6(a). In order to further confirm this identification, we calculated configuration coordinate diagrams⁵⁷ in the one-dimensional approximation, which works very well when electron–phonon coupling is very strong as is clearly the case here. The diagram in Fig. 6(b) illustrates the potential energy surfaces as a function of atomic coordinates for the N_O(III) impurity in the (ground-state, g) negative and (excited-state, e) neutral charge state, showing a large change in configuration coordinate ΔQ. The zero-phonon line (ZPL) energy E_ZPL corresponds to the charge-state transition level with respect to the conduction-band minimum, and effective phonon frequencies for ground and excited states are indicated. Within this model, the Franck–Condon (D_FC) energy for the excitation process is the difference between the peak absorption energy E_abs and E_ZPL and thus given by 4.15–2.84 = 1.31 eV, in very good agreement with the D_FC value extracted from the Pässler model shown in Fig. 6(a). 

In conclusion, this study investigates the use of N as a deep acceptor dopant in β-Ga₂O₃ through ion implantation. Strong evidence of background carrier compensation with implanted N is presented, demonstrating over 95% dopant activation under optimized conditions. This work establishes a clear correlation between the nitrogen implant concentration and the E_C-2.9 eV level determined by DLOS. As the nitrogen implantation concentration increases, there is a monotonic increase in the concentration of the E_C-2.9 eV level, resulting in effective carrier compensation. First-principles DFT calculations indicate a (0/−1) transition for this state, verifying its acceptor-like behavior and showing that the experimentally observed configuration is for nitrogen occupying O site III (N_O(III)), resulting in a deep compensating center at E_C-2.9 eV. Furthermore, the photoionization of the N_O(III) acceptor is accompanied by a large local lattice relaxation, leading to a high Franck–Condon (D_FC) energy of 1.4 eV in the configuration coordinate diagram. This energy was experimentally obtained by analyzing the optical cross section derived from DLOS. This combined experimental and theoretical effort shows that nitrogen doping is a very effective process to introduce extremely efficient deep acceptors for the purpose of achieving very high degrees of controlled carrier compensation in β-Ga₂O₃.

The authors acknowledge the funding support from the Air Force Office of Scientific Research (Grant No. FA9550-18-1-0479) (Ali Sayir, Program Manager) and from the U.S. Air Force Radiation Effects Center of Excellence (Grant No. FA9550-22-1-0012). This work was supported, in part, by The Ohio State University Institute for Materials Research. This material is based on research sponsored by the Air Force Research Laboratory and Strategic Council for Higher Education under Agreement No. FA8650-19-2-9300 and the Ohio Department of Higher Education and Strategic Council for Higher Education under Ohio House Bill 49 of the 132nd General Assembly. The authors acknowledge the funding support from the Department of Energy/National Nuclear Security Administration under Award No. DE-NA0003921. This work was supported by the Air Force Office of Scientific Research (Grant No. FA9550-22-1-0165), the Research Council of Norway through the GO-POW project (Grant No. 314017), the University of Kansas General Research Fund allocation (Grant No. 2151089), and the Office of Naval Research/NRL Basic Research Program and partially performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA27344. The computations were performed on resources provided by UNINETT Sigma2, the National Infrastructure for High Performance Computing and Data Storage in Norway, and by the Extreme Science and Engineering Discovery Environment (XSEDE), supported by the National Science Foundation (Grant No. ACI-1548562). This work was supported by Air Force Office of Scientific Research Grant No. FA9550-18-1-0479 and National Science Foundation Award Nos. ECCS 2019749 and ECCS 2231026. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding provider.

The authors have no conflicts to disclose.

Hemant Ghadi: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Joe F. McGlone: Formal analysis (supporting); Investigation (supporting); Writing – original draft (equal); Writing – review & editing (equal). Evan Cornuelle: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Alexander Senckowski: Conceptualization (supporting); Software (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Shivam Sharma: Investigation (supporting); Resources (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Man Hoi Wong: Conceptualization (equal); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Resources (supporting); Supervision (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Uttam Singisetti: Investigation (supporting); Methodology (supporting); Resources (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Ymir Kalmann Frodason: Methodology (equal); Software (equal); Validation (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Hartwin Peelaers: Methodology (supporting); Software (supporting); Validation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). John L. Lyons: Methodology (supporting); Software (supporting); Validation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Joel B. Varley: Methodology (equal); Software (equal); Validation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Chris G. Van de Walle: Methodology (equal); Software (lead); Validation (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Aaron Arehart: Investigation (supporting); Resources (supporting); Supervision (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Steven A. Ringel: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (supporting); Visualization (supporting); Writing – original draft (equal); Writing – review & editing (equal).

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