Comprehensive characterization of nitrogen-related defect states in β-Ga₂O₃ using quantitative optical and thermal defect spectroscopy methods

Extrinsic dopant incorporation in semiconductors controls the Fermi-level position in the bandgap, resulting in conductive or semi-insulating epilayers/substrates.^1–3 In beta-phase gallium oxide (β-Ga₂O₃), which possesses inherent n-type conductivity, impurities such as Si, Ge, and Sn are common donors that efficiently create free electrons and n-type conductivity due to the shallow nature of their energy levels in the bandgap.^1–4 In contrast, impurities such as nitrogen,⁵ iron,⁶ magnesium,¹ cobalt,⁷ and nickel⁸ are theoretically and experimentally verified to introduce acceptor-like bandgap states in β-Ga₂O₃ that are very deep in the bandgap at E_C-2.9 eV, E_C-0.8 eV, E_C-3.8 eV, E_C-1.9 eV, and E_C-2.2 eV, respectively. These deep acceptor states can compensate for excess electrons and pin the Fermi level at the deep acceptor energy level, thus creating highly resistive or semi-insulating layers necessary for high breakdown and radio frequency (RF) β-Ga₂O₃ devices. Our prior work investigated energy levels associated with N doping by deep-level optical spectroscopy (DLOS) since it is an intriguing and promising deep acceptor candidate.⁵ Nitrogen doping in β-Ga₂O₃ is highly stable due to its 3.87 eV barrier diffusion activation energy^1,9 and its primary acceptor energy at ∼E_C-2.9 eV as predicted by theoretical calculations for the oxygen site III (N_OIII), which DLOS corroborated.⁵ However, a complicating factor created for DLOS characterization when states are below half of the bandgap (E_G/2) for n-type material is that incoming photons can cause electron photoemission to the conduction band and competing hole emission (electron capture from) to the valence band.¹⁰ If not accounted for, this competition makes determining the accurate concentration of such defect states via DLOS difficult, and it can even change the sign of the measured steady-state photocapacitance (SSPC) depending on which process is dominant. In conventional semiconductors such as GaN, negative excursions in the SSPC due to states below midgap can be easily attributed to hole emission to the valence band and subsequent hole collection.^10,11 However, for β-Ga₂O₃, free holes are relatively immobile and are immediately captured through self-trapping (which leads to its lack of p-type conductivity).^12–14 Our prior published work on the E_C-2.9 eV (N_OIII) acceptor state circumvented this issue by using a +0.7 V forward bias filling pulse during the trap filling stage of the DLOS measurement to ensure complete saturation of this state by electrons through the current injection.⁵ Conventional DLOS measurements using a 0 V filling bias pulse revealed behavior suggesting that both conduction band and valence band emission/capture processes from the same E_C-2.9 eV state are present despite the lack of p-type conductivity. Thus, the purpose of this work is to explore and resolve this possible dual-band behavior in significant detail using a method known as double-beam DLOS.^10,15,16 Various pump–probe combinations of light source energies are used to isolate and then quantify both electron and hole emission processes related to the N_OIII defect. This study aims to offer new fundamental experimental data on conduction and valence band processes originating from deep states in β-Ga₂O₃. This analysis is crucial for accurately interpreting DLOS data and understanding the photophysics related to these processes in β-Ga₂O₃.

The dual beam DLOS studies were conducted on the samples we characterized in our prior work.⁵ Briefly, halide vapor phased epitaxial (HVPE) grown β-Ga₂O₃ samples¹⁷ with a background Si doping of 1.2 × 10¹⁷ cm⁻³ were implanted with N to create a uniform N concentration of 2 × 10¹⁶ cm⁻³ for a thickness of 1 μm.^5,9 The N-implanted sample was annealed at 1100 °C for 10 mins in N₂ ambient for N acceptor activation. Subsequently, 8 nm thick semi-transparent Ni-Schottky diodes were fabricated using a two-step lithography process, and an ohmic stack of Ti/Al/Ni/Au was deposited on the back side of the conductive substrate.^5,18–21 The extracted doping concentration from capacitance–voltage (CV) characteristics was ∼1.2 × 10¹⁷ cm⁻³, consistent with the background Si. With the addition of N co-doping, the CV net doping reduced to a value of 0.9–1 × 10¹⁷ cm⁻³, moving the calculated Fermi level to ∼0.1 eV below the conduction band. While the DLOS technique has been explained previously, the double-beam DLOS method is less known and is described herein. Conducted at a constant temperature of 305 K, the first step is to fill all defect states using a forward bias pulse of 1.5 V for 600 s. This causes a 2 mA current to flow through the Schottky diode, saturating the traps with electrons. As discussed earlier, a higher current value for the experiment is selected to ensure all defect levels are completely filled with electrons via current injection. After applying the fill pulse, an immediate reverse bias of −2 V was applied while illuminating light through the semi-transparent Ni Schottky metal using a 9 W 4.2 eV UV-LED light source (pump). The light source emits electrons to the conduction band from all states whose energy levels are less than 4.2 eV below the conduction band edge, including the N state at E_C-2.9 eV. The higher energy light source was selected such that the entire spectrum of the optical cross section^22,23 for this N state is excited,⁵ yet at an energy level low enough so that it does not result in electron emission from the commonly reported E_C-4.4 eV defect state based on the detailed optical cross section analysis of this state from our prior work.²⁰ The pump source was deactivated upon complete emission of the E_C-2.9 eV state, confirmed by observing saturation of the emission transient, followed by subsequent illumination using the probe light. The optical probe source was facilitated using a 450 W Xe-Arc lamp light dispersed through a monochromator to vary the probe photon energy from 1.2 to 3.0 eV in increments of 0.05 eV. During the probe process, the diode was maintained at a constant reverse bias of −2 V and was repeated for each probe energy step. The subsequent photocapacitance transient for each probe energy was digitally recorded. A schematic of the dual beam DLOS experiment is shown in Fig. 1, along with the corresponding band diagrams to help visualize the assumed electron and hole emission processes that the subsequently described experimental results will verify. The sign of the transient allows the differentiation between electron emission to the conduction band (i.e., a positive transient due to an increase in positive space charge) and hole emission to the valence band (i.e., a negative transient due to an increase in negative space charge). In the double beam DLOS measurements, the electron emission dominates during the pump process, followed by hole emission to the valence band during the probe process. The entire process is schematically depicted in Fig. 1.

The difference in the sign of the photocapacitance transients will manifest in the SSPC spectrum. Before describing the double-beam DLOS results, it is helpful to show this effect on the SSPC response, especially as it motivates why both conduction and valence band processes must be investigated. Figures 2(a) and 2(b) compare the SSPC spectra measured using conventional methods with a 0.7 and 0 V fill pulse bias, respectively, followed by the spectrally resolved photoemission experiment at a −2 V reverse bias. With forward bias fill pulse, we are forcing all defect levels to fill through the current injection, and the DLOS results have been published in Ghadi et al.⁵ Both positive and negative photocapacitance onsets are observed in Fig. 2(b), indicating interaction with the conduction and valence band, respectively, when using a 0 V fill pulse bias. The positive onsets are due to electron photoemission (increase in positive space charge) to the conduction band, and the negative onsets are due to hole emission (increase in negative space charge) to the valence band. The positive onsets seen at 2.3 and 3.4 eV photon energies in both Figs. 2(a) and 2(b) are from the E_C-2.0 eV and E_C-2.9 eV defect levels emission previously reported.⁵ The former has been found to possess a Franck–Condon energy (D_FC) of 0.5 eV²⁰ and has been associated with the predicted 2V_Ga-Ga_i defect level.^{19,20,24–26} The latter positive SSPC onset at E_C-3.4 eV has also been studied and is due to the N_OIII state at E_C-2.9 eV with a D_FC = 1.4 eV.^1,5 However, the SSPC spectrum measured with a 0 V fill pulse reveals the presence of negative onsets, a large one that initiates near photon energy of 2.5 eV and a smaller one near 1.5 eV, which are of primary focus here. As described above, such photocapacitance behavior can only be associated with an increase in negative space charge, and so this warrants deeper investigation with the aforementioned dual beam DLOS.

Figure 3(a) shows room temperature (305 K) double-beam DLOS experimental results. The negative slope of the recorded photocapacitance transients during the probe measurement is consistent with increasing negative space charge due to hole emission. The large timescale on the x-axis indicates that these are very slow transients, and this is consistent with a high hole effective mass, noting that it is only because of the drift field in the Schottky barrier depletion region that any hole collection is possible. Such observations of hole transport due to a drift field have been previously reported for β-Ga₂O₃ photodetectors.^27,28 A simple analytical model was developed to substantiate this further as part of this work. The model utilizes the electric field calculated by solving the Poisson equation to extract the hole drift velocity, assuming the reported hole mobility value of 10⁻⁶ cm²/V-s.²⁹ The travel time is calculated by integrating the velocity over the depletion region. This model reveals that ∼50 ms would be required to allow a photogenerated hole to drift across the depletion region and be collected for a drift field of 0.01 MV/cm. In our double-beam experiments, we applied a minimum electric field of 0.08 MV/cm across the depletion region. In addition, we measured transients over 100 s to ensure the collection of photoemitted holes.

From the photocapacitance transients, the optical cross sections associated with the hole emission transients could be extracted, as shown in Fig. 3(b). Two distinct states are immediately evident, one with a relatively sharp onset starting around 1.3 eV and saturating near 2 eV and one with a broader onset that starts around 2.6 eV. A sharp onset indicates a low D_FC energy, implying negligible local lattice relaxation associated with that defect, thus leading to similar emission energies for optical and thermal transitions. In contrast, a broad onset usually indicates a substantial D_FC linked to local lattice relaxation.^22,23 Consequently, the optical transition occurs at the sum of thermal transition energy and high D_FC.³⁰ Therefore, the optical cross section should be modeled using either the Passler model²² or the Chantre Vincent and Bois (CVB)²³ model to extract energy levels, as they incorporate Frank–Condon energies accurately.

The optical cross sections for these two hole emission states were fitted to the Passler model to extract the precise trap and Franck–Condon (D_FC) energies.²² The extracted energies correlate with the negative going excursions in the SSPC discussed earlier in Fig. 2(b). The two different energy levels are derived from fitting and are located at E_V+1.3 eV (D_FC = 0 eV) and E_V+1.9 eV (D_FC = 0.8 eV). The E_V+1.9 eV position in the bandgap lines up remarkably close to the E_C-2.9 eV state revealed by electron photoemission to the conduction band (i.e., 1.9 eV + 2.9 eV = 4.8 eV bandgap) that has been attributed to N_OIII, and perhaps this is the same defect level.⁵ The level at E_V+1.3 eV, which is also implied by the slight negative slope of the SSPC data in that energy range from Fig. 2(b), needs further investigation. Interestingly, its modeled D_FC is 0 eV, suggesting insignificant lattice relaxation. Similar to the E_C-2.9 eV/Ev+1.9 eV level, we have only seen evidence for the E_V+1.3 eV state for β-Ga₂O₃ doped with N (including not being observed in samples subjected to damage via high energy particle irradiation),^5,19,31 suggesting a possible association with an N-related defect.

We can now focus on defect concentrations of these levels based on their communication with the valence band. Figure 4 shows the comprehensive pump–probe process, allowing the direct and independent interrogation of electron and hole emission using double-beam DLOS coupled with a laser source. Figure 4(a) shows the 4.2 eV pump process that emits all trapped electrons from any state within 4.2 eV from the conduction band after the electrical electron filling pulse, including both E_C-2.9 (E_V+1.9 eV) and E_V+1.3 eV states. Subsequently, Fig. 4(b) shows the probe results that can isolate and quantify the hole emission processes via two laser sources. The laser sources are selected such that a higher photon flux, i.e., several orders higher than a xenon arc lamp, expedites the emission process. Based on the optical cross section results from Fig. 4(b), only holes from the E_V+1.3 eV state will be completely emitted using a red laser probe source (1.8 eV), while both the E_V+1.3 eV and E_V+1.9 eV states will emit holes using a purple laser probe (3.1 eV) source. The measured trap concentrations of E_V+1.3 eV and E_V+1.9 eV states based solely on saturating the hole emission were 3.1 × 10¹⁵ and 1.74 × 10¹⁶ cm⁻³, respectively. Considering the E_v+1.9 eV state, this concentration is very close to the trap concentration obtained solely based on electron emission to the conduction band at E_C-2.9 eV, with both matching the N concentration from SIMS, providing strong evidence that, indeed, this is the same N state that is also the primary source of carrier compensation that we have earlier demonstrated.⁵ 

With the E_v+1.9 eV state appearing to be satisfactorily associated with the E_C-2.9 eV level attributed to N_OIII, and with the concentration of the state closely matching between both electron emission and hole emission DLOS measurements,⁵ further characterization of the E_v+1.3 eV state is necessary to gain a complete understanding of the DLOS behavior for N doped β-Ga₂O₃. To accomplish this, we have employed an optical isothermal defect spectroscopy method. This spectroscopy combines double-beam DLOS spectroscopy and conventional thermal DLTS measurements. Optical isothermal spectroscopy has certain limitations and can only be used to characterize defect states closer to either of the bands. Since E_V+1.3 eV is relatively close to the valence band and its thermal emission time constant can be extracted within the temperature range of our DLTS measurement, characterization of this defect level by optical isothermal DLTS is viable. Using the 4.2 eV pump light source to empty electrons from this state as an effective “hole filling pulse,” subsequent isothermal DLTS can then be used to emit holes and monitor this effect on the resultant thermal capacitance transient, similar to a standard DLTS experiment. The hole thermal emission process is immediately measured after turning off the 4.2 eV light source (i.e., hole-filling pulse). A schematic of optical isothermal measurement is shown in Fig. 5(a) to visualize the process. After the electron emission process to the conduction band, the occupancy of both E_C-2.9 eV/E_v+1.9 eV and E_v+1.3 eV defect states change because the trapped electrons have been optically emitted to the conduction band, and this “empty electron” condition is maintained by virtue of the measurement occurring in the depletion region, where there are no free electrons for re-capture. However, the trapped hole or empty electron state would have thermal emission rates that are exponentially dependent on temperature, i.e., increasing the temperature can expedite the emission if this process is genuinely occurring and can be measured by DLTS. Hence, the optical isothermal measurements were conducted between 415 and 450 K in steps of 5 K to expedite the thermal emission process. The raw transients measured from isothermal experiments are exponentially decaying, and a graph of individual time constants obtained from the boxcar integrator applied to the capacitance transients at each temperature is shown in Fig. 5(b). The method for extracting and analyzing the time constants is explained in Turchanikov et al.³² The temperature range was chosen due to the maximum temperature limits of our probe station (450 K) and a practical lower limit to ensure that the hole emission time constant could be measured within a reasonable time window. Again, emission from the E_v+1.9 eV state is not observable in this temperature range since it is too far from the valence band to be thermally ionized.

In addition, to demonstrate that hole emission from E_V+1.3 eV is only observed after N-doping and is related to N, we performed double-beam DLOS on the HVPE sample without nitrogen implantation, illustrated in Fig. 6. The DLOS spectra and the summary of the defect states have been reported previously.⁵ The double beam experiment was performed with the pump source photon energy maintained at 4.2 eV while the probe source energy was applied for photon energies of 1.9 and 3.0 eV. As shown in Fig. 6, no hole emission was observed, which is in contrast to the strong hole emission transients for the N-doped samples shown earlier in Fig. 4(b). This comparison of double-beam DLOS results for HVPE materials with and without N doping demonstrates that this hole emission process at E_V+1.3 eV is due to N doping.

In conclusion, this study comprehensively explains the dominant N deep acceptor level created in N-doped β-Ga₂O₃. It elucidates and reconciles the observed hole emission features in DLOS, attributing them to measurements conducted within the depletion region under electric fields. Both electron emission from E_C-2.9 eV and hole emission from E_V+1.9 eV appear to stem from the same energy level, identified as N_OIII in nitrogen-doped β-Ga₂O₃, the primary source of carrier compensation for N-doped β-Ga₂O₃. Optical cross section analysis reveals a high D_FC associated with both electron emission (1.4 eV) and hole emission (0.8 eV) from the same energy level, suggesting the presence of two distinct atomic configurations. Double beam experiments accurately pinpoint the defect location in the bandgap and enable quantitative characterization of emission processes associated with both conduction and valence bands. Furthermore, these experiments revealed an unexpected state at E_v+1.3 eV that was thoroughly investigated through double-beam DLOS and optical isothermal measurements. A zero D_FC energy associated with the E_v+1.3 eV defect level suggests no lattice distortion or a nearly flat valence band transition. The nearly perfect match between the energy level calculated from double-beam DLOS and the optical isothermal spectroscopy further supports this conclusion. This specific state has been exclusively observed in N co-doped β-Ga₂O₃, strongly suggesting its association with nitrogen.

The authors acknowledge the work of Ohio State Ph.D. student Tal Kasher for his support in device fabrication. The authors acknowledge the funding from the Air Force Office of Scientific Research (AFOSR) GAME-MURI (Grant No. FA9550-18-1-0479) (Ali Sayir, Program Manager), AFOSR (Grant No. FA9550-22-1-0527), and 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 and Manufacturing Research. The authors also want to acknowledge NSF under Award Nos. ECCS 2019749, 2231026, and II-VI Foundation Block Gift Program. 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.