Influence of heat treatments in $H2$ and Ar on the E₁ center in β-Ga₂O₃

Monoclinic gallium sesquioxide (⁠$β$-Ga$2$O$3$⁠) is an ultra-wide bandgap semiconductor (⁠$Eg≈$ 4.9 eV ^1–3) that has shown promise for applications in power electronics and UV photodetectors.^4–9 For $β$-Ga$2$O$3$ to live up to its potential, it is important to control the electrically active defects in the material since defects play a crucial role in determining the electrical conductivity of a semiconductor by acting as dopants or compensating centers.¹⁰ Furthermore, defects can influence the operation of $β$-Ga$2$O$3$-based devices by, e.g., pinning the Fermi level^11–13 or acting as recombination centers.¹⁴ Consequently, defect levels have been studied to a great extent in $β$-Ga$2$O$3$⁠, using techniques such as electron paramagnetic resonance,^15–17 cathodoluminescence,^18,19 steady-state photo-capacitance,^20–30 and deep-level transient spectroscopy (DLTS).^{11,12,22–24,26,31–36}

Recently, H-related defects in $β$-Ga$2$O$3$ have attracted considerable attention.^37–41 It has been shown in experimental and computational studies that Ga vacancies (⁠$VGa$⁠) complexed with H are likely to form in $n$-type material in the presence of H^42,43 and are expected to exhibit deep defect levels.^33,43 There are also a number of reports that propose H to be associated with shallow donor states,^38–40,44 potentially due to the formation of interstitial H (H$i$⁠) or H substituting for O (H$O$⁠).⁴⁵ Several other H-related defects have also been reported.^{36,39,46–48}

The $E1$ center is a DLTS defect signature with an activation energy of about 0.6 eV that has been observed previously in as-received bulk crystals grown by edge-defined film-fed growth (EFG) and the Czochralski (CZ) method,^31–33 as well as in epitaxial layers grown by molecular beam epitaxy (MBE)⁴⁹ and halide vapor phase epitaxy (HVPE).²³ Polyakov et al. observed an increase in the concentration of $E1$ when subjecting EFG-grown bulk crystals with a surface orientation of (010) to a H-plasma,⁵⁰ whereas Irmscher et al. showed that the concentration of $E1$ in CZ-grown bulk crystals was not increased by a high-temperature heat treatment in O$2$ ambient.³¹ 

Different reports exist regarding the effect of irradiation on the $E1$ level. Ingebrigtsen et al. and Farzana et al. did not observe any change in the $E1$ concentration in EFG-grown bulk crystals, following 0.6 and 1.9 MeV proton,³³ and neutron irradiation,²⁸ suggesting that $E1$ cannot be solely related to intrinsic defects. In contrast, Polyakov et al. reported a slight increase in the $E1$ concentration following 20 MeV proton irradiation,²⁴ 18 MeV $α$-particle irradiation,²⁴ and pulsed fast reactor neutron irradiation⁵¹ of HVPE films.

Here, we report on the effect of H$2$ and Ar annealing on the $E1$ level in EFG-grown bulk $β$-Ga$2$O$3$ crystals. The introduction of H into the crystals by annealing in H$2$ is confirmed through Fourier transform-infrared spectroscopy (FT-IR) measurements, which reveal an O–H vibrational line previously assigned to a doubly hydrogenated Ga vacancy (⁠$VGaib$2H).⁴² From DLTS measurements, we find that H$2$ heat treatments at 900 °C promote the concentration of $E1$⁠, whereas equivalent heat treatments performed in an inert Ar flow do not generate any notable changes in the $E1$ concentration. We further find that the charge-carrier concentration is not influenced by H$2$ heat treatments. Annealing at 650 K with and without an applied reverse-bias voltage revealed that the $E1$ center is stable under these conditions. Finally, we discuss potential defect origins of the $E1$ center based on comparison with hybrid-functional calculations on H-related defects in $β$-Ga$2$O$3$⁠.

Bulk EFG-grown $β$-Ga$2$O$3$ crystals^52,53 with a surface orientation of (⁠$−201$⁠) were purchased from Tamura Corporation,⁵⁴ including two different 0.7 mm thick wafers originating from different production batches. Both wafers were unintentionally doped $n$-type. The wafers were cut into samples measuring approximately $5×5$ mm$2$ using a laser cutter.

Some of the samples were subjected to heat treatments in closed quartz ampoules filled with approximately 0.5 bar of H$2$ at room temperature. The ampoules containing the samples were evacuated with a roughing pump prior to filling with H$2$⁠. Particularly, three cycles of evacuation and filling with H$2$ were performed before eventually filling the ampoule with 0.5 bar of H$2$ and subsequently sealing the ampoule. The heat treatments were performed in a tube furnace at a temperature of 900 °C for an annealing duration (⁠$tann$⁠) of 15–75 $min$⁠. Once the furnace reached the set temperature, the ampoule containing the sample was put into the tube furnace, annealed for the desired duration, and then removed from the furnace to cool down. The samples were removed from the ampoules after they had reached room temperature; i.e., the samples were not exposed to air at elevated temperatures. In addition, three samples were subjected to heat treatments in an Ar flow at the same temperature of 900 °C for a $tann$ between 15 and 60 $min$⁠.

Using FT-IR, infrared absorbance spectra were measured at 5 K on as-received and both $H2$- and $Ar$-annealed samples. The measurements were performed utilizing a Bruker IFS 125HR spectrometer equipped with a globar light source, a KBr beam splitter, and an InSb detector. The samples were cooled in a Janis PTSHI-950-5 closed-cycle, low vibration pulse tube cryostat filled with He exchange gas and equipped with ZnSe windows. All measurements used a spectral resolution of 0.5 cm⁻¹ with unpolarized light incident along the direction normal to the (⁠$−201$⁠) surface of the crystals. The single-channel spectrum of the empty sample holder was used as a reference. The recorded transmittance (⁠$Tr$⁠) data were converted to absorbance (⁠$A$⁠) using the equation $A=−log10(Tr)$⁠.⁵⁵ 

For the electrical characterization, Schottky barrier diodes (SBDs) were fabricated on samples in the as-received state or after $H2$/$Ar$ annealing. Circular Ni pads with diameters between 300 and 900 μm were deposited using e-beam evaporation and a shadow mask.^32,33,56 Typically, a contact thickness of 150 nm was used. Stacks of Ti (thickness = 10 nm) and Al (thickness = 150 nm) were used as Ohmic contacts covering the back side of the samples.

Current–voltage (IV) and capacitance–voltage (CV) measurements were performed in the dark on all SBDs to ensure that the devices were suitable for DLTS. IV measurements were performed using a Keithley 6487 picoammeter/voltage source, whereas CV measurements were conducted using a Boonton 7200 capacitance meter or an HP 4280A capacitance meter. From CV measurements, using a probing frequency of 1 MHz, the donor concentration (⁠$ND$⁠) of the samples was determined¹⁰ assuming a static dielectric constant of 10.2.⁵⁷ Moreover, the widths of the space-charge region (⁠$W$⁠), and hence the probing depths for DLTS measurements, were estimated from the CV measurements.¹⁰ 

DLTS measurements were performed on two setups, which both are refined setups of the one described in detail in Ref. 58, covering the temperature range from 150 to 700 K. The DLTS spectra were constructed using a GS2 filter (lock-in filter).⁵⁹ The spectra are displayed as $2NDΔC/Crb$⁠, where $ΔC$ denotes the amplitude of the capacitance transient measured in DLTS, whereas $Crb$ represents the quiescent capacitance of the SBD at the applied reverse-bias voltage.^10,60 Parameters describing the electron traps observed in DLTS measurements, such as the trap concentration (⁠$Nt$⁠), the activation energy (⁠$EA$⁠), and the apparent capture cross section (⁠$σna$⁠), were obtained by comparing the recorded DLTS spectra with simulations using a python-based script.²⁰ Here, $Nt$ was computed by taking the $λ$-correction into account.^10,20,31 The uncertainty in $EA$ is estimated to be around 0.04 eV, whereas the uncertainty in $σna$ can be expected to be within $±$ one order of magnitude.³⁵ 

To gauge the stability of the $E1$ center, heat treatments of the 60 $min$ $H2$-annealed sample were performed. The annealing was conducted up to 650 K with and without an applied reverse-bias voltage of −5 V, denoted as reverse-bias annealing (RBA) and zero-bias annealing (ZBA), respectively. The annealing cycles were performed in the same manner as described in Ref. 36, except for a slower heating rate of 5 K/$min$ and an HP 4280A capacitance meter as the voltage source.

First-principles calculations were performed using the projector augmented wave method^61,62 and the Heyd–Scuseria–Ernzerhof (HSE)⁶³ screened hybrid functional, as implemented in the VASP code.⁶⁴ The Ga 3d electrons were included in the valence, and the fraction of screened Hartree–Fock exchange was adjusted to 33%. This results in a direct bandgap value of 4.9 eV and lattice parameters (⁠$a=12.23Å$⁠, $b=3.03Å$⁠, $c=5.79Å$⁠, and $β=103.8°$⁠) in good agreement with experimental data.^1,65 Defect calculations were performed using 160-atom supercells, a plane-wave cutoff of 400 eV, and a single special k-point at (0.25, 0.25, 0.25). Defect formation energies and thermodynamic charge-state transition levels were evaluated using the formalism described in Ref. 66, with finite-size corrections applied for charged defects.^67–69 Binding energies of H-related defect complexes were calculated as the difference between the formation energy of the complex and the sum of the formation energies of H$i$ and the remaining entity when one H is removed from the complex.⁶⁶ A positive binding energy indicates a stable complex.

To facilitate comparison between the hybrid-functional calculations and $EA$ extracted for $E1$ from DLTS data, we have constructed one-dimensional configuration coordinate (CC) diagrams describing the dynamics of the electron capture and emission process.^70–72 CC model parameters were derived from the hybrid-functional calculations, including the ionization energy (⁠$Ei$⁠), the change in the configuration coordinate (⁠$ΔQ$⁠), and the ground and excited state Franck–Condon shifts (⁠$dgFC$ and $deFC$⁠). $EA$ extracted from DLTS includes an energetic barrier for electron capture (⁠$Eb$⁠) in addition to $Ei$⁠. In the CC model, this barrier is obtained from the intersection point of the potential energy curves in the ground and excited state.⁷¹ 

Figure 1 shows baseline-corrected IR absorbance spectra recorded on as-received and $H2$-annealed samples. The baseline in the absorbance spectra originates from surface reflection losses, scattering at the rough back surface, and free charge-carrier absorption.⁴² The samples annealed in H$2$ exhibit an absorbance feature at around 3437 cm⁻¹, which is related to a localized vibrational mode (LVM) associated with $VGaib$2H.⁴² Indeed, $VGaib$2H has previously been found to form under $n$-type conditions during H$2$ annealing,⁴² in line with first-principles calculations.^33,43 The as-received and Ar-annealed samples did not show such an absorbance feature (FT-IR data for samples annealed in Ar are not shown), indicating that $VGaib$2H is only present in negligible amounts in the bulk of these samples. The data were modeled with Lorentzian profiles to compute the integrated absorbance of the feature related to the LVM of $VGaib$2H. The integrated absorbance is proportional to the concentration of $VGaib$2H in the bulk crystals, and hence, an approximately linear relation between the $VGaib$2H concentration and $tann$ can be seen in the inset of Fig. 1. Thus, the results displayed in Fig. 1 show that H penetrates into the bulk of $β$-Ga$2$O$3$ during H$2$ annealing. However, the concentration of H is too low to be measured by, e.g., chemical techniques, such as secondary ion mass spectrometry. Note that the small shoulder that can be discerned at 3439.5 cm⁻¹ in Fig. 1 is caused by noise in the baseline.

IV and CV measurements on SBDs comprising as-received, $H2$-annealed, and Ar-annealed samples showed that the SBDs were suitable for performing DLTS measurements. In IV measurements, SBDs fabricated on $H2$-annealed samples typically displayed a larger leakage current (current under an applied reverse-bias voltage) compared to as-received and Ar-annealed samples. This limited the $tann$ that could be used for the H$2$ heat treatments. The increase in leakage current might be related to roughening of the sample surface during the H$2$ annealing.^39,50

From CV measurements, $ND$ values between 2 × 10¹⁷ and 5×10¹⁷ cm⁻³ were determined for all samples independent of the heat treatment. The values determined for $ND$ indicate that the Fermi level is close to $EC$ in all investigated samples. From CV measurements, the typical probing depth for DLTS measurements is determined to be in the range of 150–250 nm. Notably, no correlation between $tann$ and $ND$ was observed for neither the H$2$ nor the Ar annealing. However, the as-received samples displayed a considerable spread in $ND$⁠, and hence, a possible correlation between $tann$ and $ND$ might be masked. Previously, Polyakov et al. have shown that surface treatments with H-plasma lead to an increase in carrier concentration for EFG-grown bulk crystals with a (⁠$−201$⁠) surface orientation, which the authors proposed to be related to the formation of shallow H-related donors.⁵⁰ Interestingly, H-plasma treatments caused a decrease in carrier concentration for EFG-grown bulk crystals with a (010) surface orientation.^38,50 This might be a result of distinct surface terminations on the (⁠$−201$⁠) and (010) surfaces resulting from H treatment that influence the surface band bending.⁴¹ It has also been shown that H can contribute to the unintentional doping found in as-grown bulk crystals.⁴⁰ 

DLTS spectra recorded on as-received, 30 $min$ $H2$-annealed, and 30 $min$ $Ar$-annealed crystals are presented in Fig. 2. The $E1$ peak (⁠$EA=0.60±0.04eV$⁠, $σna∼6×10−13cm2)$ is present in all three spectra (see the inset in Fig. 2 to discern the peak for the as-received and Ar-annealed sample). At temperatures of around 280 K, the onset of a signature commonly labeled as $E2$ can be seen, which has previously been shown to be related to substitutional Fe at tetrahedral Ga$1$ and octahedral Ga$2$ sites (Fe$Ga1$ and Fe$Ga2$⁠).^20,32,35 Notably, we did not observe the center commonly labeled as $E2∗$ after H$2$ anneals.^{11,23,32,33,36} For Ar anneals, however, a defect level around $E2∗$ appears as a small shoulder on the low-temperature side of $E2$ (its onset can be seen around 260 K in Fig. 2).

For the spectra presented in Fig. 2, the concentration of the $E1$ level is comparable for the as-received and Ar-annealed samples but considerably higher for the sample annealed in H$2$⁠. Note that the peak position of the DLTS signature in the Ar-annealed sample is shifted to lower temperatures compared to that of the $E1$ level, which may indicate that Ar annealing results in the formation of other defect levels with a similar energy level position. Moreover, the DLTS signature of $E1$ (Fig. 2) is somewhat broader than that expected from a single level, as indicated by the simulated line. Thus, we cannot exclude that $E1$ consists of several overlapping levels. However, we were not able to resolve a finer structure in the $E1$ peak with the use of the high-resolution weighting function GS4.⁵⁹ 

Figure 3 shows the $E1$ concentration in dependence of $tann$ obtained from multiple DLTS measurements recorded on as-received, Ar-annealed, and $H2$-annealed samples. For the as-received and $H2$-annealed samples, the mean and standard deviation values are calculated from several diodes (between 3 and 14, the latter to check for lateral inhomogeneity) for the different $tann$⁠. Note that the 15 and 60 $min$ H$2$ annealing was performed solely on a single wafer, whereas the 75 $min$ annealing was performed on a different wafer.

From Fig. 3, one can observe that the mean $E1$ concentration in as-received bulk crystals is low. Indeed, for some of the diodes on the as-received bulk crystals, the $E1$ concentration was below the detection limit of around 5 × 10¹² cm⁻³ and thus not observed in the DLTS measurements. The diodes on the as-received samples that displayed the presence of $E1$ had an $Nt$ of around 5 × 10¹³ cm⁻³ taking the $λ$-correction into account. The samples annealed in argon similarly displayed a low $E1$ concentration of around 1×10¹⁴ cm⁻³. Moreover, the Ar-annealed samples do not show a systematic increase in the $E1$ concentration with increasing $tann$⁠. For the Ar-annealed samples, it should be noted that the $E1$ concentration was extracted treating the shifted peaks as pertaining to $E1$⁠, and hence, the calculated concentrations can be considered an upper bound. The samples annealed in H$2$⁠, in contrast, display a considerably larger concentration of $E1$ in the range of 1×10¹⁵ cm⁻³. For annealing times up to and including 60 $min$⁠, the mean $E1$ concentration also increases with increased time.

For the sample annealed in H$2$ for 75 $min$⁠, a slightly lower concentration of $E1$ is measured compared to that of the 60 $min$ ones but still substantially above that of the as-received. This may indicate that for long annealing times, multiple defect reactions may influence the overall $E1$ concentration. In addition, as the 60 $min$-annealed and 75 $min$-annealed diodes stem from two separate wafers, initial differences in the relative and absolute defect concentrations can affect the resulting $E1$ concentration. Nevertheless, the results displayed in Figs. 2 and 3 lead us to propose that $E1$ is associated with a H-related defect.

Probing the thermal and field dependent stability of defect levels can provide valuable information for the identification of defects. Several defect levels in $β$-Ga$2$O$3$ have previously been shown to be metastable^36,49 with the use of RBA and ZBA. For example, we have previously found that $E2∗$ formed by H implantation can be reversibly introduced and removed by performing RBA and ZBA, respectively, at temperatures of around 650 K.³⁶ Figure 4 shows the results for the $E1$ level following RBA and ZBA cycles. More specifically, DLTS spectra recorded after 60 $min$ $H2$ annealing and after subsequent RBA and ZBA at 650 K are presented. A notable finding is that the peak intensity shows an insignificant change after the annealing cycles. The unchanged intensity suggests that $E1$ is related to a stable defect. We observe only a slight increase (decrease) in the peak intensity (temperature position) of the $E2$ signature, following RBA and no further change following ZBA. Furthermore, no distinct shoulder, which would correspond to $E2∗$⁠, emerges on the low-temperature side of $E2$ after RBA at 650 K.

Hybrid-functional calculations were performed to explore potential defects that might give rise to the $E1$ center, assuming a H-related origin. Previous calculations indicate that H$i$ behaves exclusively as a shallow donor in $β$-Ga$2$O$3$⁠, as the predicted $ε(+/−)$ level is close to $EC$⁠.⁴⁵ Isolated H could also occur in the form of interstitial molecular hydrogen (H$2$⁠)$i$⁠, which we find to be electrically inactive and stable only in n-type material with a maximum binding energy of 0.85 eV. However, H$i$ and (H$2$⁠)$i$ are expected to be highly mobile.⁴⁵ Indeed, using the climbing-image nudged elastic band method⁷³ and the strongly constrained and appropriately normed semilocal functional,⁷⁴ we calculate migration barriers along the b axis of 0.24 and 0.61 eV for H$i$ and (H$2$⁠)$i$⁠, respectively. For this reason, H most likely occurs in a trapped form, such as a defect complex involving an intrinsic defect or possibly another impurity; Si, Al, Fe, and Ir are commonly found in EFG-grown $β$-Ga$2$O$3$ crystals.^32,75

Figures 5(a) and 5(b) show the formation and binding energy diagrams, respectively, of various H-related defect complexes exhibiting charge-state transition levels in the vicinity of $E1$⁠, as discussed below. The formation energies of other defects mentioned below are reported elsewhere.^33,45,76,77 The notation used for the defects is in accordance with Ref. 77.

We start by considering intrinsic defects that can trap H. Previous calculations have shown that H can be trapped by $VO$⁠, resulting in a H$O$ complex that behaves as a shallow donor.⁴⁵ Interestingly, we find that the H$O2$ configuration can be stabilized also in the single-negative charge state for Fermi-level positions close to $EC$ (see Fig. 5). As shown in Fig. 6, the single-negative charge state involves a large structural rearrangement, where H moves off the vacant threefold coordinated O$2$ site to form a bond with the adjacent Ga$2$ atom, and two electrons are captured in a localized state. Note that charge-neutral H$O2$ is unstable for any position of the Fermi level, resulting in negative-$U$ behavior;⁷⁸ i.e., the thermodynamic charge-state transition occurs directly from single positive to single negative in Fig. 5(a). For a negative-U center, the peak observed in a conventional DLTS spectrum will correspond to the emission of two electrons, but $EA$ will be determined by the first electron emission, corresponding to the $ε(0/−)$ level for H$O2$⁠.⁷⁹ 

As shown in Table I, the corresponding $Ei$ value for H$O2$ is 0.68 eV with a small $Eb$ of 0.10 eV, which is close to the measured $EA$ of $∼$0.6 eV for $E1$⁠. However, H$O2$ is expected to show a low thermal stability, with a maximum binding energy of 0.69 eV when the Fermi-level position is near $EC$⁠, as shown in Fig. 5(b). Combining this with the low H$i$ migration barrier, one would thus expect H$O2$ to dissociate relatively easily.³³ This is hard to reconcile with the apparent stability of $E1$ upon ZBA and RBA up to 650 K.

As a donor, H$i$ is particularly likely to form stable complexes with acceptors, such as $VGa$⁠.^33,80 Indeed, the main O–H vibrational line observed by FT-IR in the hydrogen-annealed material is caused by $VGaib$2H.⁴² However, the calculated thermodynamic charge-state transition levels of $VGa$ are located in excess of 1.8 eV below $EC$⁠, and complexing with H tends to shift these levels to even lower Fermi-level positions.³³ 

Another possibility is Ga–O divacancies (⁠$VGaVO$⁠), which exhibit negative-U $ε(−/3−)$ levels in the upper part of the bandgap that are associated with the formation of Ga–Ga dimers at $VO$⁠.^33,77 $VGaVO$ can occur in a large number of crystallographically inequivalent configurations. However, the negative-U charge-state transition levels tend to (i) cluster within narrow ranges of Fermi-level positions, depending on the combination of tetrahedral Ga$1$ and octahedral Ga$2$ in the dimer, and (ii) shift to lower Fermi-level positions when $VGaVO$ is hydrogenated.⁷⁷ We have previously discussed certain configurations of the isolated and doubly hydrogenated $VGaVO$ as potential defect origins of the $E2∗$ center.⁷⁷ As shown in Fig. 5, we find that the singly hydrogenated divacancies $VGaib$H–$VO1$ and $VGa1$H–$VO1$ exhibit $ε(0/2−)$ levels that are close to $EC$ and $E1$ (four additional configurations with similar level positions can be found in Ref. 77, but these are not included here as they are higher in energy). As shown in Fig. 6, the 2- charge state correspond to the formation of a Ga$2$–Ga$2$ dimer at $VO1$⁠. In this case, $ε(−/2−)$ is the relevant level for comparison with DLTS, and the corresponding $Ei$ (⁠$Eb$⁠) values are 0.52 (0.19) and 0.49 (0.20) eV for $VGaib$H–$VO1$ and $VGa1$H–$VO1$⁠, respectively. These energies are also compatible with $E1$⁠.

In contrast to the H$O2$ complex, $VGaib$H–$VO1$ and $VGa1$H–$VO1$ are expected to show high thermal stability, with binding energies in excess of 2.2 eV under n-type conditions, as shown in Fig. 5(b). These binding energies are comparable to the 2.62 eV predicted for $VGaib$2H.⁸⁰ Furthermore, the possibility of $E1$ being composed of several overlapping defects is in agreement with this defect model, as there are several configurations of the singly hydrogenated divacancy exhibiting similar activation energies.⁷⁷ 

It should be noted that the $VGa2$H–$VO2$ and $VGaia$H–$VO2b$ configurations, which have the $ε(0/2−)$ level at $∼$1.7 eV below $EC$⁠, are $∼$0.4 eV lower in formation energy than $VGaib$H–$VO1$ when $EF=EC$⁠.⁷⁷ $VGaib$H–$VO1$ becomes preferred when the Fermi-level position is below $EC−0.46$ eV.⁷⁷ Moreover, a second H can be trapped by $VGaib$H–$VO1$⁠, resulting in the $VGaib$H–H$O1$ configuration when $EF=EC$⁠. The $VGaib$H–H$O1$ complex has a H binding energy of 2.34 eV and does not exhibit any levels in the vicinity of $E1$⁠. For these reasons, the concentration of $VGaib$H–$VO1$ (and other $E1$ compatible configurations), relative to divacancies in other configurations and with different numbers of H, can be expected to depend on several factors, such as the concentration ratio of H to $VGaVO$ and other traps, the Fermi-level position, the temperature, and the energy barriers associated with transformations between different isolated and hydrogenated $VGaVO$ configurations.^77,81

Finally, we consider complexes between H and other common impurities in $β$-Ga$2$O$3$⁠. An obvious candidate is the Fe$Ga$ acceptor (⁠$E2$⁠), which displays $ε(0/−)$ levels at 0.6-0.7 eV below $EC$⁠.^20,32,35 However, Varley⁷⁶ calculated a binding energy of 0.7 eV for the Fe$Ga2$H complex and a $ε(+/0)$ level located 1.3 eV below $EC$⁠.⁷⁶ Similarly, polaronic acceptor impurities, such as Mg, exhibit even deeper levels that are also shifted to lower Fermi-level positions when hydrogenated.^82,83 Polyakov et al.³⁸ have suggested that H can passivate shallow donor impurities by forming charge-neutral complexes. We have investigated this possibility for silicon and tin donors in their most favorable configuration, Si$Ga1$ and Sn$Ga2$ (Sn is a commonly used $n$-type dopant and is included for comparison). Although cationic H$i+$ is the energetically preferred form of isolated H, we indeed find that anionic H$i−$ can be stabilized in the vicinity of these Ga substitutional shallow donor impurities, resulting in charge-neutral Si$Ga1$H and Sn$Ga2$H pairs under n-type conditions, as shown in Fig. 5(a). However, formation of these complexes might be suppressed by screened Coulomb repulsion, as both constituents are positively charged for any position of the Fermi level in the bandgap. Moreover, these complexes are only stable in n-type material, with modest binding energies of up to 0.58 and 0.51 eV for Si$Ga1$H and Sn$Ga2$H, respectively, as shown in Fig. 5(b). Additionally, their stability rapidly decreases with the Fermi level, indicating likely complex dissociation under RBA conditions. For lower Fermi-level positions, H$i+$ is preferred over H$i−$⁠, also in the vicinity of the donor. Indeed, the $2+$ charge states shown in Fig. 5 correspond to a H$i+$ immediately adjacent to Si$Ga+$ or Sn$Ga+$ (H forms a bond with the O indicated by arrows in Fig. 6). The single-positive charge state of the complex is similar but has an electron occupying a delocalized perturbed host state⁶⁶ just below $EC$⁠. This prevents an accurate evaluation of $ε(+/0)$⁠, as the 160-atom supercell is not sufficiently large for such spatially extended defect states.⁸⁴ The upper estimates of $∼$1 eV in Table I assume a donor ionization energy of zero, which corresponds to the $ε(2+/+)$ level being located at $EC$⁠. Nonetheless, the low thermal and bias-induced stability of these donor complexes are incompatible with those observed for $E1$⁠.

In summary, we have investigated the influence of $H2$ and Ar annealing of $n$-type EFG-grown $β$-Ga$2$O$3$ on the presence of the $E1$ center. Using FT-IR, we confirmed that H is incorporated into the bulk crystals during $H2$ heat treatments. Notably, the H$2$ heat treatments did not lead to any considerable changes in charge-carrier concentration. Using DLTS, it was shown that the H$2$ annealing promotes the defect level $E1$⁠, suggesting a H-related defect origin for the $E1$ center. Based on comparison with hybrid-functional calculations for defect complexes involving H, specific defect origins of $E1$ are discussed. We find three different types of H-related defects exhibiting charge-state transition levels and capture barriers that are compatible with the measured activation energy for $E1$⁠, including (i) the $ε(+/−)$ level of H$O2$⁠, (ii) the $ε(−/2−)$ level of singly hydrogenated Ga–O divacancies exhibiting Ga$2$–Ga$2$ dimers (⁠$VGaib$H–$VO1$ and $VGa1$H–$VO1$ being the lowest energy configurations),⁷⁷ and (iii) the $ε(+/0)$ level of Ga substitutional shallow donor impurities passivated by anionic H$i−$⁠, e.g., Si$Ga1$H and Sn$Ga2$H. Among these defect candidates, only (ii) is consistent with the apparent stability of $E1$ upon RBA and ZBA up to 650 K.

Financial support is acknowledged from the Research Council of Norway through the GO2DEVICE project (Project No. 301740), the FUNDAMeNT project (Project No. 251131), the GO-POW project (Project No. 314017), the Norwegian Micro- and Nano-Fabrication Facility (NorFab, Project No. 295864), and the Faculty of Mathematics and Natural Sciences at the University of Oslo via the strategic research initiative FOXHOUND. Funding for this work was also provided by the Norwegian Research Council through the Research Center for Sustainable Solar Cell Technology (FME SUSOLTECH, Project No. 257639). This work was partially performed under the auspices of the U.S. DOE by the Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA27344 and partially supported by the LLNL Laboratory Directed Research and Development funding under Project No. 22-SI-003 and by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. DOE, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office.

The authors have no conflicts to disclose.

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