Tutorial: Microscopic properties of O–H centers in β-Ga₂O₃ revealed by infrared spectroscopy and theory

The transparent conducting oxides (TCOs) are a class of wide bandgap semiconductors that combine high conductivity with transparency in the visible region of the spectrum.^1,2 The TCO β-Ga₂O₃, with its ultrawide bandgap near 4.9 eV, is being investigated for high-power, deep UV, and extreme-environment applications.^3–7 Defects in β-Ga₂O₃ have a strong effect on electrical properties and are being widely studied.⁸ 

Hydrogen impurities in the TCOs can act as shallow donors and are a cause of the unintentional n-type conductivity in this class of materials that remained poorly understood for decades until a modern understanding of H in TCOs emerged.^9–16 The electrical properties of β-Ga₂O₃ are also strongly affected by hydrogen that can be present unintentionally or introduced intentionally by hydrogenation treatments.^17–22 This Tutorial presents a survey of O–H centers in β-Ga₂O₃ and what can be learned from their infrared spectra.

The vibrational spectroscopy of defects that contain light-mass elements provides information about microscopic defect structures.^23–25 Furthermore, theory can readily predict the structures and vibrational modes of defects, making the joint experimental and theoretical study of the vibrational properties of defects a powerful strategy for determining defect structures. This is especially true for defects that contain hydrogen, the lightest element.

For the O–H centers of interest in this Tutorial, the isotopic substitution of D for H gives rise to a large frequency shift of the vibrational lines and a frequency ratio that is near $ν ¯ H/ ν ¯ D≈√2$ because of the different isotopic masses of H and D. This isotope dependence allows a vibrational line to be unambiguously assigned to a hydrogen mode of vibration. Once a vibrational line has been discovered, the concentration of the defect species it originates from can be monitored in defect reactions. The polarization dependence of O–H vibrational spectra reveals the orientations of the O–H bonds in the lattice.^26,27

The infrared (IR) spectroscopy that reveals the vibrational lines of defects also has the ability to monitor the broad absorption that arises from free carriers.^28,29 In favorable cases, specific defects can be related to the changes in conductivity they cause, a capability that has been used to study prototypical TCOs.^30–33 

β-Ga₂O₃ has the low-symmetry monoclinic structure that is shown in Fig. 1.^34,35 There are two inequivalent Ga sites and three inequivalent O sites whose local configurations are also shown. The Ga(1) site is fourfold coordinated and the Ga(2) site is sixfold coordinated. While the low-symmetry structure of β-Ga₂O₃ appears complicated, it has the advantage of giving rise to vibrational absorption lines with polarization properties that provide additional information about microscopic defect structures.²⁷ 

Theory has predicted that interstitial hydrogen, H_i, and hydrogen at an oxygen vacancy, H_O, are shallow donors in β-Ga₂O₃.³⁸ Furthermore, a vacancy on a Ga site is predicted to be a triple acceptor with low formation energy.³⁹ The V_Ga–H complex was found to have even lower formation energy.^39, Figure 2 shows three different configurations for a vacancy on a Ga(1) site in β-Ga₂O₃, one of which is an unshifted vacancy that is shown on the upper right. Varley et al. found that a split configuration of the Ga(1) vacancy (⁠ $V Ga 1 ic$ in Fig. 2) is lower in energy than the unshifted configuration by ∼1 eV.³⁹ Kyrtsos et al. predicted the structures of three split configurations that they labeled as “a,” “b,” and “c.”⁴⁰ The “b” configuration $( V Ga 1 ib)$ is also shown in Fig. 2(b). These split-vacancy configurations consist of a Ga atom shifted into an interstitial position between two Ga vacancies. We note that different notations have been used in the literature to describe the split-vacancy configurations. In Fig. 2, we have adopted the notation used by Kyrtsos et al. and others.^40–43 

The split configurations of the $V Ga 1$ defect have been observed by electron paramagnetic resonance (EPR),^44,45 scanning transmission electron microscopy (STEM),⁴⁶ and positron annihilation methods.^42,43 The split-vacancy configuration $V Ga 1 ib$ complexed with H was identified in early experiments by vibrational spectroscopy.⁴⁷ O–H centers that involve split configurations of V_Ga have been found to be prevalent in β-Ga₂O₃^47–50 and are the focus of this Tutorial.

Both bulk and epitaxial β-Ga₂O₃ samples are available for study.^3–6 Most of the samples for the experiments discussed here were purchased from the Tamura Corp. and have been grown by the Edge-defined Film-fed Growth (EFG) method. A few additional bulk samples grown at Synoptics by the Czochralski method⁵¹ as well as epitaxial materials grown by molecular beam epitaxy (MBE) have also been investigated. Polarized absorption measurements have been made for samples with $( 2 ¯ 01)$⁠, $(010)$⁠, and $(001)$ faces.

Hydrogen and deuterium have been introduced into β-Ga₂O₃ by several methods. Intentional introduction methods include annealing at elevated temperature (≈900 °C) in an H₂ and/or D₂ ambient.⁵² Such anneals are done in sealed quartz ampoules that contain 2/3 atm of H₂ or D₂. H or D can also be introduced into $μ m$ thick surface layers from a hydrogen- or deuterium-containing plasma at a sample temperature of a few hundred °C.^53,54 Finally, ion implantation provides a method to produce hydrogenated or deuterated surface layers that are roughly $1μ m$ thick with H or D concentrations near 10²⁰ cm⁻³.^53,54 Of these hydrogenation methods, annealing in a hydrogen ambient seems to be the simplest. Other methods introduce additional lattice damage and native defects with which hydrogen can interact.

Fourier Transform Infrared (FTIR) spectrometers are now widely used to measure IR absorption spectra because of the high resolution and high signal-to-noise ratio they offer.⁵⁵ Both Bomem DA and Nicolet iS50 instruments equipped with liquid-N₂ cooled InSb detectors have been used for the measurements discussed here. Spectra are typically reported as absorbance (A) vs frequency $( ν ¯)$⁠, where absorbance is the −log₁₀ of the transmission. The frequency of the infrared light is typically given in wavenumber (cm⁻¹) units, where $ν ¯≡1/λ$ is the reciprocal of the wavelength. The polarization of the transmitted light was analyzed with a wire grid polarizer placed into the spectrometer after the sample. Samples were cooled to 5 or 77 K for our measurements with a Helitran continuous flow cryostat.

The theoretical work carried out in collaboration with the experimental work presented in this article has involved hybrid density functional calculations using the CRYSTAL06 code⁵⁶ and its successor, CRYSTAL17.⁵⁷ The flexible and versatile CRYSTAL codes utilize Gaussian basis sets and allow defect structures and vibrational properties to be calculated in the framework of supercells of chosen sizes.

While these calculations were customized to address each particular situation, the most common and typical framework involved 80 or 120 atom supercells, the B3LYP hybrid exchange,⁵⁸ and basis functions of the type 311p(1) for H (Ref. 59), 8411 for O (Ref. 60), and 864111d(41) for Ga (Ref. 61). With such a uniform framework, calculations on different defects could be compared with some confidence. Furthermore, trials with other basis functions led to results generally insensitive to choice of basis.

A spectrum is shown in Fig. 3 for a β-Ga₂O₃ sample with a $( 2 ¯ 01)$ face that had been annealed in a D₂ ambient. The dominant O–D line in the spectrum has a vibrational frequency of 2546.4 cm⁻¹.⁴⁷ The corresponding O–H line has a frequency of 3437.0 cm⁻¹. The frequency ratio $ν ¯ H/ ν ¯ D=1.35$ is typical for H or D bonded to a light-mass element like O. The O–D vibrational line is strongly polarized, and there is no absorption observed for the polarization with electric vector E//[010].

Spectra measured for samples that contain both H and D provide additional clues about defect structures.^47,48 Figure 4 shows the lines at 2546.4 and 3437.0 cm⁻¹ for samples that contained D alone and H alone [spectra labeled (i) in Figs. 4(a) and 4(b)]. For a β-Ga₂O₃ sample that contained both H and D together, new absorption lines appear at 2547.1 and 3438.2 cm⁻¹. The appearance of these additional lines is a signature of an O–H center that contains two equivalent H atoms! Examples of vibrational spectra for defects containing two weakly coupled H atoms are discussed in Ref. 23.

For defects that contain 2 H atoms, samples containing both H and D will have all possible isotopic combinations present together. That is, samples will contain defects with two H atoms, two D atoms, and both H and D. Figure 5(a) shows a sketch of two equivalent, weakly coupled, O–H oscillators that would be expected to have antisymmetric (arrows in sketch) and symmetric-stretching modes. Single lines due to the antisymmetric stretching modes are observed in our spectra while the symmetric-stretching mode is silent for the defects that contain two O–H or two O–D oscillators. [The symmetric-stretching mode in this scenario is forbidden for the two equivalent oscillators when they are oriented in the same direction, as shown in Fig. 5(a).] For a defect that contains both H and D atoms [Fig. 5(b)], the two oscillators become dynamically decoupled because of the large difference in the O–H and O–D vibrational frequencies. In this case, the defect that contains both H and D has a decoupled O–H mode and a decoupled O–D mode that give rise to the new lines seen for the spectra labeled (ii) in Figs. 4(a) and 4(b). These decoupled modes lie midway between the antisymmetric- and symmetric-stretching modes.

A careful theoretical search of possible defect structures revealed that the split configuration of a Ga(1) vacancy, $V Ga 1 ib$⁠, could trap two identical H or D atoms to yield a defect with vibrational properties that are consistent with experiment.⁴⁷ This structure is shown in Fig. 6(a). Configurations involving H or D trapped by a vacancy at a Ga(2) site could be ruled out because they would yield vibrational absorption with a component polarized along the [010] axis that was not observed.

The polarization properties of the 2546 cm⁻¹ line further support its assignment to the $V Ga 1 ib−2 D$ complex,²⁷ as will be discussed in Sec. V of this Tutorial.

More than a dozen, O–H (or O–D) lines have now been observed in β-Ga₂O₃ samples treated in H₂ (or D₂) ambients in addition to the lines at 3437 and 2546 cm⁻¹ assigned to the dominant $V Ga 1 ib−2 H$ and $V Ga 1 ib−2 D$ complexes.⁴⁹ Because O–D vibrational lines can often be measured with higher signal-to noise ratio than the corresponding O–H lines, O–D centers and their vibrational spectra will be the focus of the present section.

A puzzling behavior was observed when the annealing characteristics of the $V Ga 1 ib−2 D$ center were investigated.⁴⁸ In some samples treated in a D₂ ambient, the $V Ga 1 ib−2 D$ line at 2546 cm⁻¹ did not initially appear until a subsequent anneal in an inert ambient at a temperature above 450 °C was performed. Where had the D been hiding in a form not seen by vibrational spectroscopy until it was converted into the V_Ga–2D center by an annealing treatment?

It was later found that the polarization properties of O–D centers in the low-symmetry monoclinic structure could explain this surprising annealing behavior.⁴⁸  β-Ga₂O₃ samples with a $( 2 ¯ 01)$ face, treated in a D₂ ambient at 900 °C and cooled quickly, were found to contain additional O–D centers with a transition moment perpendicular to the $( 2 ¯ 01)$ faces of the samples. These vibrational lines could not be seen with probing light with its electric vector in the $( 2 ¯ 01)$ plane and remained hidden in early vibrational spectroscopy experiments.

Infrared absorption experiments, for samples that were prepared so that the polarization direction with $E//( 2 ¯ 01)$ could be examined, revealed several additional O–D centers with polarization properties different than those of the dominant $V Ga 1 ib−2 D$ defect.⁴⁸  Figure 7 shows spectra that were measured for a β-Ga₂O₃ sample with a $( 2 ¯ 01)$ face that had been prepared by annealing in a D₂ ambient and then cooled quickly.⁴⁹ The sample was tipped at a 45°angle with respect to the direction of the incident light, as is shown in the inset in Fig. 7. For light polarized along the [102] direction (E//[102]), the probing light has no component perpendicular to the $( 2 ¯ 01)$ face of the sample. However, for light polarized with E⊥[102], the probing beam does have a component of its polarization with electric vector perpendicular to the $( 2 ¯ 01)$ face of the tipped sample.

As can be seen in Fig. 7 for a deuterated β-Ga₂O₃ sample that was annealed at 100 °C, several new lines in addition to the dominant line at 2546 cm⁻¹ are present that can explain H or D that was hidden in early experiments.⁴⁹ Following a subsequent anneal at 440 °C, all of the additional lines have disappeared and appear to have been converted into the dominant 2546 cm⁻¹ line due to the $V Ga 1 ib−2 D$ complex. Figure 8 shows the annealing behavior of the O–D vibrational lines seen in Fig. 7.⁴⁹  Figure 8(a) shows the annealing behaviors of the new lines that appear for E⊥[102]. Figure 8(b) shows the annealing behaviors of the 2631 and 2546 cm⁻¹ lines seen for the polarization E//[102].

Our experimental results find at least two types of O–D centers with different polarization properties and different annealing behaviors. Theory finds that the $V Ga 1 ic$ configuration of a split Ga(1) vacancy can also trap D to give rise to O–D centers with different bond orientations and thermal stabilities than those of the dominant $V Ga 1 ib−2 D$ complex (along with corresponding O–H centers).⁴⁸ The predicted structure of the $V Ga 1 ic−2 D$ center is shown in Fig. 6(b).

More than a dozen, O–H and O–D lines have now been observed for hydrogenated and deuterated β-Ga₂O₃.⁴⁹ What are their possible origins? Because traps for H or D might include additional impurities and/or native defects, there may be many candidates for hydrogen-containing defects. For example, Ir impurities are introduced into β-Ga₂O₃ from the crucible used for growth,^51,62 while Si and Fe impurities are also frequent unintentional contaminants in β-Ga₂O₃^63,64 and also intentional dopants. Si sits on a Ga(1) sites and acts as an n-type dopant.⁶⁵ Fe prefers to sit on a Ga(2) site⁶⁶ and acts as a deep acceptor that compensates n-type conductivity.^67, β-Ga₂O₃ has also been doped with other deep acceptors such as Mg,^68–70 Ca,^62,71 and Zn^72,73 to compensate n-type conductivity. Vibrational lines have been reported for O–H and O–D complexes that contain all of the impurities listed in this paragraph.

A spectrum is shown in Fig. 9 for a Si-doped β-Ga₂O₃ epitaxial layer that was grown by MBE on an Fe-doped substrate.⁵⁰ This sample was treated in a plasma that contained both H and D. The lines at 2579.1 and 3479.4 cm⁻¹ were attributed to OD–Si and OH–Si complexes,⁷⁴ respectively, where the notation “OD-impurity complex” denotes an (oxygen-D)-impurity complex. The lines at 2586.0 and 3492.1 cm⁻¹ were attributed to OD–Fe and OH–Fe complexes, respectively. Assignments such as these must be viewed with caution because there is no isotope effect that identifies the additional impurity in the complex, and Si and Fe are both adventitious impurities in β-Ga₂O₃.

The O–H and O–D lines shown in Fig. 9 are sharp, without additional line components or shoulders, for a sample that contains both H and D, indicating that these defects involve a single H or D atom.

The introduction of H and D into β-Ga₂O₃ doped with Mg,⁶⁹ Ca,^62,71 and Zn⁷³ acceptors gave O–H (O–D) absorption lines at frequencies (10 K) 3492 (2586), 3441 (2556), and 3486.7 (2582.9) cm⁻¹, respectively. Spectra for samples that contained both H and D showed no additional absorption lines for the OH-acceptor complexes that might arise from defects that contain more than one H atom. Furthermore, none of these IR lines has a component with polarization E//[010].

Figure 10 shows spectra for a sample doped with Mg [spectrum (a)] and for a Si-doped epitaxial layer grown on an Fe-doped substrate [spectrum (b)]. These results, and those of others,^69,73 show that the O–D lines for several impurity-OD complexes lie close in frequency (in some cases within 1 cm⁻¹ of each other), suggesting a family of defects with similar structures.

The many O–H and O–D complexes that have been seen in hydrogenated and deuterated β-Ga₂O₃ have distinct polarization properties, which can provide valuable clues about their structure. In the present section, a strategy for a more detailed analysis of the polarization dependence of the vibrational absorption lines²⁷ is briefly described, and implications for the assignments of vibrational modes to specific defect structures based on their polarization properties are discussed.

β-Ga₂O₃, with its monoclinic structure, is optically biaxial with principal dielectric axes, X, Y, and Z.⁷⁵ The [010] axis of β-Ga₂O₃ is the Y principal axis. The X and Z dielectric axes lie in the (010) plane with orientations that depend on frequency. For light propagating along the [010] optic axis, there are different refractive indices for light polarized with its electric vector along the X and Z dielectric axes. Because of this optical anisotropy, light propagating along the [010] axis maintains its polarization only for polarizations along the X and Z dielectric axes. The orientations of the dielectric axes of β-Ga₂O₃ have been determined over a broad spectral range by ellipsometry.⁷⁵ Polarized vibrational absorption measurements have also determined the orientations of the X and Z dielectric axes in the IR range.^27,50

The polarization dependence of the 2546 cm⁻¹ line assigned to the $V Ga 1 ib−2 D$ complex is considered as an example.²⁷ A β-Ga₂O₃ sample with a (010) face was implanted with D⁺ ions with multiple energies and doses to produce a deuterated layer that was 1200 nm thick and with a D concentration of [D] ≈10²⁰ cm⁻³. Figure 11 shows spectra for the 2546 cm⁻¹ absorbance line and its dependence on the angle, $ϕ$⁠, of an analyzing polarizer defined with respect to the [102] axis of the sample. To analyze the polarization dependence of these data, a strategy given in a monograph by Turrell²⁶ and in Refs. 27 and 50 is used. The various angles that are of interest are defined in Fig. 12.

In Eq. (1), $θ$ is the angle of the analyzing polarizer measured with respect to the X dielectric axis and l is the thickness of the sample. The first term in parentheses in Eq. (1) is proportional to the transmission along the X dielectric axis, $cos 2⁡θ e − α X l$⁠. The second term is proportional to the transmission along the perpendicular Z dielectric axis, $sin 2⁡θ e − α Z l$⁠.

Equation (1) shows that when the analyzing polarizer is along the X or Z axis [i.e., when $θ$ is 0° or 90°], the extreme values of the angle dependent absorbance are obtained, thus determining the angle $ψ$ between the X dielectric axis and [102] direction. The angle $ψ$ is a property of the β-Ga₂O₃ host crystal.

It is the dichroic ratio that provides information about the transition moment direction (the angle $χ$⁠) and the O–H bond angle(s) for the defect itself. The angle $χ$ gives the transition moment direction with respect to the X dielectric axis. The sign of the angle of the defect transition moment, $χ$⁠, is not determined by Eq. (3) and remains ambiguous in this analysis. However, a comparison of the two possible signs of $χ$ with the results for O–D bond angles predicted by theory helps to assign the vibrational lines observed by experiment to specific defect structures.

The angle specifying the direction of a defect's transition moment that is more straightforward to compare with the predictions of theory is defined with respect to the [102] axis of the β-Ga₂O₃ crystal. This angle is $ψ±χ$⁠, accounting for the uncertainty in the sign of $χ$ that is determined by experiment.

Figure 13(a) shows polarized absorbance spectra measured for an Fe-doped β-Ga₂O₃ sample with a (010) face that had been deuterated by annealing in a D₂ ambient.⁵⁰ The vibrational lines at 2577.7 and 2584.6 cm⁻¹ that have been attributed to O–D complexes that involve additional Si and Fe impurities,⁷⁴ respectively, are shown. The polarization dependence for the 2546 cm⁻¹ line arising from the $V Ga 1 ib−2 D$ center was measured for this same sample following a subsequent anneal that produced it. Figures 13(b)–13(d) show the angle dependences of the integrated absorbances for the lines with frequencies 2546, 2577.7, and 2584.6 cm⁻¹, respectively.

A fit of Eq. (1) to these data yields an angle $ψ= 36 °± 4 °$ for the X dielectric axis with respect to the [102] crystal axis⁵⁰ (a clockwise angle is positive here), a value that agrees with the results of previous ellipsometry measurements,⁷⁵ within experimental error.

Table I lists the transition moment directions for a selection of the O–D centers that are of interest here. Data and its analysis for the OD–Mg center listed in Table I are given in Ref. 50. (A list of additional O–D centers whose polarization properties have also been studied is given in Ref. 49.)

Theory predicts that the transition moment direction for the $V Ga 1 ib−2 D$ complex lies 10° to 20° clockwise of the [102] axis.²⁷ This result is in good agreement with the experimental determination of the transition moment direction for the 2546 cm⁻¹ line if the negative sign for the angle $χ$ is chosen. The polarization dependence of the 2546 cm⁻¹ line provides further support for its assignment to the $V Ga 1 ib−2 D$ complex.

Theory has suggested that D trapped at the split-vacancy configuration $V Ga 1 ic$⁠, with an additional impurity nearby, is a good candidate for the family of impurity-OD centers seen by experiment that were discussed in Sec. IV C above.⁵⁰  Figure 14 shows the structure of a $V Ga 1 ic− OD$ complex along with nearby Ga(1) and Ga(2) sites where additional impurities might be located to give a family of OD-impurity complexes with similar vibration properties. Theory predicts a transition moment direction approximately 90° from the [102] axis for the defect structure shown in Fig. 14.⁵⁰ This prediction is in good agreement with the transition moment directions measured by experiment for a positive value of the angle $χ$ (Table I).

These results do not rule out other possibilities for OD-impurity structures that might be found by future experimental and theoretical work.

Several O–H and O–D centers have been discovered in β-Ga₂O₃ along with conversions between them that occur upon thermal annealing (Fig. 8). How do these defects and their reactions affect the electrical properties of β-Ga₂O₃?

Here, $m ∗$ is the effective mass, n is the refractive index, and $τ − 1$ is the carrier scattering rate. This strategy to probe optically the conductivity of a semiconductor has been used previously for TCOs such as ZnO,^30,31 SnO₂,³² and In₂O₃.³³ 

Figure 15 shows the broad free-carrier absorption due to hydrogen in β-Ga₂O₃.⁴⁹ For these experiments, an unintentionally doped β-Ga₂O₃ sample with a $( 2 ¯ 01)$ face was purchased from the Tamura Corp. To initiate the sequence of anneals whose free-carrier spectra are shown in Fig. 15, this sample was annealed in a mixture H₂ and D₂ at 900 °C to introduce both H and D.

To separate the free-carrier absorption due to H and D from that arising from the thermally stable, unintentional background doping from adventitious n-type impurities, an appropriate reference sample is required.⁴⁹ To produce this reference, this same sample was annealed at 1000 °C for 4h in flowing Ar. This annealing treatment eliminated all O–H and O–D lines from the sample's IR spectrum.

The spectrum labeled “0” in Fig. 15 was measured for the β-Ga₂O₃ immediately after it was hydrogenated by an anneal (900 °C) in an ambient containing H₂ and D₂. (This same sample, but with H and D completely annealed away, was used as a reference to reveal only the free-carrier absorption that is due to H and D.) The broad absorption at low frequency resulting from free carriers was produced by this hydrogenation treatment. This sample was then subsequently annealed in an inert ambient at successively higher temperatures. The free-carrier absorption was strongly increased by an anneal at 500 °C. The free-carrier absorption due to H and D was not eliminated until an anneal at 1000 °C.

The strengths of the O–H and O–D vibrational lines at 2546 and 3437 cm⁻¹ show a similar dependence on the annealing temperature.⁴⁹ (See the 3437 cm⁻¹ O–H line in the inset to Fig. 15). The 3437 cm⁻¹ line produced by the hydrogenation treatment is strongly increased by the anneal at 500 °C and then eliminated by the anneal at 1000 °C that causes H and D to leave the sample.

It is possible to explain the correlated annealing behaviors between the free-carrier absorption with the O–H and O–D vibrational lines without requiring that the O–H and O–D centers be shallow donors.⁴⁹  $V Ga$ is a deep triple acceptor that compensates the n-type doping that results from unintentional shallow impurities in β-Ga₂O₃. If the formation of the $V Ga 1 ib−2 D$ complex passivates (or partially passivates) $V Ga$ triple acceptors, the compensation of unintentional shallow donors will be reduced, increasing the concentration of free-electrons.⁴⁹ When H and D are completely annealed away, donor impurities will again be compensated by $V Ga$⁠.

While this mechanism for the changes in conductivity caused by O–H an O–D centers seems like a plausible explanation for our results, it gives rise to new questions that are difficult to answer. In this scenario, only the formation of $V Ga 1 ib−2 D$ passivates the V_Ga triple acceptor. What about the numerous other O–H an O–D centers that are present, and what is their electrical activity? Furthermore, what is the nature of the reaction that converts the many O–D and O–H centers that are present into the $V Ga 1 ib−2 D$ complex by an anneal at 500 °C? Is some unknown additional source of hydrogen required for these defect reactions to occur?

More than a dozen, O–H and O–D vibrational lines have been observed for H and D in β-Ga₂O₃.^49,62,69,71 For most of these O–H or O–D centers, there has been no absorption observed with a component of the polarization with E parallel to the [010] axis of β-Ga₂O₃. This experimental result has led to proposals for O–H defect structures that involve shifted configurations of a vacancy at the tetrahedrally coordinated Ga(1) site and have ruled out structures that involve a vacancy at the octahedrally coordinated Ga(2) site because these structures are predicted to show absorption for E//[010].

Figure 16 shows weak O–D lines at 2475 and 2493 cm⁻¹ with a component of their polarization with E//[010] that were reported for a β-Ga₂O₃ sample grown by the Czochralski method and annealed in a D₂ ambient.^49,76 O–D defect structures involving V_Ga2 have been suggested as assignments for these weak vibrational lines.^49,76 These lines have been seen by us only in samples prepared from an Fe-doped boule of β-Ga₂O₃ grown by the Czochralski method which suggests the involvement of an additional defect or impurity that is present in these samples. Defect structures with D trapped at an unshifted vacancy at a Ga(2) site and structures with D trapped at the “a” configuration of a split vacancy $( V Ga 1 ia)$ have been considered as possible assignments.^49,76

While the β-phase is the most thermally stable phase of Ga₂O₃, other metastable phases exist^77–79 and are sufficiently stable for device applications. α-Ga₂O₃ has a bandgap energy of 5.3 eV⁵ and has the corundum structure of α-Al₂O₃ (sapphire).⁸⁰ The vibrational properties of O–H and O–D centers in α-Ga₂O₃ have been studied by IR spectroscopy and theory.⁸¹ 

An epitaxial layer of α-Ga₂O₃, 1200 nm thick, was grown by halide-vapor-phase epitaxy on a sapphire substrate at the Korean Institute of Ceramic Engineering and Technology for study by vibrational spectroscopy.⁸¹ H and D were introduced by ion implantation to produce hydrogenated and deuterated layers that were 1200 nm thick (i.e., designed to match the thickness of the epilayer) and with H or D concentrations near 10²⁰ cm⁻³.

Vibrational spectra shown in Fig. 17 for D⁺ implanted into α-Ga₂O₃ show O–D lines at 2431, 2440, and 2472 cm⁻¹. A spectrum is also shown for D⁺ implanted into the α-Al₂O₃ substrate material. The vibrational line at 2440 cm⁻¹ is due to an O–D center in α-Al₂O₃ (Ref. 82) and has a frequency that agrees with the previous result of Engstrom et al.⁸³ This line appears as a weak, partially resolved shoulder, in the spectrum for the implanted epilayer of α-Ga₂O₃ because a portion of the D⁺ implant has reached the sapphire substrate.

The Al and Ga vacancies in α-Al₂O₃ and α-Ga₂O₃, respectively, have been studied by theory.^81, Figure 18(a) shows the corundum structure. With respect to a given c axis location for a cation, there are two inequivalent O sites with the O atoms shown in red forming a larger equilateral triangle than the equilateral triangle formed by the O atoms shown in yellow. The equilibrium configuration of a cation vacancy in both α-Al₂O₃ and α-Ga₂O₃ was found to have a shifted configuration [Fig. 18(b)] where the cation lies between two vacancies.⁸¹ However, the addition of H or D stabilizes the unshifted vacancy, giving the structure for H or D trapped at a cation vacancy shown in Fig. 18(c) with H bonded to one of the oxygens (shown in red) in the larger triangle. This structure for H trapped by $V Al$ was predicted by Thienprasert et al. for H in α-Al₂O₃.⁸⁴ A similar structure has been predicted to be the equilibrium structure for H or D trapped by $V Ga$ in α-Ga₂O₃.⁸¹ 

The vibrational frequency for O–D trapped by $V Ga$ in α-Ga₂O₃ [Fig. 18(c)] is predicted to lie ∼100 to 150 cm⁻¹ lower than the frequency for O–D in β-Ga₂O₃, a result that is consistent with experiment for the 2431 cm⁻¹ line.⁸¹ Defect structures that contain two D atoms have been considered as candidates for the weak O–D line seen at 2472 cm⁻¹.

Thus, while a shifted cation vacancy has been found to be the equilibrium configuration in both α-Al₂O₃ and α-Ga₂O₃, similar to the situation in β-Ga₂O₃, the unshifted vacancy is stabilized by the presence of H or D in the corundum structure.⁸¹ 

While several O–H and O–D vibrational lines have been discovered, and theory has made progress with their assignments to defect complexes with H or D trapped at the different configurations of Ga vacancies in both β-Ga₂O₃ and α-Ga₂O₃, many puzzles remain. For example, while attempts have been made to assign a few of the many vibrational lines that have been observed to specific OH-impurity (or OD-impurity) complexes, these assignments are not definitive, and there are several lines without even tentative assignments.⁴⁹ 

The O–H centers in β-Ga₂O₃ evolve upon annealing and participate in reactions that affect the conductivity of the host crystal.⁴⁹ The $V Ga 1 ib−2 D$ complex is often the final sink for H or D. The identities of the defects that are involved and the mechanisms for these reactions remain poorly understood. Is there a defect that provides a hidden source of hydrogen that participates in these reactions? Interstitial H₂ and D₂ molecules in Ga₂O₃ could be interesting possibilities.

Adding additional defects and impurities into β-Ga₂O₃ complicates the defect reactions that occur. While not discussed in this Tutorial, lattice damage that is introduced into β-Ga₂O₃ by the ion implantation of H⁺ or D⁺ has been found to change the reactions involving the $V Ga 1 ib−2 D$ complex that occur upon annealing at elevated temperatures.⁸⁵ Native defects in β-Ga₂O₃ have been predicted to be mobile at typical annealing temperatures, giving several possibilities for defect reactions.⁸⁶ Furthermore, in samples that contain a high concentration of impurities, the OH-impurity (or OD-impurity) complexes that result act as an important source of H (or D) that modifies the hydrogen reactions that occur upon annealing.⁴⁹ 

There are also hydrogen centers that are expected to be important that have not been identified. Interstitial hydrogen is predicted to be a shallow donor in β-Ga₂O₃³⁸ and is also suggested to form complexes with deep-acceptor impurities.^69,73 O–H lines with polarization properties consistent with interstitial H have not yet been identified. Furthermore, conductivity changes that are due to shallow donors arising from H at an oxygen vacancy have been identified for other TCOs, but not yet for β-Ga₂O₃. Will these H_i and H_O centers be produced and identified in other experiments? Furthermore, other experimental techniques like deep-level-transient spectroscopy (DLTS) have also recently found defects due to H.^87,88 Are any of the O–H centers seen by IR spectroscopy related to the defects seen by other methods like DLTS?

Hydrogen has an important effect on the electrical properties of Ga₂O₃, and much exciting work remains to be done to understand its fascinating behavior.

The work at Lehigh University was supported by National Science Foundation (NSF) (Grant No. DMR 1901563). The work at UF was sponsored by Department of the Defense, Defense Threat Reduction Agency, HDTRA1-17-1-011, monitored by J. Calkins, DTRA Interaction of Ionizing Radiation with Matter University Research Alliance, HDTRA1-19-S-0004 (Jacob Calkins) and also by NSF (DMR 1856662). Portions of this research were conducted on Research Computing resources provided by Lehigh University supported by the NSF award 2019035. E.R. Glaser acknowledges the support of the Office of Naval Research.

The authors have no conflicts to disclose.

Michael Stavola: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal). W. Beall Fowler: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – original draft (equal). Amanda Portoff: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Andrew Venzie: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Evan R. Glaser: Investigation (equal); Resources (equal); Writing – review & editing (equal). Stephen J. Pearton: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – review & editing (equal).

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