Deep-level defects in Ta-doped β-Ga2O3 single crystals grown using the optical floating zone method are investigated. Deep-level transient spectroscopy (DLTS) in conjunction with Laplace-DLTS (L-DLTS) and photoluminescence (PL) has been applied to (100) oriented β-Ga2O3:Ta bulk crystals. The temperature dependence of the bias capacitance of diodes indicates no significant sign of carrier freeze-out down to 20 K. This confirms the predicted shallow donor behavior of Ta impurity atoms in β-Ga2O3 samples with a carrier concentration of (1.0–1.2) × 1018 cm−3. DLTS and L-DLTS analysis show six traps with activation energies of electron emission of 0.28 (Es), 0.46 (E9), 0.52 (E1), 0.69 (E2a), 0.75 (E2b), and 0.97 (E3) eV, with trap concentrations in the range of 1015–1017 cm−3. In addition, temperature-dependent PL has been used to study the broad luminescence bands with their maxima at 3.10 and 3.40 eV. Subsequent Arrhenius analysis extracted activation energy values (EA of 20 ± 1 and 79 ± 4 meV for quenching of the PL peaks at 3.10 and 3.40 eV, respectively.

Beta-phase gallium oxide (β-Ga2O3) is an ultrawide bandgap (UWBG) semiconductor (∼4.8 eV) that has gained considerable interest in recent years, owing to its impressive Baliga figure of merit (BFOM),1 a theoretical breakdown field of 8 MV cm−1, and ability to grow large-area single crystals from the melt.2,3 These advantages make β-Ga2O3 a strong candidate for deep ultraviolet photodetectors4,5 and high-power electronics,6 potentially supplementing more established wide bandgap materials, such as gallium nitride (GaN) and silicon carbide (SiC).7,8 Conventional group IV dopants, Si, Ge, and Sn, can be readily introduced to produce n-type material, with free electron concentrations in the range of 1016–1018 cm−3.9–13 However, there has been growing interest in exploring alternative dopants that can improve doping efficiencies while inducing minimal strain. Tantalum (Ta) has emerged as a promising candidate as a donor doping impurity due to its favorable properties.14–16 First principle calculations based on density functional theory (DFT) indicate that Ta-doping can be utilized to enhance the conductivity of β-Ga2O3.17 This is primarily due to Ta possessing five valence electrons (Ta5+) rather than four when doping with Si (Si4+) or Sn (Sn4+), which facilitates more effective donor substitution at Ga3+ sites.17–20 In addition, Ta has an ionic radius of 0.064 nm, which is closer to that of Ga (0.062 nm) when compared to both Si (0.040 nm) and Sn (0.069 nm),17–20 reducing the likelihood of structural defects. Recently, Hall effect measurements on β-Ga2O3:Ta revealed a superior carrier concentration and mobility in comparison to Sn-doped β-Ga2O3 material with the same nominal doping concentration.16 

Most commercially available β-Ga2O3 substrates are grown via the edge-defined film-fed growth (EFG) method, which can maintain high growth rates for large diameter crystals while being cost-effective.21,22 In 2023, Novel Crystalline Technology, Inc. (NCT) reported β-Ga2O3 substrates with diameters of 6 in. grown using the vertical Bridgman technique.23 However, substrates grown using these methods require large crucibles that are prone to contamination, and the overall manufacturing cost is highly dependent upon the cost of iridium,24 thereby incentivizing growth in crucible-free environments using methods such as Optical Floating Zone (OFZ).16,25 Single crystals with high purities can be achieved using OFZ with precise control of the doping level.26 This is particularly beneficial for defect-related studies within research settings, which do not require large-area wafers.

In this work, both optical and electrical characterization techniques have been applied to Ta-doped β-Ga2O3 to investigate the electrically active states present in the material. This has been achieved through deep-level transient spectroscopy (DLTS)27 in conjunction with high-resolution Laplace-DLTS (L-DLTS),28,29 which can provide information about electron traps within ∼1 eV from the conduction band minimum (CBM).30,31 In addition, photoluminescence (PL) has been applied to investigate the broad luminescence bands observed in β-Ga2O3 at ∼3.0–3.6 eV.32–36 Despite the inherent advantages of OFZ growth, numerous studies have reported the presence of deep-level defects that may hinder device control and reliability. Perrier et al.26 applied DLTS to Si-doped substrates grown via OFZ and observed four deep-level traps—so called, Es, E1, E2, and E3. Cui et al.19 reported a single defect level located at 0.73 eV relative to the conduction band, using conventional-DLTS on Ta-doped β-Ga2O3 grown by the OFZ method. This level possesses a similar electron activation energy for electron emission as the E2 trap, which has been firmly associated with FeGa defects.31,37–40 It has been argued that the E2 trap has acceptor properties, and it is commonly reported in bulk β-Ga2O3 in significant concentrations of ∼1016 cm−3,37,39,41 making it a prominent compensating center. From our results, deep levels with activation energies for electron emission close to those for the Es, E9, E1, E2a, E2b, and E3 traps have been observed, as per the labeling convention used by Perrier et al.26 and Wang et al.42 The origin and nature of each of these traps will be discussed.

Using the optical floating zone method (CSC made FZ-4000 system), Ta-doped β-Ga2O3 crystals were grown - growth details are also provided in Ref. 16. For the initial material preparation, high-purity Ga2O3 (5N) and Ta2O5 (4N) powders were sourced from Alfa Aesar. The precursor materials were precisely weighed and thoroughly homogenized through grinding to ensure uniform Ta distribution throughout the mixture, with Ta concentration set at 0.05 mol. %. The homogenized powder was subsequently loaded into a latex tube to create a cylindrical feed rod (10 mm in diameter and 60 mm in length), followed by hydrostatic compression at 70 MPa. The feed rod was extracted from the latex tube and subjected to sintering at 1350 °C for a 24-h period, resulting in a highly compact ceramic rod with minimal void content. The crystal growth process utilized a previously grown β-Ga2O3 crystal with (100) orientation as the seed. The OFZ system’s 4000 W halogen lamps, coupled with focusing mirrors, generated the necessary heat to melt the feed rod. To maintain optimal growth conditions and ensure a stable crystal–melt interface, both the seed and feed rods were rotated in opposite directions at 20 rpm. Growth proceeded at a controlled rate of 10–12 mm/h under compressed dry air flow (2 l/min). The resulting crystal boule was sliced into wafers using diamond wire cutting technology, and the wafer surfaces were prepared through chemical mechanical polishing to achieve the surface quality required for device fabrication.

For electrical measurements, topside Ni/Au (30/150 nm) Schottky contacts and large area backside Ti/Au (30/150 nm) ohmic contacts were fabricated to form vertical Schottky barrier diodes (SBDs). Prior to metal deposition, the samples were cleaned using acetone, isopropyl alcohol, and de-ionized water. The samples were subsequently cleaned with HCl and then H2O2 held at 85 °C. Following this, ohmic contacts were produced using e-beam evaporation, with a post-deposition heat-treatment for 5 min at 450 °C in a N2 atmosphere. Subsequently, circular topside Schottky contacts were deposited with diameters between 200 and 500 μm using a lithography and lift-off process. For optical analysis, as-grown samples were studied with no post-growth processing, except standard cleaning procedures. The PL measurements were performed in a closed cycle cryostat with helium exchange gas, using a 255 nm UV-LED for excitation at a power density of 71 μW/cm2.

Figure 1(a) shows the current density-voltage (J–V) characteristics of a typical SBD, which were measured in the voltage range from −10 to 1 V using a HP 4140 pA meter at temperatures of 295 and 40 K on a 400 μm diameter device. Using the same diode, capacitance–voltage (C–V) measurements [Fig. 1(b)] were conducted using a HP 34192A impedance analyzer with voltage varying from −8.0 to 0 V at a 1 MHz frequency of the probing AC signal. Across this voltage range, at both 295 and 40 K, the phase angle was between 84° and 89°, indicating a good quality of the diode. The spatial profile of the concentration of uncompensated donors [Nd+(W)] was extracted from the C–V dependencies [Fig. 1(c)], using a static dielectric constant (ε) value for (100) oriented β-Ga2O3 of 10.2.43 This yielded a carrier concentration in the range (1.0–1.2) × 1018 cm−3 down to ∼100 nm from the metal–semiconductor (M–S) junction. The free carrier concentration was also determined for an unintentionally doped (UID) β-Ga2O3 sample, which was grown under identical conditions and from the same source powder batch used to produce the β-Ga2O3:Ta material. This UID crystal underwent the same SBD processing steps outlined in the section titled Experimental Details, and subsequent C–V measurements were performed on a 400 μm diameter SBD. The UID sample exhibits a lower free carrier concentration in the range (2.5–6.5) × 1017 cm−3, indicating that Ta-doping increases the n-type conductivity. It is important to note that the C–V measurements on the UID material, using the same voltage range, probed deeper into the sample because of the lower carrier concentration. Following this, a capacitance–temperature (CT) scan was conducted [Fig. 1(d)] by cooling the sample down to 20 K without any applied bias, then at low temperature, a bias of −5.0 V was applied. Thereafter, the temperature was increased with a ramping rate of 2 K/min up to 430 K. The results shown in Figs. 1(a) and 1(d) reveal no significant sign of carrier freeze out down to 20 K, confirming that any doping donor levels in the β-Ga2O3:Ta sample are shallow. It is important to note, however, that additional unintentional shallow donor impurities, such as Si,44,45 may be contributing to the free carrier concentration as well as to the CT dependence shown in Fig. 1(d). However, a comparison with the UID material shows that Ta is the dominant donor in the doped material. Similarly, Li et al.46 conducted capacitance vs temperature measurements on unintentionally doped (UID) β-Ga2O3 grown via EFG, with a doping concentration of 1 × 1017 cm−3, and observed a significant drop in capacitance in the temperature range from 40 to 20 K. Subsequent admittance spectroscopy analysis revealed a level at about 11 meV below Ec, potentially related to Si, which could be a source of unintentional doping.

FIG. 1.

(a) Current density–voltage (J–V) and (b) 1/Cb2 vs the applied reverse bias voltage dependence for a 400 μm Ni/Au SBD on Ta-doped and unintentionally doped β-Ga2O3, measured at 295 and 40 K. (c) Corresponding depth profile of uncompensated donors, derived from C–V measurements. (d) Capacitance-temperature (CT) scan in the temperature range of 20–430 K, recorded with an applied bias of −5.0 V.

FIG. 1.

(a) Current density–voltage (J–V) and (b) 1/Cb2 vs the applied reverse bias voltage dependence for a 400 μm Ni/Au SBD on Ta-doped and unintentionally doped β-Ga2O3, measured at 295 and 40 K. (c) Corresponding depth profile of uncompensated donors, derived from C–V measurements. (d) Capacitance-temperature (CT) scan in the temperature range of 20–430 K, recorded with an applied bias of −5.0 V.

Close modal
Conventional DLTS spectra are shown in Fig. 2 across a temperature range from 50 to 450 K. Two scans have been conducted, so-called “sub-surface” and “bulk,” which probe the regions at depths of 47–61 and 67–78 nm relative to the metal–semiconductor (M–S) interface, respectively, as determined from prior C–V measurements. For the “sub-surface” scan, a constant reverse bias (Ub) of −2 V was applied with a pulse bias (Up) of −0.1 V, whereas the “bulk” scan utilizes a fixed Ub of −5 V and a Up of −3 V. In each case, a filling pulse length (tp) of 1 ms and a rate window (en) of 200 s−1 were used. The y-axis values have been calculated to show the average trap concentrations (NT) in the probed regions, according to
(1)
where ΔC is the amplitude of the capacitive transient, Cb is the capacitance at Ub, and f is the correction factor, which considers the depletion depths at reverse (wb) and pulse bias (wp) [f=wb2wb2wp2]. The DLTS spectra are dominated by a peak with its maximum at about 400 K [Fig. 2(a)], with a trap concentration of the order 1017 cm−3. This DLTS signal at ∼400 K is consistent with the commonly reported E2 trap, related to FeGa defects, which is observed in β-Ga2O3 crystals grown via Czochralski (Cz),47 EFG,37–39 and OFZ techniques.18,48 Three additional peaks were detected in the temperature range of 100–300 K [Fig. 2(b)], resembling peaks reported in the literature, the so-called Es, E9, and E1 traps. These deep-level traps have average trap concentrations in the range of 1015 cm−3 close to the surface; however, NT decreased significantly in the bulk region, particularly for the Es trap with its peak maximum at ∼170 K.
FIG. 2.

“Sub-surface” and “bulk” conventional-DLTS spectra for the Ta-doped β-Ga2O3 sample (a) from 50 up to 450 K. (b) Magnification of the conventional-DLTS spectra shown in (a), within the temperature range of 70–320 K.

FIG. 2.

“Sub-surface” and “bulk” conventional-DLTS spectra for the Ta-doped β-Ga2O3 sample (a) from 50 up to 450 K. (b) Magnification of the conventional-DLTS spectra shown in (a), within the temperature range of 70–320 K.

Close modal
To accurately determine the activation energy for electron emission to the conduction band (ΔEem) and the apparent capture cross section (σapp), L-DLTS was applied. These “trap signatures” were extracted through the Arrhenius-type equation,
(2)
where eem is the electron emission rate determined using L-DLTS, kB is the Boltzmann constant, and A=[(Nc×T32)×(vth×T12)]. Here, Nc is the density of states in the conduction band, and vth is the thermal velocity of electrons, calculated using an effective mass of electrons (me*) of 0.28 m0.49,50 

The L-DLTS analysis is shown in Fig. 3, obtained using the “double” L-DLTS technique,51 in which two filling biases and a fixed reverse bias are utilized to probe a narrow window in the depletion region. This technique minimizes the influence of the electric field on the electron emission rate. For the case of the peak at 170 K (Es), an analysis of the conventional DLTS spectra has been used to obtain ΔEem and σapp values, due to the proximity of the defect to the M–S interface complicating effective “double” L-DLTS analysis—shown in the supplementary material. Figure 3(a) shows the L-DLTS spectrum recorded at 270 K using parameters Ub = −6 V, Up1 = −2 V, Up2 = −3 V, and tp = 1 ms. From this, the broad conventional-DLTS signal can be separated into two discrete electron emission signals with ΔEem values of 0.46 eV (E9) and 0.52 eV (E1). These activation energies are close to those reported in the literature for the traps referred to as E9 and E1, respectively.42  Figure 3(b) represents the L-DLTS spectrum measured at 440 K using Ub = −6 V, Up1 = −3 V, Up2 = −4 V, and tp = 10 ms, which enables the broad E2 peak to be separated into its constituent components—E2a, E2b, and E3—as initially reported by Zimmermann et al.39 

FIG. 3.

L-DLTS spectra recorded at (a) 270 K, illustrating the electron emission rate of traps E1 and E9, as well as at (b) 440 K for traps E2a, E2b, and E3.

FIG. 3.

L-DLTS spectra recorded at (a) 270 K, illustrating the electron emission rate of traps E1 and E9, as well as at (b) 440 K for traps E2a, E2b, and E3.

Close modal

The resulting Arrhenius plots are given in Fig. 4 for each of the six observed traps, with their corresponding properties summarized in Table I. The ΔEem, σapp, and NT values for Es are consistent with those reported by Perrier et al.,26 relating to a sub-surface point defect that originates from polishing-induced scratches. More specifically, Es was observed in their Si-doped β-Ga2O3 sample, which underwent a mechanical polishing process. This agrees with our observation, as Es is only present in the “sub-surface” DLTS scan; the Ta-doped material studied in this work was also subjected to a chemical–mechanical polishing process. In another report, Polyakov et al.52 revealed that a trap with the activation energy for an electron emission of 0.28 eV has been observed following exposure to 18 MeV α-particles, implying a native defect that could have a similar position of an energy level as Es within the bandgap. A more detailed comparison of the characteristics of the Es trap and the irradiation-induced defect detected by Polyakov et al. is yet to be made.

FIG. 4.

Arrhenius plots for the Es, E9, E1, E2a, E2b, and E3 traps detected in the Ta-doped β-Ga2O3 material grown using the optical floating zone method.

FIG. 4.

Arrhenius plots for the Es, E9, E1, E2a, E2b, and E3 traps detected in the Ta-doped β-Ga2O3 material grown using the optical floating zone method.

Close modal
TABLE I.

Activation energies for electron emission, apparent capture cross sections, and average trap concentrations in the sub-surface region probed at depths ∼50–60 nm for all observed deep levels.

EsE9E1E2aE2bE3
ΔEem (eV) 0.28 ± 0.01 0.46 ± 0.02 0.52 ± 0.01 0.69 ± 0.02 0.75 ± 0.02 0.97 ± 0.09 
σapp (cm29.3 × 10−16 3.0 × 10−15 8.5 × 10−15 1.1 × 10−15 1.7 × 10−15 2.0 × 10−13 
NT (cm−32.5 × 1015 2.0 × 1015 3.0 × 1015 2.0 × 1017 2.0 ×1017 3.5 × 1016 
EsE9E1E2aE2bE3
ΔEem (eV) 0.28 ± 0.01 0.46 ± 0.02 0.52 ± 0.01 0.69 ± 0.02 0.75 ± 0.02 0.97 ± 0.09 
σapp (cm29.3 × 10−16 3.0 × 10−15 8.5 × 10−15 1.1 × 10−15 1.7 × 10−15 2.0 × 10−13 
NT (cm−32.5 × 1015 2.0 × 1015 3.0 × 1015 2.0 × 1017 2.0 ×1017 3.5 × 1016 

For the deep level at 0.46 eV relative to the CBM, it is inconclusive as to whether this trap relates to the E9 trap with a similar activation energy of ∼0.4 eV reported in Ref. 42. E9 has been detected in β-Ga2O3 epilayers grown via metal–organic chemical vapor deposition (MOCVD), with evidence suggesting it is an extrinsic point defect that acts as a deep acceptor level.53–55 In our previous work,55 we showed that the concentration of E9 increased with depth from the M–S junction in the UID and Si doped epilayers grown by MOCVD, implying it could originate from the melt-grown EFG material that the epilayers were grown upon. However, this trap is not commonly reported in DLTS studies of bulk β-Ga2O3 materials. Notably, Seyidov et al.56 reported on a trap of 0.41 eV from the CBM in a material grown using the Cz method, which they also concluded is likely to be extrinsic in nature. In addition, Kruszewski et al.57 observe a trap at Ec−0.46 in Cz-grown material, with a trap concentration of ∼2.0 × 1014 cm−3. It is important to note that Perrier et al.26 did not observe the E9 center in Si-doped β-Ga2O3 grown using the OFZ method. This could imply that, in our β-Ga2O3:Ta material, the E9 electronic signature originates from a defect associated with the Ta source powder. Further investigation is required to determine whether the Ec−0.46 eV electron trap detected in our study relates to the E9 defect reported in the literature.

The E1 trap is commonly reported throughout Refs. 38, 47, 55, 56, and 58–63. Notably, Langørgen et al.63 observed that annealing β-Ga2O3 in hydrogen increases the concentration of E1, implying it is linked to a hydrogen-related complex. Subsequent hybrid-functional calculations suggested its properties are consistent with singly hydrogenated divacancies (VGaibHVO1 and VGa1H − VO1).63 This suggestion is supported by Seyidov et al.,56 who observed that E1 was present in their bulk Cz material after it had been subjected to a heat-treatment up to 650 K upon a DLTS scan. To explain this observation, Seyidov et al.56 propose a rearrangement of the doubly hydrogenated divacancy (VGa12H−VO2), which is assigned to the E4 defect, into the more stable VGaibHVO1 complex during their DLTS measurements. Contrastingly, Polyakov et al.60 argued E1 to be a deep donor level, with SiGa1-H or SnGa2-H being likely candidates.

In bulk β-Ga2O3, E2 and E3 are commonly observed DLTS signals, and it is well established that they are related to deep acceptor and deep donor levels, respectively.41 Through a comparison between DLTS measurements and results from secondary ion mass spectrometry (SIMS), Ingebrigtsen et al.37 showed that E2 is associated with FeGa defects. Similarly to our findings, E2 was present in significant concentrations of 1016–1017 cm−3, making Fe a prominent compensating impurity in n-type β-Ga2O3. The ΔEem values for E2a (0.69 eV) and E2b (0.75 eV) obtained using L-DLTS are consistent with the values reported by Zimmerman et al. (E2a = 0.66 eV; E2b = 0.73 eV),39 in addition to the corresponding ΔEem values predicted by theoretical calculations, which yielded E2a = 0.68 eV and E2b = 0.78 eV for Fe atoms at the tetrahedrally and octahedrally coordinated Ga sites, respectively.31 Using a similar analysis, E3 was linked to Ti via a combination of SIMS results with the results of DLTS measurements.39 However, it is important to note that Seyidov et al.56 only observe E3 in Cz grown β-Ga2O3 with Au and Pt Schottky contacts, whereas for Ni-based SBDs, E3 is only present after a thermal load up to 650 K. This observation extends the potential candidates for E3 to VO-related defects, which could induce a DLTS signature overlapping with that of the TiGa point defect. This suggestion by Seyidov et al.56, that an intrinsic defect state is close to the TiGa level, is supported by an observation by Polyakov et al.52, whereby an increase in the E3 concentration following irradiation with α-particles occurred—implying that E3 is sensitive to irradiation. Moreover, theoretical predictions based on DFT reveal that the transition level of VOIII is ∼1.0 eV from the CBM, and it acts as a deep donor.64 Therefore, it is difficult to distinguish the emission signals from TiGa and VOIII in DLTS.

The origin and nature of all these observed deep-level defects are reported extensively in reviews by Langørgen et al.,31 Polyakov et al.,40 and Wang et al.42 

From the DLTS and L-DLTS analysis, no peaks have been observed that can be directly related to TaGa. This observation suggests that tantalum has a donor level that is too shallow (<Ec−0.1 eV) to be detected using DLTS measurements down to ∼40 K. Combining this result with the lack of significant carrier freeze-out down to 20 K and the increase in the free carrier concentration in Ta-doped samples compared to UID material, which is shown in Fig. 1(c), it can be argued that tantalum is an effective shallow donor impurity in β-Ga2O3.

To obtain further information about the defects in the investigated as-grown 0.05 mol. % β-Ga2O3:Ta (100) material, temperature-dependent (TD) PL measurements were conducted, as shown in Fig. 5. The PL measurements were performed under excitation using a 255 nm UV-LED, with a power density of 71 μW/cm2. Figure 5 reveals that the PL signal intensity decreases gradually with increasing temperature but without any significant change in the peak energy. Onuma et al.32 reported similar behavior for Si-doped (100) β-Ga2O3, whereby cathodoluminescence (CL) analysis was applied that demonstrated the growth direction influences the peak position with respect to measurement temperature. This provides a possible explanation for the observed red shift of the peak in the TD PL conducted by Liu et al.15 for Ta-doped (010) material as well as in the temperature-resolved CL performed by Huynh et al.65 on single crystals grown in the (−201) direction. The inset of Fig. 5 presents the normalized TD-PL spectra and shows that while the peak position remains nearly unchanged with temperature, the full width at half maximum (FWHM) broadens significantly, expanding from 0.7 eV at 15 K to 0.9 eV at 300 K.

FIG. 5.

Temperature-dependent PL of as-grown 0.05 mol% β-Ga2O3:Ta (100) crystals, measured from 15 to 300 K. The inset corresponds to the normalized TD-PL spectra with the value of the full width at half maximum (FWHM) changing from 0.7 eV at 15 K to 0.9 eV at 300 K.

FIG. 5.

Temperature-dependent PL of as-grown 0.05 mol% β-Ga2O3:Ta (100) crystals, measured from 15 to 300 K. The inset corresponds to the normalized TD-PL spectra with the value of the full width at half maximum (FWHM) changing from 0.7 eV at 15 K to 0.9 eV at 300 K.

Close modal

Previous work has shown that the PL spectra of β-Ga2O3 are largely composed of four emission bands, which correspond to two ultraviolet bands (UV at around 350 nm and UV’ at around 400 nm), one blue band (BL at around 450 nm), and a green band (GL at around 500 nm).36,66 It has been reported by Shimamura et al.36 that three emission bands are present at 2.5–2.8, 3.1, and 3.6 eV, which correspond to BL, UV, and UV’, respectively. However, there is a discrepancy in the literature on the number of UV bands, either one or two. Liu et al.15 previously analyzed Ta-doped material and proposed two UV bands, which are attributed to recombination involving self-trapped holes (STHs) on the trigonally coordinated oxygen lattice sites, O and O.15,32,66 Whereas Binet and Gourier35 and Huynh et al.65 reveal a single UV band that is also related to loosely bound electrons that form self-trapped excitons. Through deconvolution of the PL spectra measured at 15 K, our β-Ga2O3:Ta (100) material shows two dominant yet broad emission bands at 3.10 and 3.40 eV, as shown in Fig. 6. This suggests that two UV bands are present in our material, which could be related to recombination via STHs. Hybrid functional calculations by Frodason et al.67 reveal that the STHO1++eCBM and STHO2++eCBM transitions have peak positions at 3.11 and 3.04 eV, respectively. These PPs are particularly close to our UV band, and Frodason et al. note that these PPs could even be underestimated. Other experimental work has also categorized UV-related emission in the range of 3.1–3.6 eV,32,33,36,66–72 which is consistent with our observations.

FIG. 6.

Low temperature PL spectra on a semi-log scale, fitted with four Gaussian peaks for the GL, BL/UV, UV′, and UVB emission bands of the as-grown 0.05 mol. % β-Ga2O3:Ta (100) crystals, measured at 15 K.

FIG. 6.

Low temperature PL spectra on a semi-log scale, fitted with four Gaussian peaks for the GL, BL/UV, UV′, and UVB emission bands of the as-grown 0.05 mol. % β-Ga2O3:Ta (100) crystals, measured at 15 K.

Close modal

It could also be argued that the band at 3.10 eV in Fig. 6 is associated with BL, which is reported in the range of 2.5–3.0 eV,15,32,72 as opposed to UV. For instance, Huynh et al.65 observed a peak at 3.05 eV, which they attributed to BL, based on CL measurements. This BL has been linked to the recombination of a trapped electron from a donor level with a trapped hole at an acceptor level, i.e., a donor–acceptor pair (DAP) transition,32 whereby the donor level is related to the doping impurities and the acceptor level is tentatively assigned to VGa2− vacancies at the tetrahedral site,15,36 but some studies suggested that a divacancy (VOVGa) could also be a potential candidate.32,36 Work by Liu et al.15 on Ta-doped β-Ga2O3 identified two UV bands in addition to a BL band at 2.73 eV, which they assigned to a DAP transition involving Ta located at Ec−0.04 eV.

The low temperature PL spectrum in Fig. 6 shows two small shoulder peaks at 2.17 eV (GL) and 4.29 eV (UVB), with Gaussian areas approximately two orders of magnitude lower than those of the dominant UV and UV′ emission bands. The intensity of the green band in β-Ga2O3 crystals depends on the concentration of specific unintentionally incorporated impurities, such as Si, Be, Ge, Sn, Zr, and Li,34,36 and is correlated to the O partial pressure during growth in low purity (4N) undoped crystals.36,73–75 The low relative intensity of the impurity-dependent GL emission band suggests that the OFZ grown β-Ga2O3:Ta material contains low concentrations of the impurities responsible for the GL. Theoretical predictions by Frodason et al.67 propose a wide range of impurities that could induce an emission band near the 2.17 eV peak that we observe, including ZnGa1 (2.15 eV), MgGa2 (2.32 eV), BeGa1 (1.71 eV), CaGa2 (2.40 eV), NO1 (2.28 eV), NO3 (1.87 eV), NO1H (2.25 eV), and NO3H (2.10 eV). In addition, numerous intrinsic-related states have predicted PL PPs close to that of our observed GL band, such as VGaib (1.93 eV), VGaib2H (2.12 eV), VGaib3H (2.54 eV), VGaic2H (1.95 eV), and VGaicSii2H (2.55 eV). Further discussion about these defect states and their luminescent properties is provided in Ref. 67. The other shoulder peak, centered at 4.29 eV and labeled UVB, has a PL intensity about half that of the GL band, and its origin remains unclear. Thapa et al.70 observed peaks at 4.08 and 4.6 eV, which are close to our UVB band, but the authors stated that these PL peaks are still under investigation. We have found no conclusive explanation for the emission mechanisms responsible for this peak, and further investigation is needed to elucidate the nature of the UVB band.

To study the broad PL spectrum in Fig. 6 further, the activation energies of quenching of the feature at 3.10 eV and the UV’ band at 3.40 eV were determined. The GL and UVB peaks were excluded from this analysis due to their relatively low intensities compared to the peaks at 3.10 and 3.40 eV. In the supplementary material, Fig. S2 shows the temperature dependence of the PL spectra on a semi-log scale, highlighting the thermal quenching of the GL and UVB.

To analyze the temperature-dependent PL results, the integrated PL intensity for the two dominant UV-related Gaussian fitting peaks was plotted vs temperature, as shown in Fig. 7, and fitted to the following relationship:15,76 
(3)
where IPLT is the integrated PL intensity, I0PL is the scaling factor, C is the process rate parameter, EA is the activation energy (the defect ionization energy), and kB is Boltzmann’s constant.
FIG. 7.

Integrated PL intensity of the Gaussian fitting for the BL/UV (3.10 eV) and UV′ (3.40 eV) bands, with temperature variation of the as-grown 0.05 mol. % β-Ga2O3:Ta (100) crystals. The solid red lines are fitted according to the Arrhenius formula. Arrhenius plots of the (a) BL/UV band (3.10 eV) with an (R-squared) R2 = 0.989, EA = 20 ± 1 meV; and (b) the UV’ band (3.40 eV) with an R2 = 0.995, EA = 79 ± 4 meV.

FIG. 7.

Integrated PL intensity of the Gaussian fitting for the BL/UV (3.10 eV) and UV′ (3.40 eV) bands, with temperature variation of the as-grown 0.05 mol. % β-Ga2O3:Ta (100) crystals. The solid red lines are fitted according to the Arrhenius formula. Arrhenius plots of the (a) BL/UV band (3.10 eV) with an (R-squared) R2 = 0.989, EA = 20 ± 1 meV; and (b) the UV’ band (3.40 eV) with an R2 = 0.995, EA = 79 ± 4 meV.

Close modal

The activation energy values (EA extracted for the 3.10 eV feature and the UV′ emission band are 20 ± 1 and 79 ± 4 meV, respectively, with corresponding R-squared (R2) values of 0.989 and 0.995. It can be observed that the fitting for both UV-related emission bands closely follows the integrated PL intensity. This observation is consistent with the R2 values, which are both close to 1. For the peak at 3.10 eV, the EA value aligns with previous studies that have calculated activation energy values for donor states in β-Ga2O3 within the range of 0.02–0.03 eV.77 Onuma et al.72 propose a mechanism for the UV band observed in heavily Si-doped β-Ga2O3, involving a DAP transition, where SiGa serves as the donor state in the range Ec−16–36 meV. A similar DAP mechanism has been reported for the BL, involving acceptors such as VGa, VOVGa, MgGa, or NO.15,36,72 For our β-Ga2O3:Ta material, it remains inconclusive as to whether the EA value of 20 meV corresponds to a DAP involving Si,72 Ta,15 or potentially another mechanism altogether. For the UV’ band at 3.40 eV [Fig. 7(b)], the fitting calculation yields an activation energy EA of 79 ± 4 meV, which is comparable to the ∼72 meV value reported by Lukman and Bergman71 for a PL peak at ∼3.5 eV. They proposed a non-radiative mechanism involving STHs and phonons to explain the thermal-quenching of the PL signal. This conclusion was supported by correlating phonon energies determined via Raman scattering analysis with their PL EA values.

We have studied electrically active defects in Ta-doped (100) β-Ga2O3 single crystals grown using the optical floating zone method. From C–V and CT analysis, a relatively uniform carrier concentration in the range (1.0–1.2) × 1018 cm−3 was derived, with no sign of significant carrier freeze out down to 20 K. These findings confirm the theoretical predictions that Ta can be an effective n-type dopant in β-Ga2O3. Both conventional- and L-DLTS were applied to Ni-based SBDs to extract the electronic properties of the six observed DLTS defect signals, referred to as Es, E9, E1, E2a, E2b, and E3. For the Es, E9, and E1 traps, their concentration decreases significantly when probing further away from the sample surface. The concentration of the Fe-related E2 center is of the order of 1017 cm−3 in the bulk, which makes it an important compensating defect in this material. The PL spectra reveal two dominant emission bands centered at 3.10 and 3.40 eV at 15 K, with extracted activation energy values of 20 ± 1 and 79 ± 4 meV, respectively, for temperature-induced PL quenching.

See the supplementary material for Figs. S1 and S2. To obtain the data in the Arrhenius plot (Fig. 4) for the Es trap, a series of conventional-DLTS scans were taken with varying rate windows. The proximity of the Es trap to the surface prevented effective “double” L-DLTS from being applied. These conventional-DLTS spectra are presented in Fig. S1. The temperature-dependence of the PL intensity (Fig. 5) is also presented on a semi-log scale in Fig. S2. This highlights the thermal quenching of the GL (2.17 eV) and UVB (4.29 eV) bands.

The authors in Manchester would like to acknowledge the support by the EPSRC-UK under Contract Nos. EP/T025131/1 and EP/S024441/1. Christopher A. Dawe would also like to acknowledge the support from the EPSRC CDT in compound semiconductor manufacturing. We acknowledge the partial financial support from the UKRI Innovation and Knowledge Center (IKC) REWIRE under Grant No. EP/Z531091. M. Kuball acknowledges the financial support from the Royal Academy of Engineering through the Chair in Emerging Technologies Scheme. We would like to greatly acknowledge the Commonwealth Scholarship Commission (CSC) for funding this research under the Commonwealth Split-Site Ph.D. scholarship (2023–2024) under Grant No. INCN-2023-373 and the SJSGC fellowship by the University Grant Commission, Ministry of Education, Government of India for V. L. Ananthu Vijayan under Grant No. UGCES-22-OB-KER-F-SJSGC-7611.

The authors have no conflicts to disclose.

Christopher Dawe: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead). Lijie Sun: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). V. L. Ananthu Vijayan: Conceptualization (equal); Formal analysis (supporting); Investigation (supporting); Methodology (equal); Resources (equal); Visualization (supporting); Writing – review & editing (supporting). Vladimir Markevich: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (equal). Janet Jacobs: Resources (equal); Supervision (equal). Ian Hawkins: Resources (equal); Supervision (equal). Matthew Halsall: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Methodology (supporting); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (supporting). Anthony Peaker: Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Resources (equal); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (supporting). David Binks: Formal analysis (supporting); Investigation (supporting); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (supporting). Sai Charan Vanjari: Investigation (supporting); Supervision (supporting); Validation (equal); Writing – review & editing (supporting). Sridharan Moorthy Babu: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (supporting). Martin Kuball: Conceptualization (equal); Data curation (supporting); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

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

1.
B. J.
Baliga
, “
Semiconductors for high-voltage, vertical channel field-effect transistors
,”
J. Appl. Phys.
53
(
3
),
1759
1764
(
1982
).
2.
M.
Higashiwaki
,
K.
Sasaki
,
A.
Kuramata
,
T.
Masui
, and
S.
Yamakoshi
, “
Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates
,”
Appl. Phys. Lett.
100
(
1
),
013504
(
2012
).
3.
M.
Higashiwaki
,
K.
Sasaki
,
A.
Kuramata
,
T.
Masui
, and
S.
Yamakoshi
, “
Development of gallium oxide power devices
,”
Physica Status Solidi A
211
(
1
),
21
26
(
2014
).
4.
T.
Oshima
,
T.
Okuno
,
N.
Arai
,
N.
Suzuki
,
S.
Ohira
, and
S.
Fujita
, “
Vertical solar-blind deep-ultraviolet Schottky photodetectors based on β-Ga2O3 substrates
,”
Appl. Phys. Express
1
(
1
),
011202
(
2008
).
5.
C.
Wu
,
F.
Wu
,
H.
Hu
,
S.
Wang
,
A.
Liu
, and
D.
Guo
, “
Review of self-powered solar-blind photodetectors based on Ga2O3
,”
Mater. Today Phys.
28
,
100883
(
2022
).
6.
A. J.
Green
,
J.
Speck
,
G.
Xing
,
P.
Moens
,
F.
Allerstam
,
K.
Gumaelius
,
T.
Neyer
,
A.
Arias-Purdue
,
V.
Mehrotra
,
A.
Kuramata
,
K.
Sasaki
,
S.
Watanabe
,
K.
Koshi
,
J.
Blevins
,
O.
Bierwagen
,
S.
Krishnamoorthy
,
K.
Leedy
,
A. R.
Arehart
,
A. T.
Neal
,
S.
Mou
,
S. A.
Ringel
,
A.
Kumar
,
A.
Sharma
,
K.
Ghosh
,
U.
Singisetti
,
W.
Li
,
K.
Chabak
,
K.
Liddy
,
A.
Islam
,
S.
Rajan
,
S.
Graham
,
S.
Choi
,
Z.
Cheng
, and
M.
Higashiwaki
, “
β-Gallium oxide power electronics
,”
APL Mater.
10
(
2
),
029201
(
2022
).
7.
M.
Higashiwaki
and
G. H.
Jessen
, “
Guest editorial: The dawn of gallium oxide microelectronics
,”
Appl. Phys. Lett.
112
(
6
),
060401
(
2018
).
8.
Y.
He
,
F.
Zhao
,
B.
Huang
,
T.
Zhang
, and
H.
Zhu
, “
A review of β-Ga2O3 power diodes
,”
Materials
17
(
8
),
1870
(
2024
).
9.
E. G.
Víllora
,
K.
Shimamura
,
Y.
Yoshikawa
,
T.
Ujiie
, and
K.
Aoki
, “
Electrical conductivity and carrier concentration control in β-Ga2O3 by Si doping
,”
Appl. Phys. Lett.
92
(
20
),
202120
(
2008
).
10.
E.
Ahmadi
,
O. S.
Koksaldi
,
S. W.
Kaun
,
Y.
Oshima
,
D. B.
Short
,
U. K.
Mishra
, and
J. S.
Speck
, “
Ge doping of β-Ga2O3 films grown by plasma-assisted molecular beam epitaxy
,”
Appl. Phys. Express
10
(
4
),
041102
(
2017
).
11.
K.
Sasaki
,
A.
Kuramata
,
T.
Masui
,
E. G.
Víllora
,
K.
Shimamura
, and
S.
Yamakoshi
, “
Device-quality β-Ga2O3 epitaxial films fabricated by ozone molecular beam epitaxy
,”
Appl. Phys. Express
5
(
3
),
035502
(
2012
).
12.
M.
Baldini
,
M.
Albrecht
,
A.
Fiedler
,
K.
Irmscher
,
D.
Klimm
,
R.
Schewski
, and
G.
Wagner
, “
Semiconducting Sn-doped β-Ga2O3 homoepitaxial layers grown by metal organic vapour-phase epitaxy
,”
J. Mater. Sci.
51
(
7
),
3650
3656
(
2016
).
13.
V. L. A.
Vijayan
,
D.
Dhanabalan
,
K. V.
Akshita
, and
S. M.
Babu
, “
Investigation of Sn incorporation in β-Ga2O3 single crystals and its effect on structural and optical properties
,”
ECS J. Solid State Sci. Technol.
11
(
10
),
104003
(
2022
).
14.
X.
Meng
,
J.
Deng
,
R.
Li
,
Q.
Zhang
,
K.
Tian
,
J.
Xu
,
X.
Yang
,
L.
Meng
,
J.
Du
, and
G.
Wang
, “
Effects of Ta concentration on microstructure, optical and optoelectronic properties of Ga2O3:Ta films
,”
Vacuum
224
,
113142
(
2024
).
15.
H.
Liu
,
N.
Zhang
,
J.
Yin
,
C.
Xia
,
Z. C.
Feng
,
K.
He
,
L.
Wan
, and
H. F.
Mohamed
, “
Characterization of defect levels in β-Ga2O3 single crystals doped with tantalum
,”
CrystEngComm
23
(
15
),
2835
2841
(
2021
).
16.
A. V.
V L
,
S. C.
Vanjari
,
A. K.
Bhat
,
U. U.
Muazzam
,
J. W.
Pomeroy
,
M. D.
Smith
,
S.
Moorthy Babu
, and
M.
Kuball
, “
Low on-resistance and high carrier mobility in β-Ga2O3 single-crystal substrates through tantalum doping
,”
ACS Appl. Electron. Mater.
7
,
400
(
2024
).
17.
X.
Yang
,
S.
Wen
,
D.
Chen
,
X.
Liu
, and
E.
Zhao
, “
First-principles study on the effects of Ta doping and point defects of Hi and VO on the photoelectric properties of β-Ga2O3
,”
Physica Status Solidi B
261
(
3
),
2300461
(
2024
).
18.
D.
Wang
,
X.
Ma
,
H.
Xiao
,
Y.
Le
, and
J.
Ma
, “
Ta-doped epitaxial β-Ga2O3 films deposited on SrTiO3(100) substrates by MOCVD
,”
Mater. Sci. Semicond. Process.
128
,
105749
(
2021
).
19.
H.
Cui
,
H. F.
Mohamed
,
C.
Xia
,
Q.
Sai
,
W.
Zhou
,
H.
Qi
,
J.
Zhao
,
J.
Si
, and
X.
Ji
, “
Tuning electrical conductivity of β-Ga2O3 single crystals by Ta doping
,”
J. Alloys Compd.
788
,
925
928
(
2019
).
20.
Y.
Shang
,
K.
Tang
,
Z.
Chen
,
Z.
Zhang
,
J.
Deng
,
Y.
Hu
,
K.
Gu
,
M.
Cao
,
L.
Wang
, and
J.
Huang
, “
Growth and characterization of Ta-doped Ga2O3 films deposited by magnetron sputtering
,”
Mater. Sci. Semicond. Process.
134
,
106040
(
2021
).
21.
K.
Sasaki
, “
Prospects for β-Ga2O3: Now and into the future
,”
Appl. Phys. Express
17
(
9
),
090101
(
2024
).
22.
K. N.
Heinselman
,
D.
Haven
,
A.
Zakutayev
, and
S. B.
Reese
, “
Projected cost of gallium oxide wafers from edge-defined film-fed crystal growth
,”
Cryst. Growth Des.
22
(
8
),
4854
4863
(
2022
).
23.
Novel Crystal Technology and Shinshu University
, “
Novel crystal technology achieves breakthrough in Ga2O3 crystal growth, paving way for larger, higher-quality wafers
,”
(Published Online)
(
2024
); available at https://www.novelcrystal.co.jp/eng/2023/2340/.
24.
S. B.
Reese
,
T.
Remo
,
J.
Green
, and
A.
Zakutayev
, “
How much will gallium oxide power electronics cost?
,”
Joule
3
(
4
),
903
907
(
2019
).
25.
J.
Zhang
,
B.
Li
,
C.
Xia
,
G.
Pei
,
Q.
Deng
,
Z.
Yang
,
W.
Xu
,
H.
Shi
,
F.
Wu
,
Y.
Wu
, and
J.
Xu
, “
Growth and spectral characterization of β-Ga2O3 single crystals
,”
J. Phys. Chem. Solids
67
(
12
),
2448
2451
(
2006
).
26.
C.
Perrier
,
A.
Traoré
,
T.
Ito
,
H.
Umezawa
,
E.
Gheeraert
, and
P.
Ferrandis
, “
Surface defects related to polishing cycle in ß-Ga2O3 crystals grown by floating zone
,”
Appl. Phys. Lett.
122
(
22
),
222105
(
2023
).
27.
D. V.
Lang
, “
Deep-level transient spectroscopy: A new method to characterize traps in semiconductors
,”
J. Appl. Phys.
45
(
7
),
3023
3032
(
1974
).
28.
L.
Dobaczewski
,
A. R.
Peaker
, and
K.
Bonde Nielsen
, “
Laplace-transform deep-level spectroscopy: The technique and its applications to the study of point defects in semiconductors
,”
J. Appl. Phys.
96
(
9
),
4689
4728
(
2004
).
29.
A. R.
Peaker
,
V. P.
Markevich
,
I. D.
Hawkins
,
B.
Hamilton
,
K.
Bonde Nielsen
, and
K.
Gościński
, “
Laplace deep level transient spectroscopy: Embodiment and evolution
,”
Physica B
407
(
15
),
3026
3030
(
2012
).
30.
A. R.
Peaker
,
V. P.
Markevich
, and
J.
Coutinho
, “
Tutorial: Junction spectroscopy techniques and deep-level defects in semiconductors
,”
J. Appl. Phys.
123
(
16
),
161559
(
2018
).
31.
A.
Langørgen
,
L.
Vines
, and
Y.
Kalmann Frodason
, “
Perspective on electrically active defects in â-Ga2O3 from deep-level transient spectroscopy and first-principles calculations
,”
J. Appl. Phys.
135
(
19
),
195702
(
2024
).
32.
T.
Onuma
,
S.
Fujioka
,
T.
Yamaguchi
,
M.
Higashiwaki
,
K.
Sasaki
,
T.
Masui
, and
T.
Honda
, “
Correlation between blue luminescence intensity and resistivity in β-Ga2O3 single crystals
,”
Appl. Phys. Lett.
103
(
4
),
041910
(
2013
).
33.
T.
Harwig
,
F.
Kellendonk
, and
S.
Slappendel
, “
The ultraviolet luminescence of β-galliumsesquioxide
,”
J. Phys. Chem. Solids
39
(
6
),
675
680
(
1978
).
34.
T.
Harwig
and
F.
Kellendonk
, “
Some observations on the photoluminescence of doped β-galliumsesquioxide
,”
J. Solid State Chem.
24
(
3–4
),
255
263
(
1978
).
35.
L.
Binet
and
D.
Gourier
, “
Origin of the blue luminescence of β-Ga2O3
,”
J. Phys. Chem. Solids
59
(
8
),
1241
1249
(
1998
).
36.
K.
Shimamura
,
E. G.
Víllora
,
T.
Ujiie
, and
K.
Aoki
, “
Excitation and photoluminescence of pure and Si-doped β-Ga2O3 single crystals
,”
Appl. Phys. Lett.
92
(
20
),
201914
(
2008
).
37.
M. E.
Ingebrigtsen
,
J. B.
Varley
,
A. Yu.
Kuznetsov
,
B. G.
Svensson
,
G.
Alfieri
,
A.
Mihaila
,
U.
Badstübner
, and
L.
Vines
, “
Iron and intrinsic deep level states in Ga2O3
,”
Appl. Phys. Lett.
112
(
4
),
042104
(
2018
).
38.
M. E.
Ingebrigtsen
,
A. Yu.
Kuznetsov
,
B. G.
Svensson
,
G.
Alfieri
,
A.
Mihaila
,
U.
Badstübner
,
A.
Perron
,
L.
Vines
, and
J. B.
Varley
, “
Impact of proton irradiation on conductivity and deep level defects in β-Ga2O3
,”
APL Mater.
7
(
2
),
022510
(
2019
).
39.
C.
Zimmermann
,
Y. K.
Frodason
,
A. W.
Barnard
,
J. B.
Varley
,
K.
Irmscher
,
Z.
Galazka
,
A.
Karjalainen
,
W. E.
Meyer
,
F. D.
Auret
, and
L.
Vines
, “
Ti- and Fe-related charge transition levels in β−Ga2O3
,”
Appl. Phys. Lett.
116
(
7
),
072101
(
2020
).
40.
A. Y.
Polyakov
,
V. I.
Nikolaev
,
E. B.
Yakimov
,
F.
Ren
,
S. J.
Pearton
, and
J.
Kim
, “
Deep level defect states in β-α-and ɛ-Ga2O3 crystals and films: Impact on device performance
,”
J. Vacuum Sci. Technol. A
40
(
2
),
020804
(
2022
).
41.
A. Y.
Polyakov
,
I.-H.
Lee
,
N. B.
Smirnov
,
I. V.
Shchemerov
,
A. A.
Vasilev
,
A. V.
Chernykh
, and
S. J.
Pearton
, “
Electric field dependence of major electron trap emission in bulk β-Ga2O3: Poole–Frenkel effect versus phonon-assisted tunneling
,”
J. Phys. D: Appl. Phys.
53
(
30
),
304001
(
2020
).
42.
Z.
Wang
,
X.
Chen
,
F.-F.
Ren
,
S.
Gu
, and
J.
Ye
, “
Deep-level defects in gallium oxide
,”
J. Phys. D: Appl. Phys.
54
(
4
),
043002
(
2021
).
43.
A.
Fiedler
,
R.
Schewski
,
Z.
Galazka
, and
K.
Irmscher
, “
Static dielectric constant of β-Ga2O3 perpendicular to the principal planes (100), (010), and (001)
,”
ECS J. Solid State Sci. Technol.
8
(
7
),
Q3083
Q3085
(
2019
).
44.
A. T.
Neal
,
S.
Mou
,
R.
Lopez
,
J. V.
Li
,
D. B.
Thomson
,
K. D.
Chabak
, and
G. H.
Jessen
, “
Incomplete ionization of a 110 meV unintentional donor in β-Ga2O3 and its effect on power devices
,”
Sci. Rep.
7
(
1
),
13218
(
2017
).
45.
N. T.
Son
,
K.
Goto
,
K.
Nomura
,
Q. T.
Thieu
,
R.
Togashi
,
H.
Murakami
,
Y.
Kumagai
,
A.
Kuramata
,
M.
Higashiwaki
,
A.
Koukitu
,
S.
Yamakoshi
,
B.
Monemar
, and
E.
Janzén
, “
Electronic properties of the residual donor in unintentionally doped β-Ga2O3
,”
J. Appl. Phys.
120
(
23
),
235703
(
2016
).
46.
J. V.
Li
,
J.
Hendricks
,
A.
Charnas
,
B. A.
Noesges
,
A. T.
Neal
,
T. J.
Asel
,
Y.
Kim
, and
S.
Mou
, “
Admittance spectroscopy study of defects in β-Ga2O3
,”
Thin Solid Films
789
,
140196
(
2024
).
47.
K.
Irmscher
,
Z.
Galazka
,
M.
Pietsch
,
R.
Uecker
, and
R.
Fornari
, “
Electrical properties of β-Ga2O3 single crystals grown by the Czochralski method
,”
J. Appl. Phys.
110
(
6
),
063720
(
2011
).
48.
Q.
Sai
,
H.
Cui
,
C.
Xia
,
H.
Qi
,
M.
Pan
,
A. M.
Ahmed
, and
H. F.
Mohamed
, “
Conduction mechanism and shallow donor defects in Nb-doped β-Ga2O3 single crystals
,”
AIP Adv.
14
(
4
),
045244
(
2024
).
49.
C.
Janowitz
,
V.
Scherer
,
M.
Mohamed
,
A.
Krapf
,
H.
Dwelk
,
R.
Manzke
,
Z.
Galazka
,
R.
Uecker
,
K.
Irmscher
,
R.
Fornari
,
M.
Michling
,
D.
Schmeißer
,
J. R.
Weber
,
J. B.
Varley
, and
C. G. V. D.
Walle
, “
Experimental electronic structure of In2O3and Ga2O3
,”
New J. Phys.
13
(
8
),
085014
(
2011
).
50.
M.
Mohamed
,
C.
Janowitz
,
I.
Unger
,
R.
Manzke
,
Z.
Galazka
,
R.
Uecker
,
R.
Fornari
,
J. R.
Weber
,
J. B.
Varley
, and
C. G.
Van De Walle
, “
The electronic structure of β-Ga2O3
,”
Appl. Phys. Lett.
97
(
21
),
211903
(
2010
).
51.
H.
Lefèvre
and
M.
Schulz
, “
Double correlation technique (DDLTS) for the analysis of deep level profiles in semiconductors
,”
Appl. Phys.
12
(
1
),
45
53
(
1977
).
52.
A. Y.
Polyakov
,
N. B.
Smirnov
,
I. V.
Shchemerov
,
E. B.
Yakimov
,
S. J.
Pearton
,
C.
Fares
,
J.
Yang
,
F.
Ren
,
J.
Kim
,
P. B.
Lagov
,
V. S.
Stolbunov
, and
A.
Kochkova
, “
Defects responsible for charge carrier removal and correlation with deep level introduction in irradiated β-Ga2O3
,”
Appl. Phys. Lett.
113
(
9
),
092102
(
2018
).
53.
H.
Ghadi
,
J. F.
McGlone
,
C. M.
Jackson
,
E.
Farzana
,
Z.
Feng
,
A. F. M. A. U.
Bhuiyan
,
H.
Zhao
,
A. R.
Arehart
, and
S. A.
Ringel
, “
Full bandgap defect state characterization of β-Ga2O3 grown by metal organic chemical vapor deposition
,”
APL Mater.
8
(
2
),
021111
(
2020
).
54.
J. F.
McGlone
,
H.
Ghadi
,
E.
Cornuelle
,
A.
Armstrong
,
G.
Burns
,
Z.
Feng
,
A. F. M. A.
Uddin Bhuiyan
,
H.
Zhao
,
A. R.
Arehart
, and
S. A.
Ringel
, “
Proton radiation effects on electronic defect states in MOCVD-grown (010) β-Ga2O3
,”
J. Appl. Phys.
133
(
4
),
045702
(
2023
).
55.
C. A.
Dawe
,
V. P.
Markevich
,
M. P.
Halsall
,
I. D.
Hawkins
,
A. R.
Peaker
,
A.
Nandi
,
I.
Sanyal
, and
M.
Kuball
, “
Deep level traps in (010) β-Ga2O3 epilayers grown by metal organic chemical vapor deposition on Sn-doped β-Ga2O3 substrates
,”
J. Appl. Phys.
136
(
4
),
045705
(
2024
).
56.
P.
Seyidov
,
J. B.
Varley
,
Y. K.
Frodason
,
D.
Klimm
,
L.
Vines
,
Z.
Galazka
,
T.
Chou
,
A.
Popp
,
K.
Irmscher
, and
A.
Fiedler
, “
Thermal stability of Schottky contacts and rearrangement of defects in β-Ga2O3 crystals
,”
Adv. Electron. Mater.
11
,
2300428
(
2023
).
57.
P.
Kruszewski
,
A.
Fiedler
, and
Z.
Galazka
, “
The electric field influence on EC-0.18 eV electron trap level in (100)-oriented β-Ga2O3 crystals grown by the Czochralski method
,”
Appl. Phys. Lett.
126
(
6
),
062110
(
2025
).
58.
Z.
Zhang
,
E.
Farzana
,
A. R.
Arehart
, and
S. A.
Ringel
, “
Deep level defects throughout the bandgap of (010) β-Ga2O3 detected by optically and thermally stimulated defect spectroscopy
,”
Appl. Phys. Lett.
108
(
5
),
052105
(
2016
).
59.
E.
Farzana
,
A.
Mauze
,
J. B.
Varley
,
T. E.
Blue
,
J. S.
Speck
,
A. R.
Arehart
, and
S. A.
Ringel
, “
Influence of neutron irradiation on deep levels in Ge-doped (010) β-Ga2O3 layers grown by plasma-assisted molecular beam epitaxy
,”
APL Mater.
7
(
12
),
121102
(
2019
).
60.
A. Y.
Polyakov
,
A. I.
Kochkova
,
A.
Langørgen
,
L.
Vines
,
A.
Vasilev
,
I. V.
Shchemerov
,
A. A.
Romanov
, and
S. J.
Pearton
, “
On the possible nature of deep centers in Ga2O3
,”
J. Vacuum Sci. Technol. A
41
(
2
),
023401
(
2023
).
61.
M.
Labed
,
N.
Sengouga
,
C.
Venkata Prasad
,
M.
Henini
, and
Y. S.
Rim
, “
On the nature of majority and minority traps in β-Ga2O3: A review
,”
Mater. Today Phys.
36
,
101155
(
2023
).
62.
M. E.
Ingebrigtsen
,
A. Yu.
Kuznetsov
,
B. G.
Svensson
,
G.
Alfieri
,
A.
Mihaila
, and
L.
Vines
, “
Generation and metastability of deep level states in β-Ga2O3 exposed to reverse bias at elevated temperatures
,”
J. Appl. Phys.
125
(
18
),
185706
(
2019
).
63.
A.
Langørgen
,
C.
Zimmermann
,
Y.
Kalmann Frodason
,
E.
Førdestrøm Verhoeven
,
P.
Michael Weiser
,
R.
Michael Karsthof
,
J.
Basile Varley
, and
L.
Vines
, “
Influence of heat treatments in H2 and Ar on the E1 center in β-Ga2O3
,”
J. Appl. Phys.
131
(
11
),
115702
(
2022
).
64.
L.
Dong
,
R.
Jia
,
B.
Xin
,
B.
Peng
, and
Y.
Zhang
, “
Effects of oxygen vacancies on the structural and optical properties of β-Ga2O3
,”
Sci. Rep.
7
(
1
),
40160
(
2017
).
65.
T. T.
Huynh
,
L. L. C.
Lem
,
A.
Kuramata
,
M. R.
Phillips
, and
C.
Ton-That
, “
Kinetics of charge carrier recombination in β-Ga2O3 crystals
,”
Phys. Rev. Mater.
2
(
10
),
105203
(
2018
).
66.
Y.
Wang
,
P. T.
Dickens
,
J. B.
Varley
,
X.
Ni
,
E.
Lotubai
,
S.
Sprawls
,
F.
Liu
,
V.
Lordi
,
S.
Krishnamoorthy
,
S.
Blair
,
K. G.
Lynn
,
M.
Scarpulla
, and
B.
Sensale-Rodriguez
, “
Incident wavelength and polarization dependence of spectral shifts in β-Ga2O3 UV photoluminescence
,”
Sci. Rep.
8
(
1
),
18075
(
2018
).
67.
Y. K.
Frodason
,
K. M.
Johansen
,
L.
Vines
, and
J. B.
Varley
, “
Self-trapped hole and impurity-related broad luminescence in β-Ga2O3
,”
J. Appl. Phys.
127
(
7
),
075701
(
2020
).
68.
L. T.
Penman
,
Z. M.
Johnston
,
P. R.
Edwards
,
Y.
Oshima
,
C.
McAleese
,
P.
Mazzolini
,
M.
Bosi
,
L.
Seravalli
,
R.
Fornari
,
R. W.
Martin
, and
F. C. -P.
Massabuau
, “
Comparative study of the optical properties of α-, β-, and κ-Ga2O3
,”
Physica Status Solidi B
2025
,
2400615
.
69.
Z.
Wang
,
F.
Tang
,
F.
Ren
,
H.
Liang
,
X.
Cui
,
S.
Xu
,
S.
Gu
,
R.
Zhang
,
Y.
Zheng
, and
J.
Ye
, “
Unraveling abnormal thermal quenching of sub-gap emission in β-Ga2O3
,”
Adv. Electron. Mater.
11
(
1
),
2400315
(
2025
).
70.
D.
Thapa
,
J.
Lapp
,
I.
Lukman
, and
L.
Bergman
, “
Ultra-wide bandgap β-Ga2O3 films: Optical, phonon, and temperature response properties
,”
AIP Adv.
11
(
12
),
125022
(
2021
).
71.
I.
Lukman
and
L.
Bergman
, “
The Nonradiative properties of self-trapped holes in ultra-wide bandgap gallium oxide film
,”
Physica Status Solidi B
261
(
8
),
2300590
(
2024
).
72.
T.
Onuma
,
Y.
Nakata
,
K.
Sasaki
,
T.
Masui
,
T.
Yamaguchi
,
T.
Honda
,
A.
Kuramata
,
S.
Yamakoshi
, and
M.
Higashiwaki
, “
Modeling and interpretation of UV and blue luminescence intensity in β-Ga2O3 by silicon and nitrogen doping
,”
J. Appl. Phys.
124
(
7
),
075103
(
2018
).
73.
E. G.
Víllora
,
M.
Yamaga
,
T.
Inoue
,
S.
Yabasi
,
Y.
Masui
,
T.
Sugawara
, and
T.
Fukuda
, “
Optical spectroscopy study on β-Ga2O3
,”
Jpn. J. Appl. Phys.
41
,
L622
L625
(
2002
).
74.
G.
Blasse
and
A.
Bril
, “
Some observations on the luminescence of β-Ga2O3
,”
J. Phys. Chem. Solids
31
(
4
),
707
711
(
1970
).
75.
E. G.
Villora
,
T.
Atou
,
T.
Sekiguchi
,
T.
Sugawara
,
M.
Kikuchi
, and
T.
Fukuda
, “
Cathodoluminescence of undoped β-Ga2O3 single crystals
,”
Solid State Commun.
120
(
11
),
455
458
(
2001
).
76.
J. I.
Pankove
,
Optical Processes in Semiconductors
(
Dover
,
New York
,
1971
).
77.
M. R.
Lorenz
,
J. F.
Woods
, and
R. J.
Gambino
, “
Some electrical properties of the semiconductor β-Ga2O3
,”
J. Phys. Chem. Solids
28
(
3
),
403
404
(
1967
).