Performing deep level transient spectroscopy (DLTS) on Schottky diodes, we investigated defect levels below the conduction band minima (Ec) in Czochralski-grown unintentionally doped (UID) and vertical gradient freeze-grown Zr-doped β-Ga2O3 crystals. In UID crystals with an electron concentration of 1017 cm−3, we observe levels at 0.18 eV and 0.46 eV in addition to the previously reported 0.86 (E2) and 1.03 eV (E3) levels. For 1018 cm−3 Zr-doped Ga2O3, signatures at 0.30 eV (E15) and 0.71 eV (E16) are present. For the highest Zr doping of 5 × 1018 cm−3, we observe only one signature at 0.59 eV. Electric field-enhanced emission rates are demonstrated via increasing the reverse bias during measurement. The 0.86 eV signature in the UID sample displays phonon-assisted tunneling enhanced thermal emission and is consistent with the widely reported E2 (FeGa) defect. The 0.71 eV (E16) signature in the lower-Zr-doped crystal also exhibits phonon-assisted tunneling emission enhancement. Taking into account that the high doping in the Zr-doped diodes also increases the electric field, we propose that the 0.59 eV signature in the highest Zr-doped sample likely corresponds to the 0.71 eV signature in lower-doped samples. Our analysis highlights the importance of testing for and reporting on field-enhanced emission, especially the electric field present during DLTS and other characterization experiments on β-Ga2O3 along with the standard emission energy, cross section, and lambda-corrected trap density. This is important because of the intended use of β-Ga2O3 in high-field devices and the many orders of magnitude of possible doping.

Ultra-wide bandgap β-Ga2O3 is promising in applications such as power electronic devices, solar-blind UV photodetectors, solar cells, and sensors due to its n-type dopability from 1015 to 1020 cm−3 and bandgap of 4.5 to 4.8 eV depending on the optical axis and measurement methods.1,2 Melt growth techniques, such as edge-defined film-fed growth3 (EFG), the Czochralski method4 (CZ), and floating-zone5 (FZ), have been successfully used for large-size single crystals. Conductive β-Ga2O3 substrates, essential components for high breakdown voltage vertical devices, are achieved by Si6 and Sn4,7 doping with a carrier concentration exceeding 1018 cm−3. Elements like Zr,8 Hf,9 Nb,10 and Ta11 have also been demonstrated as shallow, high concentration dopants in Ga2O3 crystals. The Zr-doped Ga2O3 crystals grown by the Verneuil technique exhibit high conductivity with blue color.12 Recently, larger size Zr-doped β-Ga2O3 crystals have been grown by the vertical gradient freeze (VGF) technique8 with a free carrier concentration above 1018 cm−3. A higher shallow dopant concentration results in a higher free carrier concentration but lowers the mobility due to impurity scattering.13 Free carrier absorption is observed, especially for heavily doped Ga2O3, and the plasma frequency shifts to shorter wavelengths with a higher free carrier concentration.14 

Deep defect states also play a critical role in electrical and optical properties, not only in terms of the familiar lowering of minority carrier lifetimes via non-radiative recombination but also in terms of creating semi-insulating material. For example, in β-Ga2O3:Fe semi-insulating crystals, the Fermi energy is pinned at the Fe3+/Fe2+ charge transition level approximately Ec-0.78 eV [the E2 level from deep level transient spectroscopy (DLTS)],15 resulting in vanishingly small carrier densities. Acceptors of Mg can also compensate intentional or unintentional shallow donors, reducing net doping and mobility.4,16 In terms of native defects, the relaxed Ga vacancy, sometimes described as a (2VGa + Gai) complex or split vacancy, is a compensating acceptor and has been observed directly in electron microscopy in heavily Sn-doped EFG β-Ga2O3 crystals.17 MOVPE-grown homoepitaxial β-Ga2O3 thin films are still resistive even when they are doped to 1022 cm−3 of Si in O-rich conditions, indicating the abundance of the compensating defects, in which the activation energy of 0.50–0.65 eV has been characterized by thermally stimulated luminescence (TSL).18 While nominally, effective mass donors are interchangeable in terms of adding net shallow doping, each particular extrinsic impurity can form a unique variety of complexes with all defects present and thus each different dopant, in principle, can result in a different ensemble of defect states in the bandgap. Thus, it is important to characterize the defect ensembles present for different shallow dopants across available ranges of doping, as this investigation begins to do for Zr.

Deep level transient spectroscopy (DLTS) uses thermal emission from traps to probe defects within approximately 1.0 eV from the band edges and is sensitive to defect concentrations as small as ∼10−4 times the net shallow doping in typical circumstances. For defects with Coulomb or similar potentials for thermal emission, the presence of a strong electric field (F) within the depletion region lowers the apparent emission barrier via the Poole–Frenkel effect.19,20 Phonon-assisted tunneling21,22 emission can also increase the emission rate in high fields. Both effects typically manifest by enhancing the thermal emission rate, which can be described as a lowering of the apparent thermal emission activation energy with the increasing field. The emission rate for an electron occupying a trap at energy Et is given by

where vth is the thermal velocity, σn is the capture cross section, Nc–n is the density of unoccupied states in the conduction band (=Nc in a depletion width), E = Ec − Et, and ΔE=constFγ. For the Poole–Frenkel effect, γ = ½, while for phonon-assisted tunneling, γ = 2. The apparent energy Eapp measured in a DLTS experiment would be Eapp=ECEtconstFγ and by linearly extrapolating a plot of ln en vs Fγ to F = 0 at a specific temperature, one could determine the field-free value of Ec–Et.

DLTS has been primarily measured on unintentionally doped (UID) bulk crystals and rather lightly doped epitaxial β-Ga2O3 layers for which the effects of the electric field on the emission rate are similar and relatively small, and thus results can be compared with limited discrepancies. For example, several deep electron trap signatures have been reported in β-Ga2O3, e.g., Ec-0.21 eV (Ref. 23) (E10), Ec-0.33 eV (Ref. 23) (E11, a native defect), EC-0.40 eV (Ref. 24) (E9), EC-0.6 eV (E1), EC-0.75 eV (E2*, a native defect),15EC-0.78 eV (E2, FeGa),15EC-0.95 eV (E3, TiGa),25EC-1.04 eV (E3), and EC-1.2 eV (E4).15,24–29 Amongst these reported defects, the E3 state is donor-like and its apparent emission energy shifts with the electric field according to the Poole–Frenkel effect.30,31 The E2 state exhibits phonon-assisted tunneling emission enhancement.31 

In this work, we investigate deep states in heavily Zr-doped Ga2O3 using DLTS and demonstrate the electric field-dependent emission rates. In these heavily doped samples, the diffusion potential and applied bias are sufficient to induce field-induced emission enhancement. In addition to displaying smaller apparent activation energies compared to those from UID samples, the Zr-doped Ga2O3 crystals show broadening of some DLTS trap signatures. We interpret this broadening to the emission of one trap type in the steep spatial field gradient, which causes a distribution of emission rates for defects at different depths, as opposed to a real distribution of trap energies which might be the case, e.g., for interface defects. By variation of the measuring bias in DLTS and modeling of the wide emission feature using the emission rate equation, we find that the 0.86 eV (E2) in the UID sample and the 0.71 eV (E16) and 0.59 eV (E16) signatures in Zr-doped samples exhibit phonon-assisted tunneling effects.

Unintentionally doped (UID) and Zr-doped β-Ga2O3 were grown by the Czochralski (CZ) and vertical gradient freeze (VGF) techniques, respectively.8,9 Heavily doped crystals tend to grow as spirals in CZ, and thus VGF was used for the Zr-doped crystals. Three types of samples were investigated, namely, UID, #1 Zr (∼l × 1018 cm−3), and #2 Zr (∼5 × 1018 cm−3) where the UID crystal was utilized as a control sample. Before the contact deposition, the samples were cleaned with acetone, isopropyl alcohol, and de-ionized water. Ni/Au Schottky contacts and Ti/Au Ohmic contacts were deposited on cleaved (100) planes. As seen in Fig. 1(d), lateral and vertical geometries were used for Zr-doped and UID samples, respectively. JV and CV measurements were performed using a Keithley 4200A parameter analyzer. DLTS was performed using a Sula DLTS spectrometer from 80 K to 430 K (temperature recorded on the sample surface) in the dark with a 100 mV, 1 MHz AC signal. Except for the experiments used for investigating field-dependent emission rates, the fill voltage was 0 V and the measure voltage was −2 V for Zr-doped samples and 0 and −1 V, respectively, for the UID one.

FIG. 1.

(a) J–V at 310 K, (b) ωCp/Gp from CV characteristics for UID and Zr-doped β-Ga2O3 Schottky diodes at 390 K, (c) carrier density vs depletion width from zero to −5.0 V at 310 K, and (d) Vbi derived from A2/C2 vs voltage from −2 V to 0 V at 310 K and the schematics of Schottky diodes are included.

FIG. 1.

(a) J–V at 310 K, (b) ωCp/Gp from CV characteristics for UID and Zr-doped β-Ga2O3 Schottky diodes at 390 K, (c) carrier density vs depletion width from zero to −5.0 V at 310 K, and (d) Vbi derived from A2/C2 vs voltage from −2 V to 0 V at 310 K and the schematics of Schottky diodes are included.

Close modal

We first tested the general characteristic of the Schottky junctions before DLTS measurements. Figure 1(a) shows the JV curves of UID, #1, and #2 Zr-doped Ga2O3 Schottky diodes. UID and #1 samples show leakage current less than 10−7 A/cm2 from 0 V to −5.0 V. A notable leakage current is observed under reverse bias in the higher-doped Zr sample #2, which is likely caused by tunneling and image force lowering over the Schottky barrier. The ideality factor n is defined as n=qkBTddVln(J) using the thermionic emission (TE) model and was determined over a forward voltage (Vf) range from 0.50 to 0.80 V (VfkBT/q), where q is the electron charge, kB is the Boltzmann constant, T is the temperature, J is the current density, and V is the applied voltage. The ideality factors for the representative UID, #1, and #2 Zr-doped Ga2O3 Schottky diodes are 1.11, 1.09, and 1.37, respectively. The increased ideality factor in the #2 Zr sample indicates some mixed thermionic and field emission instead of a pure TE model. The ωCp/Gp values derived from CV measurements for all samples are much greater than 5 for all biases including near −5 V near 390 K [Fig. 1(b)], indicating the reliability of the capacitance measurements including DLTS.32 Their leakage current values are also within the tolerable current range (150 μA) of the Sula system for performing the DLTS measurement. Profiles of the doping concentration as a function of the depletion width calculated from CV data are shown in Fig. 1(c). The net doping concentrations for UID, #1, and #2 Zr-doped Ga2O3 are 1.8 × 1017 cm−3, 1.5 × 1018 cm−3, and 5.0 × 1018 cm−3, respectively. In Fig. 1(d), the built-in voltages (Vbi) derived from Mott–Schottky analysis of 1/C2 vs voltage curves for the UID, #1 Zr, and #2 Zr samples are 1.38, 1.58, and 1.23 V, respectively. Ideally, the Vbi should increase at 60 mV per decade of net doping; our results indicate that some non-ideal factors help to determine the Vbi.

The activation energy, electron capture cross section, and number density of deep defects can be extracted from conventional DLTS measurements on these n-type Schottky diodes. The voltage is pulsed to a less-negative or 0 bias during the filling pulse and held at a reverse bias during the measurement of emission. At steady state near equilibrium, the thermal emission rate from an electron trap is en=g0g1σnvnthNCexpEappkBT derived from the principle of detailed balance,33 in which σn is the electron capture cross section, vnth is the thermal velocity, NC is the conduction band effective density of states, and g0g1 is the ratio of electronic degeneracies of empty and occupied deep states, which is taken as 1.0 by convention to obtain an apparent cross section. For a concentration of traps small compared to the net doping and uniform doping and defects vs depth, the trap concentration is determined using NT=2NdΔC/Crb{Wr2/((Wrλ)2(W0λ)2))}, where Crb is the limiting capacitance under reverse bias, ΔC is the magnitude of the emission capacitance transient, and the term in curly brackets is the so-called lambda correction in which Wr and W0 are the depletion widths at the pulse and reverse biases, respectively, and λ=2ε0εrq2Nd(EFET) for a trap with energy ET.34 

Representative DLTS spectra of UID, #1, and #2 Zr-doped β-Ga2O3 are shown in Fig. 2(a). The labeling of defect signatures up to 10 (13 including another 323) follows the designations from Ref. 35 and we add E14–16 here in this work. The UID sample shows four majority defects located at 0.18 eV (E14), 0.46 eV (E12), 0.86 eV (E2), and 1.03 eV (E3) below EC, respectively. Their corresponding cross sections σn are 7.7 × 10−16, 1.1 × 10−14, 1.1 × 10−13, and 8.6 × 10−13 cm2. For the sample Zr-doped to 1018 cm−3, a signature E15 at 0.30 eV (σ = 2.8 × 10−17 cm2) is observed coexisting with a dominant 0.71 eV (E16) signature (σ = 2.6 × 10−15 cm2). When the concentration of Zr is increased to 5 × 1018 cm−3, only one defect at 0.59 eV (E16) (σ = 7.5 × 10−15 cm2) is observed. The signature of Ec-0.86 eV from UID has the highest concentration of 4.1 × 1016 cm−3 (Table I), which is at the same order magnitude of the reported highest defect density from E2 and E3 defects in other UID crystals by CZ and EFG methods.26,27 Note that the broad DLTS signal in Zr-doped samples is broader than what would be predicted from a single ET value using the emission rate equation and rate window analysis.36 An additional feature in the data is that broad positive ΔC signals (as opposed to the negative signals for the traps discussed so far) are observed from the Zr-doped samples above 340 K and are more pronounced for the sample with a higher Zr concentration. A change in polarity of the DLTS transient conventional DLTS could arise from a majority capture transient or possibly from minority emission36 in the bulk layer as well as from artifacts such as high series resistance (high Rs is not our case).37 We are dubious of the possibility of minority carrier emission transients since these are Schottky not p–n junctions and no above gap light was present. The origins of these signals are the subject of further investigations; however, the broad and asymmetric DLTS signals vs temperature are consistent with a surface defect origin.34 This is further supported by the DLTS signals pulsing from −6 V to −4 V, which probes a deeper depth from the surface (>50 nm) in #1 Zr sample in Fig. 2(c) for which the positive transient becomes smaller. Since the depletion depths for #1 and #2 Zr-doped samples at −2 V are 30 nm and 15 nm, respectively, the occupation could change under filling bias if localized charges exist near the surface due to possibly un-optimized surface preparation.

FIG. 2.

(a) Representative DLTS spectra of devices from UID, #1, and #2 Zr-doped β-Ga2O3 crystals. DLTS spectra measured with different noted reverse biases pulsed to 0 V for (b) UID and (c) #1 Zr-doped crystals (except −6 to −4 V as noted). Other peaks behaved similarly in the Zr-doped samples but are not shown here. (d) Electric field as a function of depth electron occupation changes for different samples and under the applied reverse biases. The colorful points at left and right for each defect represent electric fields at positions of the (W0 − λ) and (Wrλ), respectively, at t = 0 under reverse bias. (e) The maximal emission rate vs calculated local maximum electric field for E2 in UID, and (f) 0.71 eV in #1 Zr-doped sample and 0.59 eV in #2 Zr-doped sample. For Zr-doped samples, positive transient is subtracted for simulating.

FIG. 2.

(a) Representative DLTS spectra of devices from UID, #1, and #2 Zr-doped β-Ga2O3 crystals. DLTS spectra measured with different noted reverse biases pulsed to 0 V for (b) UID and (c) #1 Zr-doped crystals (except −6 to −4 V as noted). Other peaks behaved similarly in the Zr-doped samples but are not shown here. (d) Electric field as a function of depth electron occupation changes for different samples and under the applied reverse biases. The colorful points at left and right for each defect represent electric fields at positions of the (W0 − λ) and (Wrλ), respectively, at t = 0 under reverse bias. (e) The maximal emission rate vs calculated local maximum electric field for E2 in UID, and (f) 0.71 eV in #1 Zr-doped sample and 0.59 eV in #2 Zr-doped sample. For Zr-doped samples, positive transient is subtracted for simulating.

Close modal
TABLE I.

Summary of defect levels below EC, its behaviors under varying electric fields and comparisons with reported defects. We have introduced the E14–E16 signatures herein as new because they do not correspond to previously reported DLTS signatures.

SamplesET (eV)σ (cm2)NT (cm−3)NotationNotes
UID 0.18 7.7 × 10−16 2.2 × 1015 E14 Shift and split under higher F 
0.46 1.1 × 10−14 5.0 × 1015 E12 Asymmetrically broadened toward lower temperatures under higher F 
0.86 1.1 × 10−13 4.1 × 1016 E2 Phonon-assisted tunneling 
1.03 8.6 × 10−13 1.5 × 1016 E3  
#1 Zr low 0.30 2.8 × 10−17 1.2 × 1015 E15 Asymmetrically broadened toward lower temperatures under higher F 
0.71 2.6 × 10−15 1.6 × 1016 E16 Phonon-assisted tunneling 
#2 Zr high 0.59 1.2 × 10−15 1.2 × 1016 E16  
SamplesET (eV)σ (cm2)NT (cm−3)NotationNotes
UID 0.18 7.7 × 10−16 2.2 × 1015 E14 Shift and split under higher F 
0.46 1.1 × 10−14 5.0 × 1015 E12 Asymmetrically broadened toward lower temperatures under higher F 
0.86 1.1 × 10−13 4.1 × 1016 E2 Phonon-assisted tunneling 
1.03 8.6 × 10−13 1.5 × 1016 E3  
#1 Zr low 0.30 2.8 × 10−17 1.2 × 1015 E15 Asymmetrically broadened toward lower temperatures under higher F 
0.71 2.6 × 10−15 1.6 × 1016 E16 Phonon-assisted tunneling 
#2 Zr high 0.59 1.2 × 10−15 1.2 × 1016 E16  

For negative majority emission transients, the energy levels obtained from DLTS measurements can vary depending on the electrical field in which the defect sits during the measurement phase of the experiment, which in turn changes as a function of built-in and applied bias and doping density.20,30,34,38 As shown in Fig. 2(b), the DLTS signals in the UID sample shift toward lower temperature and the asymmetric tails at lower temperature side enlarge for increasing reverse biases—effects that are more pronounced for the #1 Zr-doped sample [Fig. 2(c)]. Note the E14 signature in UID not only shifts but also seems to split into two peaks (Fig. S1). These suggest that E14 might consist of two defect signatures, and their DLTS shapes shift at different rates under field. Poole–Frenkel and tunneling models are two primary mechanisms for the enhancement of emission rates, which can be distinguished by plotting the logarithm of the emission rate against the square root of the electric field or the square of the electric field, respectively.21 The Poole–Frenkel effect results in moderate enhancement of emission rate and typically applies for the deep donor, while the phonon-assisted tunneling is possible for all charge states in a strong field and does not, in general, require a Coulomb potential. The electric field-dependent emission rate can be investigated by double-correlation DLTS and isothermal capacitance transient analysis,19 which are unfortunately outside of our instrument's ability. We attempted to model the broad DLTS signatures using the superposition of multiple defect signatures with different weightings, by applying the same rate windows as used in measurements.39 The physical motivation here is trying to capture the fact that defects in different locations in the depletion width would experience different fields, which in turn would result in different emission energies for the same defect type as a function of depth. Tentatively, we simulate the corresponding DLTS spectra with the minimum possible number of ET values (we found three values captured most of the behavior without having to introduce a continuous distribution), each sharing the same σ extracted from the peak maximum from Fig. 2(a) (see the supplementary material). Among the inputs ET (actually ET + ΔE), the smallest ET value corresponds to the largest emission rate, which is related to the electric field at the left boundary of x in Fig. 2(d). Figure 2(d) shows the electric field Fx=2qNd(VbiV)ε0εrqNdε0εrx at the locations that electron occupation at defect changes under emptying bias. The left boundary of the x value is at (W0λ) depth where each trap level crosses the Fermi level under 0 V, and then we can calculate the field at that point. We recalculated the emission rate using the smallest ET with its σ at a specific temperature and check the relationship between en and F. Figure 2(e) shows the emission rate for the E2 signature in UID at 375 K vs maximal F where electron occupation at defect changes. It turns out to follow the square of F, indicating the emission rate enhanced by phonon-assisted tunneling mode.

Interestingly, the 0.71 eV signature in low Zr-doped sample #1 and the 0.59 eV signature in high Zr-doped sample #2 also follow the F2 rule [Fig. 2(f)], indicating that they may arise from the same defect emitting at different rates by virtue of the different electric fields in the two samples. The fact that the extracted cross sections are also close suggests this possibility. Thus, both are labeled as E16 signature. Figure 2(f) provides the best evidence that the defect seen in Zr#2 is the same defect seen in Zr#1. The simulated results for the E14 and E12 signatures in UID and E15 in #1 Zr are hard to gain good agreement with the measured signals due to the existence of the long asymmetry tail under the high electric field, suggesting a different enhanced mechanism.

We also plot our emission rate data along with those from prior reports in terms of ln(enT2) vs 1/T in Fig. 3. For the UID crystal, the signature at 1.03 eV with a cross section of 8.6 × 10−13 cm2 agrees well with the E3 in EFG and CZ UID crystals27 and is likely from native defects since its concentration has been observed to increase after neutron irradiation29 but we cannot rule out the possibility of Ti origin yet.25 The signature we observe at 0.86 eV is consistent with E2, which has been attributed to the FeGa3+/2+ acceptor charge transition level. The dependence of emission on the electric field in this paper and Polyakov's work31 also supports this conclusion. The signatures at 0.46 eV (E12) and 0.18 eV (E14) have not been reported previously in CZ UID crystals. The 0.46 eV signature is consistent with a defect level at Ec-0.42 eV (E12) in plasma-assisted molecular beam epitaxy (PAMBE) Ge-doped films23 considering similar doping, bias conditions, and measured capture cross sections. Due to the high purity in PAMBE growth, it might be from a native defect instead of an impurity; however, this remains to be proven. The E14 signature we observe at 0.18 eV appears similar to a defect signature at Ec-0.21 eV reported from Ge-doped PAMBE-grown samples considering ET, σ and F-field values; however, more work is needed to confirm this.

FIG. 3.

Arrhenius plot of each detected defect by this work and from literatures.15,23,25–27,29

FIG. 3.

Arrhenius plot of each detected defect by this work and from literatures.15,23,25–27,29

Close modal

In the Zr-doped samples, the apparent ET is lowered by the electric field and thus cannot be directly compared with the reported ET from UID or lightly doped samples. Considering one order of magnitude uncertainty for σ and the lowering of apparent activation energy, the measured 0.71 eV from #1 and 0.59 eV from #2 of Zr-doped crystals likely correspond to the reported 0.75 eV (E2*) in UID crystals. Table I summarizes the measured defect levels, their behaviors under varying electric fields, and comparisons with reported defects. Given the complexity of electron emission at defects, more work is needed to reveal the charge state and donor/acceptor nature of measured defects by DLTS. However, our analysis points out the importance of reporting DLTS signatures considering electric field enhanced emission rate for β-Ga2O3 due to many orders of magnitude of possible doping and the expected applications in high-field applications.

In conclusion, Zr-doped and UID β-Ga2O3 crystals grown by the VGF and CZ methods were investigated by DLTS. The apparent electron emission activation energies of the CZ UID crystal were 0.18 (E14), 0.46 (E12), 0.86 (E2), and 1.03 eV (E3) below EC. For the 1# low-Zr-doped Ga2O3, apparent energies of 0.30 eV (E15) and 0.71 eV (E16) were present. For the #2 higher-Zr-doped sample, only a signature at 0.59 eV (E16) was observed. Electric-field-dependent emission rates were demonstrated by varying the reverse bias and showing the consistency of the measured defect energies for differently doped Zr samples. The 0.86 eV (E2) in UID exhibits emission field enhancement consistent with phonon-assisted tunneling. The signatures observed at 0.71 eV and 0.59 eV in the two differently Zr-doped crystals are assigned to the same E16 signature after demonstrating that the combination of applied and built-in fields with phonon-assisted tunneling enhanced emission can account for their different apparent emission energies.

See the supplementary material for DLTS spectra of the UID sample in the 80–110 K range (E14 signature) under different reverse biases, and simulated spectra of E2 and E12 in UID as examples to demonstrate how the DLTS simulation performs in this work.

This material is based upon work supported by the Air Force Office of Scientific Research under Award No. FA9550-18-1-0507 (Program Manager: Dr. Ali Sayir). Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force. This work is dedicated to the memory of the late Professor Kelvin G. Lynn.

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

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