The energetic positions of the two Fe dopant levels in the bandgap of β-Ga2O3 are determined to be at 3.05(±0.05) and 3.85(±0.05) eV below the conduction band minimum from transmission measurements employing a sub-picosecond tunable ultraviolet laser radiation source. A further measurement of the quantum efficiency of photoelectron emission from the Fe:Ga2O3(010) photocathode is consistent with the obtained absorption data and a dominant optical phonon assisted Franck–Condon emission mechanism, while also providing an estimate of 100 ps for the conduction band electron lifetime.

The β crystalline form of gallium oxide (β-Ga2O3) is a material that has inspired significant development efforts due to its desirable electronic properties, among them a large bandgap energy (∼4.8 eV)1 and high critical electric field,2 combined with a potential to be cheaply produced at scale via methods like EFG (edge-defined film-fed growth).3 The intended applications of this wide bandgap semiconductor commonly include high-power electronic4 and optical devices,5 the material being especially attractive in cases where radiation hardening is a concern.6,7 Many such applications require semi-insulating material, which may be achieved through iron doping8—a p-type doping that depletes the ∼1016 cm−3 optically active and populated oxygen vacancy states in the bandgap9 to produce a crystal transparent in the 400–700 nm (1.8–3.0 eV) visible spectral region. The exact energetic positions of the two expected Fe dopant states are, however, the subject of some debate in the literature: (i) Ingebrigtsen et al.10 in their deep level transient spectroscopy (DLTS) measurements of n-type Ga2O3 materials reported an energy of 0.78 eV below the conduction band (CB) minimum and also suggested the existence of a Fe state ∼0.5 eV above the valence band (VB) maximum, while (ii) Lyons11 indicated, citing Ref. 10, that the Fe dopant states are expected to be in the energetic vicinity of the deep acceptor Ca dopant states at 0.7–1.5 eV above the VB maximum. Accordingly, an accurate determination of the Fe energy levels in β-Ga2O3 at the ∼1018 cm−3 dopant densities employed to achieve semi-insulating behavior is of direct interest for ab initio acceptor state modeling11,12 and clearly of relevance for device design due to the consequent likely Fermi level pinning at the dopant state energy. Recent reports13–15 of shallow acceptor p-type doping could then complete the practical requirements for β-Ga2O3 based optical and electronic device design.

In this Letter, we present two separate experimental measurements into the properties of a Fe doped β-Ga2O3(010) crystal provided by Kyma Technologies, Inc.16 The first is based on a standard spectral absorption measurement technique, albeit using a tunable sub-picosecond ultraviolet (UV) laser radiation source, which reveals the energetic positions of the two iron dopant states. The second employs a low energy photoemission measurement with the same UV laser system for which the quantum efficiency (QE) of electron emission is dependent upon the photoexcitation into and electron transport dynamics in the oxide's conduction band. The measured spectral dependence of the QE (in the studied ultrafast regime) is shown to be consistent with photoexcitation from the Fe dopant states at their determined energetic positions in the oxide's bandgap and subsequent emission into the vacuum through an optical phonon mediated Franck–Condon mechanism.17–19 

The studied 450(±50) μm-thick β-Ga2O3(010) material is semi-insulating due to ∼1018 cm−3 iron doping. The wide-gap semiconductor wafer is colorless and has an epi-ready front surface finish (RMS roughness <0.5 nm) with the back surface polished to optical quality (better than λ/4 at 632 nm). The transparency of the oxide wafer over the visible spectrum (1.8–3.0 eV) indicates that the Fermi level is almost certainly pinned at least 3 eV below the CB minimum and very likely at a Fe dopant state due to the moderately high dopant density. Consequently, optical transitions into the CB from the VB, occupied Fe dopant states, and perhaps oxygen vacancy states9 below the Fermi level are only possible at near UV (and shorter) wavelengths (i.e., ℏω >3.0 eV). The presented experimental measurement techniques employ sub-picosecond (∼0.5 ps) UV pulses tunable from 230 to 400 nm (3.0–5.3 eV) that have a typical pulse energy of ∼10 pJ. The UV pulses are generated using a 16.7 MHz repetition rate laser-based radiation source driven by a 20 W Yb:fiber laser system (aeroPULSE FS20; NKT Photonics) producing ∼350 fs duration laser pulses at 1030 nm.20,21

For the spectral absorption measurements of the uncoated Fe:Ga2O3(010) wafer, the incident UV laser beam is collimated to a diameter of ∼2 mm, giving a peak pulse intensity of less than 1 kW/cm2, and the transmission determined as a function of the incident photon energy ℏω for radiation at near normal incidence (i.e., angle of incidence < 5°). The results, shown as the black data points in Fig. 1, include the second harmonic of the Yb:fiber laser system at 515 nm (ℏω = 2.4 eV). They clearly indicate a transmission of ∼70% in the visible (λ > 400 nm), primarily due to loss by surface reflections, and an increasing absorption to near zero (<0.1%) transmission for ℏω > 4.6 eV. The latter value is slightly less than the expected bandgap energy of 4.8 eV (Ref. 1) due to either a strong Urbach absorption tail22 or transitions from the VB to a higher density of oxygen vacancy states in the vicinity of the CB.9 We note that interference effects from multiple surface reflections are minimized (if not effectively eliminated) using the ∼0.5 ps pulses in the transmission measurements since the ∼150 μm spatial pulse length is significantly less than the 2nl ≈ 2 mm optical thickness of the wafer (assuming a refractive index n ≈ 223 and a thickness of l = 450 μm).

FIG. 1.

Spectral dependence of the transmission (right axis) and αl (left axis) for the Fe:Ga2O3(010) wafer: experimental transmission (open blue circles), (1 − R)2 using refractive index of Ref. 17 (dashed black line), (1 − R)2S with S = 0.919 (solid black line), and extracted values of αl (black points) and their fit to two linear functions (solid and dashed red lines).

FIG. 1.

Spectral dependence of the transmission (right axis) and αl (left axis) for the Fe:Ga2O3(010) wafer: experimental transmission (open blue circles), (1 − R)2 using refractive index of Ref. 17 (dashed black line), (1 − R)2S with S = 0.919 (solid black line), and extracted values of αl (black points) and their fit to two linear functions (solid and dashed red lines).

Close modal

For the spectral photoemission measurements, a ∼7 × 7 mm2 portion of the Fe:Ga2O3 wafer is mounted in the cathode of a 16 kV DC electron gun based on the design of Togawa et al.24 The tunable and p-polarized UV pulsed laser radiation at a 60° angle of incidence is focused to an elliptical 35 × 70 μm2 (half-width at half irradiance maximum) Gaussian spot on the Ga2O3 photocathode. After acceleration across the 1 cm DC gun length, the photoemitted electrons are incident on a micro-channel plate (MCP) detector with a P43 phosphor screen (BOS-18; Beam Imaging Solutions). The resultant optical signal due to the electron beam is then relay imaged onto a 2.5 μm pixel CMOS camera. The sensitivity of the MCP/camera system is calibrated against the known electron photoemission quantum efficiency (QE) of a Rh(110) photocathode whose spectral QE dependence has been determined using a Faraday cup.20 The integrated camera image of the electron beam and the incident UV laser power can then be directly related to the QE of the Ga2O3 photocathode once the transmission of the UV fused silica vacuum window and reflectivity of the front surface of Ga2O3 crystal are accounted for. The latter is minimal (less than 1%) for our p-polarized 230–400 nm radiation since the tangent of the 60° angle of incidence is close to the refractive index of Ga2O3.23 The spectral dependence of the QE for our Fe:Ga2O3 photocathode measured in this manner is plotted as the square root of the QE vs the incident photon energy ℏω in Fig. 2.

FIG. 2.

Spectral dependence of the square root of the QE for Fe:Ga2O3(010): fit for ℏω < 3.8 eV using Eq. (3) (dashed blue line) and fit for ℏω < 4.8 eV using Eq. (4) (solid red line).

FIG. 2.

Spectral dependence of the square root of the QE for Fe:Ga2O3(010): fit for ℏω < 3.8 eV using Eq. (3) (dashed blue line) and fit for ℏω < 4.8 eV using Eq. (4) (solid red line).

Close modal

We note that the incident laser irradiances of less than 100 kW/cm2 employed in both measurements are expected to be significantly less than those required to observe nonlinear optical effects. For Ga2O3 with its 4.8 eV bandgap, the band to band two-photon absorption coefficient is expected to be ∼1 cm/GW (Refs. 25 and 26) so that for the 450 μm-thick wafer, a two-photon absorption of 1% would require an incident laser pulse intensity of at least 1 MW/cm2. Further, the birefringence of Ga2O3 is not expected to play a major role in both sets of measurements since the (010) wafer orientation places the most dissimilar optical axis1 closest to the direction of propagation of the UV radiation.

Without interference effects, the irradiance transmission T through an uncoated absorbing material of thickness l is given in general by
T = ( 1 R ) 2 S e α l ,
(1)
where R is the reflectivity of each face, α is the optical absorption coefficient, and S is an additional loss term accounting for scattering effects, background absorption (e.g., from the valence band to unoccupied oxygen vacancy states in the bandgap), etc. This relation is used to evaluate αl using the measured transmission data displayed as the black data points in Fig. 1. Under our conditions of normal incidence and assuming a negligible imaginary component to the refractive index, the reflection of each surface is R = n 1 n + 1 2 for a (real) refractive index n. The resulting spectral dependence of (1 − R)2 using the dispersion of the refractive index determined by Rebien et al.23 is plotted as the black dashed line in Fig. 1. Incorporating a value of S = 0.919 to fit the value of (1 − R)2 = 0.741 measured at ℏω = 2.4 eV (the second harmonic of the Yb:fiber laser at 515 nm) produces the solid black line. Evaluation of αl for each experimental data point using Eq. (1) generates the red points plotted in Fig. 1. The spectral trend of α(ℏω)l below ℏω ≈ 4.4 eV can be well fit by the addition of two linear dependences of the form A i ω E i, valid for ℏω > Ei, where Ai is a constant and Ei is a threshold energy. This fit is shown by the solid red line in Fig. 1 for E1 = 3.05 eV and E2 = 3.85 eV.
A linear increase in the absorption with incident photon energy ℏω from a threshold energy is consistent with expectations for transitions from an atomic-like dopant state to an unpopulated CB centered on the Γ point of the Brillouin zone. In the limit of an energetically narrow dopant state with a constant density of states (i.e., a momentum width significantly larger than the momentum of the excited state in the CB), an evaluation of the absorption through the joint density of states associated with the optical transition reduces to an integral of the form,
α i 0 p 2 d p δ p 2 m * ω E i = 2 m * ( ω E i ) ,
(2)
where the delta function (Fermi's golden rule) defines energy conservation in the optical transition. Here, both the dopant state and CB with an effective mass m* are assumed to be isotropic in momentum space, and Ei is the energy of the dopant state below the CB minimum. The observed threshold energies E1 and E2 in Fig. 1 can therefore now be identified as the energetic positions of the two Fe dopant states in Fe:Ga2O3. Also of note is that the fitted values of A1 and A2 are comparable (A2 = 2.07A1), implying that the product of the absorption cross sections and occupied state density for the two Fe states is also comparable—the observation that A2 is greater than A1 by a factor of 2 may simply be due to the upper Fe dopant state pining the Fermi level.

Under our experimental conditions with 3.0–5.3 eV incident UV photon energies, the observation of photoemission from Fe:Ga2O3 when ℏω < 4 eV (Fig. 2) is perhaps somewhat surprising since our density functional theory (DFT) calculations (using the Amsterdam Suite27 and the thin slab technique28) indicate that the vacuum level is 1 to 1.5 eV above the CB minimum. These calculations employ the rSCAN functional29 with an undoped semi-slab of 2n atomic layers (with a clean un-passivated surface) and an “infinite” vacuum and are terminated for increasing n when both the energetic position of the VB maximum in the slab and the vacuum energy level converge to ±50 meV, giving a typical ±0.1 eV computational uncertainty in the work function. For the complex monoclinic crystal structure of β-Ga2O3, this energy convergence is more difficult to attain, leading to a larger work function uncertainty. Nonetheless, for conventional one-photon photoemission from this p-type doped wide-gap semiconductor where the Fermi level is pinned ∼1 eV above the VB maximum (i.e., greater than 3 eV below the CB minimum), our work function calculations indicate that a photon energy greater than 4 eV should be required. However, our experiments are performed using sub-picosecond laser pulses, which require ultrafast effects to be considered. In particular, the photoexcitation of “hot” electrons into the CB with an excess energy ΔE = ℏωEi, where Ei is the internal ionization energy of the ith dopant (or defect) state in the material's bandgap, will initially generate an electron distribution with a temperature Te given by k B T e = 2 3 Δ E, where kB is Boltzmann's constant. In crystals, like Ga2O3, with a strong coupling between electrons and optical phonons, the initial temperature of the electron distribution is further reduced by energy equipartition with the optical phonon modes.30,31 Thereafter, the transport dynamics of the electrons under the applied field in the Fe:Ga2O3(010) crystal, due to the 16 MV/cm acceleration field in the DC gun, determine the temperature of the electron distribution as it approaches the crystal emission face. In the non-degenerate photoexcitation limit, which is applicable under our experimental conditions, this means that a small fraction of the electrons in the high energy portion of the population tail in their Boltzmann distribution will have sufficient energy to overcome the ∼1 eV potential barrier to be emitted into the vacuum from the CB.

The QE of this photoemission mechanism has been shown to be proportional to the square of the initial excited carrier energy ΔE in the CB;30 fundamentally, this is because (i) the fraction of electrons in the CB above the ≥1 eV emission barrier is proportional to Te and (ii) the emission probability into the vacuum is the product of the transmission coefficient for the potential barrier and the density of the recipient vacuum states (both being proportional to the square root of the emission energy in the vacuum). For the two optically active Fe dopant states in Ga2O3 with internal ionization energies E1 and E2, the square root of the photoemission QE is therefore expected to be of the following form:
Q E k B T e = B A 1 ω E 1 2 + A 2 ω E 2 2 A 1 ( ω E 1 ) + A 2 ( ω E 2 ) ,
(3)
where B is a constant and from the transmission data analysis A2/A1 = 2.07. As shown by the blue dashed line in Fig. 2, this form for the spectral dependence of the QE is clearly not consistent with the experimental data when E1 = 3.05 eV and E2 = 3.85 eV; Eq. (3) can only be fit to the QE data below ℏω ≈ 3.9 eV.
A more sophisticated fit, which is consistent with the measured spectral QE data, is shown by the red line in Fig. 2. It is given by the following expression:
Q E = C 1 e α l α ( 1 e α + β l ) ( α + β ) ( 1 e α l ) 9 k B T e 2 ,
(4)
where C is a constant [not equal to B in Eq. (3)] and kBTe is given by Eq. (3). The first term in the brackets reflects the modification required to correctly model the absorbed UV radiation over the 450 μm Fe:Ga2O3 wafer thickness since the QE can only be due to photoexcited electrons. The second bracketed term deals with the fraction of the photoexcited electrons that can be emitted from an escape depth β−1 =  associated with the electron drift velocity v to the emission face due to the applied field in the DC gun and recombination (presumably primarily into the empty oxygen vacancy states) in a characteristic time τ; that is, it deals with the physics of the second transport step in Spicer's three-step photoemission model.32 This fraction is raised to a power k + 1 = 9, which is reflective of the physics of the electron emission mechanism into the vacuum.

For Ga2O3, we observe the dominant electron emission process to be due to a momentum resonant Franck–Condon effect17–19 based on optical phonon scattering. A similar emission process has also been observed from a H-terminated diamond (001) surface,33 where an average of two phonon scattering (emission) events occurs for every emitted electron. Due to its strong ionic nature and monoclinic crystal structure, Ga2O3 has many more (∼5–6) strong and active optical phonon modes ranging in energy from ∼100 meV to below kBTL = 25 meV (Ref. 34) (where TL is the 300 K lattice temperature). Consequently, it is probable that several (perhaps as many as 6–10, reflective of ∼2 per mode) optical phonon scattering events could be involved in a single electron emission from this oxide material. Further, as the phonon population is generated by the electron distribution as it drifts toward the (010) emission face under the applied field,31 it is reasonable to expect its spatial distribution (in the emission direction) to mimic closely that of the electrons. Hence, the square bracketed fraction of photoexcited electrons within the escape depth in Eq. (4) is raised to the power k + 1 for k phonon scattering events plus the original electron distribution. The best fit of Eq. (4) to the spectral QE data (red line in Fig. 2) is obtained for k = 8 and βl = 15, with uncertainties of ±10% for both quantities. The fit also explicitly uses the spectral values of αl obtained from our transmission measurements; that is, the extracted values of E1 and E2 for the energies of the Fe dopant states and their relative absorption strengths A2/A1 = 2.07. The fit is good even between 4.4 and 4.8 eV, supporting the notion that the additional absorbance noted in this spectral region (Fig. 1) is likely due to transitions from the valence band into empty oxygen vacancy states just below the conduction band9—generating trapped electrons that cannot contribute to photoemission. Beyond 4.8 eV, the fit overestimates the QE since direct band to band transitions are now possible, thereby exciting many more electrons into the conduction band but with a much-reduced excess energy and therefore significantly decreasing the total energy kBTe of the photoexcited electron distribution. We also note that although the employed theoretical interpretation is consistent with the measured spectral QE trend below 4.8 eV, it cannot be considered exact as it does not account for all possible photoexcitation mechanisms such as those from occupied oxygen vacancy states between the two Fe states.9 

If one assumes that the electrons are accelerated to the emission surface to a limiting average energy of kBTD = 62 meV,35 where TD is the Debye temperature, before energy relaxation in the conduction band by optical phonon emission, then the obtained 30(±5) μm value of the electron escape depth β−1 can be used to estimate the electron lifetime τ in the conduction band of our Fe:Ga2O3 material. Specifically, 1 2 m * v 2 = k B T D with m* = 0.2–0.25me for the conduction band effective mass1 (me is the free electron mass) gives an average electron drift velocity of v ≈ 3 × 105 m/s and hence τ = ()−1 ≈ 100 ps. This value for the CB electron lifetime is quite reasonable considering the anticipated ∼1016 cm−3 density of available unpopulated oxygen vacancy states in the oxide bandgap9 produced by the iron doping pinning the Fermi level ∼3 eV below the CBM (i.e., at the upper Fe dopant state energy).36 

The properties of an iron doped β-Ga2O3(010) crystal wafer have been investigated using two experimental techniques employing a sub-picosecond tunable UV laser system: (i) a standard spectral transmission measurement and (ii) a measurement of the spectral dependence of the QE of photoemission. The analysis of the UV transmission data indicates the presence of two Fe dopant states located 3.05(±0.05) and 3.85(±0.05) eV below the CB minimum—values that are consistent with Ab initio calculations of other deep acceptor dopant states in β-Ga2O3.11,12 At the ∼1018 cm−3 Fe dopant density, the observed photoemission threshold of 3.1(±0.1) eV for our ultrafast (sub-ps) measurement strongly suggests that the Fermi level is indeed pinned at the upper Fe dopant state—in agreement with visible optical clarity of the Fe:Ga2O3 wafer. The measured spectral dependence of the QE of photoemission is also shown to be consistent with emission from the high energy tail of a hot thermalized electron distribution generated by photoexcitation into the CB from the Fe dopant states, if recombination effects are included and a dominant Franck–Condon emission mechanism involving optical phonon scattering is assumed. The inclusion of the former allows for an estimate of 100 ps to be made for the electron lifetime in the CB of our Fe:Ga2O3 sample under the assumption that the electron energy gained in the applied DC gun field is limited to kBTD—the energy at the Debye temperature. The assumption of the latter momentum resonant electron emission mechanism is consistent with the expected strong optical deformation potential scattering in β-Ga2O3(010) and has been observed in prior studies of a H-terminated diamond (001) photocathode.33 

This work was supported by the U.S. Department of Energy under Award No. DE-SC0020387. The authors gratefully acknowledge the expert assistance of the Liberal Arts and Sciences Machine Shop at the University of Illinois at Chicago.

The authors have no conflicts to disclose.

Louis A. Angeloni: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (equal); Software (lead); Visualization (lead); Writing – original draft (supporting); Writing – review & editing (equal). I.-J. Shan: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Writing – review & editing (equal). J. H. Leach: Resources (lead); Writing – review & editing (equal). W. Andreas Schroeder: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – original draft (lead).

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

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