Variable temperature probing of minority carrier transport and optical properties in p-Ga₂O₃

β-Ga₂O₃ is an emerging fourth-generation power electronics platform with a wide-bandgap of ∼4.8 eV and a high breakdown field (8 × 10⁶ V cm⁻¹).^1–6 It is becoming increasingly attractive due to its applications in high-power electronics, true solar-blind UV detection, and optoelectronic devices.^2,3,7–10 Undoped β-Ga₂O₃ tends to be n-type due to unintentional donor impurities such as Si. Intentionally, n-type β-Ga₂O₃ can be obtained by adding controlled amounts of impurities such as Si, Sn, and Ge, which is well documented.^3,5 Carrier transport characterization revealed impurity bands and the hopping mechanism of electrical transport in such doped films.^11–14 Low-temperature electron mobilities up to 796 cm²/V s¹³ have been reported. The incorporation of doped layers in devices such as Schottky diodes and field-effect transistors (FETs), including metal–oxide–semiconductor FETs (MOSFETs), and their ability to withstand high energy particle radiation have been explored.^15–24 Replicating these results to achieve p-type conductivity in β-Ga₂O₃ has proven very difficult due to factors such as doping asymmetry, high compensation of acceptors, the high ionization energy of acceptor levels, and hole-trapping at O(I) and O(II) sites.^25–30 Despite these difficulties, native p-type conductivity was demonstrated at high temperatures in undoped β-Ga₂O₃.^31,32 It was observed that native p-type conductivity is achievable by creating a significant number of native acceptors (V_Ga) and suppressing the compensation due to native donors (V_O). The thermodynamic balance required to weaken the self-compensation in undoped β-Ga₂O₃ was achieved by adjusting the growth temperatures and oxygen partial pressures during the deposition of Ga₂O₃ on sapphire substrates by Metal–Organic Chemical Vapor Deposition (MOCVD).^32,33

p-type β-Ga₂O₃ is a relatively recent discovery and an uncharted territory in terms of minority carrier transport and luminescence characterization as well as their temperature dependences. Knowledge of minority carrier (electrons) transport properties in p-type β-Ga₂O₃ is essential for achieving bipolar technology on the gallium oxide platform. In this report, the diffusion length of minority carriers (electrons), cathodoluminescence, and their temperature dependence are studied in p-type β-Ga₂O₃ with two different majority carrier (holes) concentrations.

Undoped β-Ga₂O₃ samples, analyzed in this study, were grown in an RF-heated horizontal MOCVD reactor with separate inlets to avoid premature reactions in the manifold between oxygen and organometallics precursors. Trimethylgallium (TMGa) and 5.5 N pure oxygen were used as gallium and oxygen sources, respectively. Argon was used as the carrier gas (cf. Ref. 32). The β-Ga₂O₃ layer was grown on a c-oriented sapphire substrate using Ga/O ratio and growth temperature as 1.4 × 10⁻⁴ and 775 °C, respectively. Two different total reactor pressures of 30 and 38 Torr and variable growth rates (gallium and oxygen precursor fluxes) were used to create two different native defect (V_Ga and V_O) concentrations in the Ga₂O₃ films, leading to the different values of p-type conductivity. The difference between the total reactor pressures for the deposition of the two samples is due to a change in the oxygen partial pressure. The concentration of native defects responsible for p-type conductivity is sensitive to the oxygen partial pressure. The epitaxial layer thickness was ∼450 nm. X-ray diffraction scans revealed highly textured films of gallium oxide in the β-Ga₂O₃ phase with a monoclinic space group (C2/m) symmetry. Hereinafter, the sample grown under 30 Torr total reactor pressure will be labeled A and that grown under 38 Torr will be labeled B.

A detailed study of the electrical transport properties for the above-referenced highly resistive (close to stoichiometric) Ga₂O₃ samples has been performed. Ohmic contacts were prepared with silver paint at the four corners of the sample. Hall effect measurements were conducted in a van der Pauw configuration in the 500–850 K temperature range for magnetic fields perpendicular to the film plane varying from −1.6 to 1.6 T using a high impedance high-temperature custom-designed measurement setup. Resistivities at highest measured T = 850 K were found to be ρ (A) = 1.2 × 10³ Ω cm and ρ (B) = 1.3 × 10⁴ Ω cm. Hall effect measurements demonstrated (cf. Refs. 31 and 32) the positive sign for majority carriers in both samples, thus confirming the p-type conductivity. The free hole concentrations and mobilities at 850 K were estimated as follows: p = 5.6 × 10¹⁴ cm⁻³ and μ = 8.0 cm² V⁻¹ s⁻¹ for sample A and p = 2.7 × 10¹³ cm⁻³ and μ = 16 cm² V⁻¹ s⁻¹ for sample B. Temperature-dependent measurements were possible to perform only down to 520 K (p = 2.0 × 10¹⁰ cm⁻³) for sample A and only to 620 K for sample B (p = 7.1 × 10¹⁰ cm⁻³) due to the samples’ high resistivity. The difference in hole concentrations is due to the difference in growth conditions (total reactor pressure and the ratio of gallium–oxygen precursor fluxes), resulting in the variation of electrical compensation degree K = N_A/N_D, i.e., the ratio of native acceptor to native donor concentrations. Ni/Au (20/80 nm) asymmetrical pseudo-Schottky contacts were created on the film with lithography/liftoff techniques for further analysis.

Electron Beam-Induced Current (EBIC) and cathodoluminescence (CL) measurements were performed in situ in a Phillips XL-30 Scanning Electron Microscope (SEM) to characterize the diffusion length (L) of minority carriers (electrons) and luminescence behavior of the samples, respectively. The measurements were carried out in the 304–404 K temperature range using a Gatan MonoCL2 temperature-controlled stage integrated into the SEM. For both EBIC and CL measurements, the electron beam energy was kept at 10 keV. The EBIC line scans were obtained in a planar configuration (Fig. 1). The EBIC signal was amplified with a Stanford Research Systems SR 570 low-noise current amplifier and digitized with a Keithley digital multimeter (DMM) 2000 controlled by a personal computer (PC) using homemade software. CL measurements were carried out using a Gatan MonoCL2 attachment to the SEM. Spectra were recorded with a Hamamatsu photomultiplier tube sensitive in 150–850 nm range and a single grating monochromator (blazed at 1200 lines/mm).

EBIC line-scans were used to extract diffusion length, L, from the following equation:^34,35

where C(x) is the EBIC signal at distance x from the Schottky junction, C₀ is a scaling constant, x is the distance of the electron beam from the Schottky barrier, and α is the linearization parameter, related to surface recombination velocity. The coefficient α was set at −0.5, corresponding to the low influence of surface recombination. Since the carrier concentration is low in both samples, the Schottky barrier depletion width is significantly larger than L and, therefore, the approach outlined in Ref. 36 was used. Figures 2(a) and 2(b) show the raw EBIC signals and a fit with x^α exp(−x/L) used in extracting L for samples A and B, respectively. The temperature dependence of L for samples A and B is shown in Fig. 3. L decreased with increasing temperature, with values for samples A and B at 304 K of 1040 and 8506 nm, respectively. At 404 K, L reduced to 640 and 6193 nm, respectively. Relatively large values of L are partially due to the shallow majority carrier concentration. Within the current temperature range of measurements, the origin of L decrease is likely due to phonon scattering.³⁷ Reported values of L for minority carrier (holes) in n-type β-Ga₂O₃ are within 50–600 nm,^{20,21,38–41} lower than those of electrons measured in this work for minority carrier electrons. A likely reason could be the large effective mass for holes (18–25 m₀).⁴² It is worth noting that a similar dependence of L on temperature was found for n-type β-Ga₂O₃, but it is attributed to scattering on ionized impurities due to heavy Si doping.⁴¹ The activation energy for the temperature dependence of L is given by^43,44

where L₀ is a scaling constant, ΔE_L,T is the thermal activation energy, k is the Boltzmann constant, and T is the temperature. The activation energy pertaining to the reduction of L with temperature is 67 and 113 meV for samples A and B, respectively. A detailed discussion regarding the origin of ΔE_L,T is given later in the text.

Raw CL spectra and their Gaussian decompositions at 304 K are presented in Figs. 4(a) and 4(b) for samples A and B, respectively. The CL spectra exhibit four characteristic luminescence bands: ultraviolet (UVL′ and UVL) at 375 and 415 nm, blue (BL) at 450 nm, and green (GL) at 520 nm. The UVL′ and UVL bands are commonly ascribed to recombination of self-trapped excitons, considering the absence of near band edge emission and their lack in β-Ga₂O₃ for sub-bandgap excitation.^{26,27,29,45–48} The self-localization of excitons occurs at O(I) and O(II) site, corresponding to UVL′ and UVL bands, respectively.^47,49 Although, as has been shown from Electron Paramagnetic Resonance (EPR) measurements⁵⁰ and confirmed by several independent EBIC studies on n-type β-Ga₂O₃,^{20–23,39,51,52} the self-localization of holes is unstable above 110 K, the optical signature of the self-trapped excitons persists in CL and photoluminescence (PL) measurements. Note that the relative contribution of UVL′ and UVL bands in both A and B samples is much lower than in n-type β-Ga₂O₃, found in earlier reports.^{26,47,49,53–58} The BL band arises from donor–acceptor pair recombination involving a V_O donor and V_Ga or a (V_O, V_Ga) complex as an acceptor. GL has several different origins, mentioned in the literature, and was observed with an array of various dopants, such as Mg,⁵⁹ Si,⁵⁴ and Er.⁶⁰ In undoped β-Ga₂O₃, grown by floating zone technique, Víllora et al.⁶¹ ascribed GL to self-trapped excitons as it existed only for PL excitation energies below the bandgap. Moreover, this band was also observed in β-Ga₂O₃ nanoflakes, structurally consisting of a crystalline core and amorphous shell.^62,63 In a recent study on β-Ga₂O₃ films on a c-plane sapphire substrate with (201) orientation, deposited with magnetron sputtering,⁶⁴ the intensities of BL and GL were modulated by changing the oxygen flow rate, and the origin of the GL was attributed to the presence of isolated V_Ga. Furthermore, the presence of isolated V_O did not independently play a role in enhancing BL, and the origin of BL was assigned to a defect complex involving V_O and V_Ga. Given the abundance of isolated V_Ga acceptors and (V_O, V_Ga) complexes in both samples, a relatively large contribution of both BL and GL to the CL emission spectrum is observed in this work. Binet and Gourier⁵³ and Onuma et al.⁴⁹ independently found a correlation between conductivity and concentration of the V_O donors in n-type β-Ga₂O₃. In this case, since V_O compensates the acceptors, and due to the high ionization energy of acceptors, p-type β-Ga₂O₃ has relatively high resistivity below 450 K.^31,32 The presence of a rather large number of V_Ga acceptors and (V_O, V_Ga) acceptor complexes, promoting p-type conductivity, was confirmed from the CL emission spectrum.

The temperature dependence of the CL signal follows the form⁵³ 

where I(T) is the integrated CL intensity, I₀ is a constant, and ΔE_CL is the process activation energy. Figure 5 shows the Arrhenius plot of ln(I₀/I(T) − 1). The process activation energy ΔE_CL, obtained from a linear fit of the temperature dependence depicted in Fig. 5, was 88 and 101 meV for samples A and B, respectively. The total CL intensity is used in Fig. 5 because the relative contributions of the individual luminescence bands remained approximately constant in the temperature range of the measurements. The activation energies ΔE_L,T and ΔE_CL for sample A (67 and 88 meV, respectively) and sample B (113 and 101 meV, respectively) are comparable and can be attributed to a common origin.

Temperature-dependent resistivity measurements between 300 and 850 K in our earlier study³² on deep V_Ga acceptor defects in similar Ga₂O₃ samples showed two activation energies due to temperature-activated processes. In the high temperature region (T > 400 K), the acceptors are ionized with an activation energy of 0.56 eV. However, for temperatures between 300 and 400 K, a shallower V_Ga⁻–V_O⁺⁺ acceptor complex is present. The concentration of this complex strongly increases in off stoichiometric samples (after oxygen post-annealing) detectable by the Hall effect. The electrical activation energy has been determined as 0.17 eV (170 meV), and these complexes are responsible for forming an impurity band and hopping conductivity below 400 K.³² It is suggested in this study that the non-equilibrium electrons in as-grown (close to stoichiometry) Ga₂O₃ thin films, generated during the excitation with an electron beam, are captured by V_Ga⁻–V_O⁺⁺ acceptor defect complexes. The thermal emission of these captured electrons is represented by activation energies extracted from EBIC and CL experiments. In other words, V_Ga⁻–V_O⁺⁺ acceptor complexes are detectable by electron beam excitation even in close to stoichiometric samples when electrical measurements are insensitive, probably due to their insufficient concentration. Moreover, based on the discussion given above, the nature of the native defects probed with EBIC and CL in both samples is alike. The difference in the activation energies is primarily due to the difference in their concentration, which is governed by the oxygen partial pressure during the growth process. The process of non-equilibrium electron de-trapping in this work has an analogy with Mg-doped p-GaN, where the release of a non-equilibrium electron from deep acceptor levels is seen in the thermal activation of L.⁶⁵ 

In summary, EBIC and CL techniques were employed to understand the temperature dependence of the diffusion length of minority carriers and CL emission in p-type β-Ga₂O₃ with two different hole concentrations. Optical signatures of native acceptor defects (isolated V_Ga and V_Ga⁻–V_O²⁺ complex) were identified in the CL spectrum. In addition, the activation energies for change of L with temperature (ΔE_{L, T}) and thermal quenching of CL intensity (ΔE_CL) were experimentally obtained as 67 and 88 meV for sample A and 113 and 101 meV for sample B within the temperature range of 304–404 K. Comparable values of ΔE_L,T and ΔE_CL indicate a common origin for both processes, which is attributed to the thermal de-trapping of electrons from the V_Ga⁻–V_O⁺⁺ acceptor level. The current development in the characterization of p-type β-Ga₂O₃ could serve a pivotal role in realizing bipolar gallium oxide devices.

The research at UCF was supported, in part, by the NSF (Grant Nos. ECCS1802208 and ECCS2127916). The research at UCF and Tel Aviv University was supported partially by the US–Israel BSF (Award No. 2018010) and NATO (Award No. G5748). The work at UF was performed as part of the Interaction of Ionizing Radiation with Matter University Research Alliance (IIRM-URA), sponsored by the Department of the Defense, Defense Threat Reduction Agency (Award No. HDTRA1-20-2-0002), monitored by Jacob Calkins and by the NSF DMR (Grant No. 1856662) (J. H. Edgar). This work is a part of the “GALLIA” International Research Project, CNRS, France.