EBIC studies of minority electron diffusion length in undoped p-type gallium oxide

The minority electron diffusion length in p-type gallium oxide is a critical parameter that significantly influences the performance of devices based on this material. Understanding the factors that affect diffusion length and employing appropriate measurement techniques are essential for optimizing the design and fabrication of high-performance gallium oxide-based devices.^1–6 

Minority electron diffusion length in gallium oxide is affected by various factors, which include the following:⁷ 

1. Material quality: The presence of defects, impurities, and crystal imperfections can act as recombination centers, reducing the diffusion length. High-quality gallium oxide with minimal defects is essential for achieving longer diffusion lengths.

2. Impurity concentration: The acceptor/donor doping level in gallium oxide affects the concentration of minority carriers. A higher doping concentration can lead to increased recombination, reducing the diffusion length.

3. Temperature: In gallium oxide, the diffusion length generally decreases with increasing temperature due to enhanced thermal vibrations and increased recombination rates.

4. Electric field: The presence of an electric field can influence the diffusion of minority carriers, potentially affecting the diffusion length.

A long minority electron diffusion length is desirable for several reasons:⁸ 

1. Efficient charge carrier transport: Longer diffusion lengths allow minority carriers to travel further before recombining, improving the efficiency of devices such as solar cells and light-emitting diodes.

2. Reduced recombination losses: A longer diffusion length reduces the rate of recombination, leading to lower power losses in devices such as power transistors.

3. Improved device performance: Devices with longer diffusion lengths generally exhibit better performance characteristics, such as higher efficiency, lower operating voltage, and improved reliability.

During the past several decades, extensive studies were carried out to understand the impact of temperature and doping level on the minority carrier diffusion length in such wide bandgap semiconductors as GaN, AlGaN, and ZnO.^9–11 These studies were complemented by investigation of charge injection impact on minority carrier transport.^12–15 The latter injection results in a several-fold temperature-sensitive increase in diffusion length followed by its saturation. The effect was ascribed to charge trapping on metastable native defect levels.

Minority carrier transport studies in gallium oxide were first carried out in n-type materials, because Ga₂O₃ epitaxial layers are very often grown with electrons being majority carriers.^16,17 With p-type hetero-epitaxial gallium oxide becoming available, minority electron diffusion length was first measured as a function of temperature and charge injection in the highly resistive (π-type) material.¹⁸ Very recently, undoped p-type homoepitaxial Ga₂O₃ layers with much higher electrical conductivity have been grown and tested by purely optical means [cathodoluminescence (CL)] in situ using a scanning electron microscope under continuous electron beam irradiation (charge injection).¹⁹ CL intensity decay with increasing duration of electron beam irradiation was ascribed to non-equilibrium electron trapping on gallium vacancy-related levels in gallium oxide forbidden gap, which, in turn, leads to a longer non-equilibrium minority carrier lifetime in the conduction band and consequently to the longer minority electron diffusion length. The activation energy associated with the impact of electron beam irradiation (injection) on CL emission intensity was estimated at ∼0.3 eV.

In this work, the systematic Electron Beam-Induced Current (EBIC) measurements were performed on (010) Ga₂O₃ homoepitaxial films, as in Ref. 19, under variable temperatures and durations of electron beam irradiation to obtain the activation energies for the impact of both parameters (temperature and duration of charge injection) on the minority carrier transport. Another goal was to complement the independent variable temperature CL measurements reported in Ref. 19. This work is especially relevant, given the recent advances in exploiting bipolar transport in NiO/Ga₂O₃ heterojunction rectifiers for power switching applications to overcome limitations in native p-type doping of Ga₂O₃.^20,21

Undoped 1 μm-thick β-Ga₂O₃ was grown on (010)-oriented insulating Fe-doped Ga₂O₃ in a RF-heated horizontal metalorganic chemical vapor deposition (MOCVD) reactor using a Ga/O ratio and a growth temperature of 1.4 × 10⁻⁴ and 775 °C, respectively.^22,23 X-ray diffraction revealed a high quality layer of β-Ga₂O₃ with monoclinic space group (C2/m) symmetry.

Metal contacts for electrical characterization were prepared by Ti/Au deposited at the four corners of the sample in a van der Pauw configuration. The contacts were tested by measuring I–V characteristics, which showed the Ohmic dependence in the temperature range of 450–850 K. Because the contacts exhibited deviation from the linear I–V dependence below 450 K, the Hall effect measurements were not conducted at room temperature. The positive Hall voltage increased with increasing magnetic field, thus confirming the p-type nature of the epitaxial layer with hole concentration p ∼ 2.8 × 10¹⁷ cm⁻³ and resistivity ρ ∼ 0.39 Ω·cm at 450 K.

Minority carrier diffusion length, L, measurements were carried out using the electron beam-induced current technique in situ in a Phillips XL-30 SEM using planar line-scan electron beam excitation with an electron beam moving along the sample’s surface.^7,9,12,17,18 The EBIC measurements were carried out at room temperature under an electron beam accelerating voltage of 20 kV (to cover the whole epitaxial layer thickness), corresponding to ∼0.6 nA absorbed current (measured with a Keithley 480 picoammeter) and ∼1 μm electron range (penetration depth) in the material.²⁴ The EBIC line-scans (16.3 μm lateral length) for diffusion length extraction were carried out using Ni/Au (20 nm/80 nm) asymmetrical pseudo-Schottky contacts created on the film with lithography/liftoff techniques.

Figure 1 shows the initial (nearly zero-injection; no more than 12 s) room temperature dependence of the electron beam-induced current on the distance from the edge of the Schottky barrier. The EBIC signal was amplified with a Stanford Research Systems SR 570 low-noise current amplifier and digitized with Keithley DMM 2000, controlled by a PC using home-made software.

The inset of Fig. 1 shows the ln(I × d^1/2) dependence on coordinate d. The minority carrier (electron) diffusion length, L, is extracted as an inverse slope of the linear dependence in the inset of Fig. 1. The value of L ∼ 0.95 μm was obtained for a nearly zero injection duration.

To perform electron injection in the region of EBIC measurements, line-scans were not interrupted for the total time of up to ∼800 s (corresponding to the primary excitation electron charge density of 2.1 × 10⁻⁷ C/μm³). The values of diffusion length were periodically extracted using Eq. (1) for different incremental durations of electron injection varying from nearly zero (for the first line-scan) to 800 s. At each measurement temperature, the EBIC dependence as a function of electron beam irradiation duration was measured in a different region in the vicinity of the Schottky barrier under test, to avoid the uncontrolled impact of charge injection on minority carrier diffusion length.

It should be noted that the primary excitation SEM electron beam serves for the generation of non-equilibrium electron–hole pairs in the material due to the band-to-band (valence band to conduction band) transition of excited electrons. The primary excitation electrons do not accumulate in the material since the sample is grounded, thus preserving the sample’s electroneutrality.

The experiments started with variable temperature minority electron diffusion length measurements prior to continuous electron beam irradiation. The results presented in Fig. 2 show a decrease in L with increasing temperature, which is consistent with the previous findings in n-type and highly resistive π-type Ga₂O₃.^16,18 The relatively large (∼1 μm at room temperature) values of L, obtained in this work, as compared to the n-type samples (several hundred nm) measured in Ref. 16, provide an additional proof for the material’s p-type of conductivity. Within the current temperature range of measurements, it is likely that the origin of L decrease is due to phonon scattering.²⁵ 

Figure 3 presents the results of the electron injection experiments carried out at various temperatures. The minority electron diffusion length exhibits a linear increase with the duration of electron injection before saturation occurs (not shown in Fig. 3). The linear increase in L with electron injection duration was previously observed in p-GaN and p-AlGaN,^12–14, p-ZnO,¹⁵ unintentionally doped GaN,²⁶ n-Ga₂O₃,¹⁷ and π-Ga₂O₃.¹⁸ The minority carrier diffusion length increase in Fig. 3 is characterized by the rate R (dL/dt, where t is the duration of electron injection), which drops from 4 nm/s at 233 K to 0.8 nm/s at 353 K as shown in the inset of Fig. 3.

References 27 and 28 summarize traps in Ga₂O₃, which are associated with native defects and impurities. According to Ref. 27, gallium vacancy (V_Ga)-related energetic levels are located at 0.1–0.3 and 0.3–0.5 eV above the top of the valence band. In a previous study, focused on electron beam irradiation impact on minority carrier diffusion length in highly resistive π-type Ga₂O₃,¹⁸ an activation energy around 91 meV was identified. The relatively close values for the activation energies (72 meV, measured in this work, vs 91 meV, reported in Ref. 18) obtained for the different samples with the different majority hole concentrations suggest involvement of the same defect levels in both cases. At the same time, the lower value of ΔE_A,I reported here is likely related to the higher majority hole concentration for the material tested in this investigation.

The activation energy of ∼0.3 eV, associated with the impact of electron beam irradiation (injection) on CL emission intensity as reported in Ref. 19, was ascribed to gallium vacancy-related point defects.²⁷ These defects do not necessarily determine the p-type electrical conductivity in the sample but play a significant role in charge trapping effects. The relative proximity of the activation energies, previously obtained from the CL measurements for the same material, as studied in Ref. 19, and the EBIC measurements reported here suggest similarity of involved defect levels in both cases.

It should be finally noted that the recent results in n-type gallium oxide provide more information on the possible location of V_Ga-related traps.^30–32 In relation to these findings in the n-type material, more research is needed in still poorly investigated p-type gallium oxide.

Minority electron diffusion length measurements carried out in this work using the EBIC technique under various temperatures and durations of electron beam irradiation revealed a continuous decrease in L with increasing temperature and a continuous elongation of the same parameter with increasing duration of irradiation. Both trends are consistent with the previously published results for highly resistive π-type Ga₂O₃¹⁸ and indicate involvement of the same gallium vacancy-related levels in the majority hole conductivity. The lower value of ΔE_A,I reported in this work, as compared to Ref. 18, is likely related to the higher majority hole concentration for the material tested in this investigation. To conclude, the gallium vacancy-related acceptor concentration was estimated at N_A ∼ 1.8 × 10¹⁸ cm⁻³.

The research at UCF was supported in part by NSF (Grant Nos. ECCS2310285, ECCS2341747, and ECCS 2427262), US–Israel BSF (Award No. 2022056), and NATO (Award Nos. G6072 and G6194). 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, under Award No. HDTRA1-20-2-0002, monitored by Jacob Calkins. The present work is a part of “GALLIA” International Research Project, CNRS, France. GEMaC colleagues acknowledge financial support of French National Agency of Research (ANR), project “GOPOWER,” Grant No. CE-50 N0015-01. French and Israeli researchers acknowledge the collaborative PHC-Maimonide project N50047TD. The research at Tel Aviv University was partially supported by the US–Israel BSF (Award No. 2022056) and NATO (Award No. G6072).

The authors have no conflicts to disclose.

Leonid Chernyak: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Supervision (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Seth Lovo: Data curation (equal); Formal analysis (equal); Investigation (equal). Jian-Sian Li: Investigation (equal); Resources (equal). Chao-Ching Chiang: Investigation (equal); Resources (equal). Fan Ren: Methodology (lead); Project administration (lead); Resources (lead); Supervision (lead). Stephen J. Pearton: Conceptualization (lead); Formal analysis (lead); Funding acquisition (lead); Methodology (lead); Project administration (lead); Writing – original draft (lead); Writing – review & editing (lead). Corinne Sartel: Investigation (equal); Methodology (equal); Resources (equal). Zeyu Chi: Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal). Yves Dumont: Conceptualization (lead); Funding acquisition (lead); Methodology (lead); Resources (lead); Supervision (lead). Ekaterine Chikoidze: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Supervision (lead). Alfons Schulte: Investigation (equal); Resources (equal). Arie Ruzin: Investigation (equal); Resources (equal). Ulyana Shimanovich: Investigation (equal); Resources (equal).

The data that support the findings of this study are available within the article.