Ultrawide bandgap vertical β-(Al_xGa_1−x)₂O₃ Schottky barrier diodes on free-standing β-Ga₂O₃ substrates

Ultrawide bandgap (UWBG) semiconductors have garnered considerable attention in recent years due to their promising applications in power electronics, optoelectronics, and RF electronics.^1–8 β-Ga₂O₃ is a promising candidate for UWBG semiconductors due to a high breakdown field of 8 MV/cm and a large bandgap of 4.6–4.9 eV, and a high Baliga's figure of merit (BFOM) compared with GaN and SiC.⁹ Furthermore, due to the availability of large native substrates, β-Ga₂O₃ has great potential for cost-effective high-voltage power electronics.¹⁰ Moreover, alloying Ga₂O₃ with Al₂O₃ can produce (Al_xGa_1−x)₂O₃ with increased bandgap (e.g., 4.8–6.2 eV for x = 0 to 0.71).¹¹ β-(Al_xGa_1–x)₂O₃ is a monoclinic ternary alloy that is expected to have a higher BFOM than Ga₂O₃, making it more suitable for power electronic applications.³ Recently, there have been several optoelectronic and power devices demonstrated using β-(Al_xGa_1–x)₂O₃. Chen et al.¹² reported the effect of O₂ concentration on sputtered (Al_xGa_1–x)₂O₃ films for deep UV photodetectors. β-(Al_xGa_1−x)₂O₃/Ga₂O₃ heterojunction modulation-doped field effect transistors (MODFETs) have been extensively studied.^13–19 Zhang et al.¹⁵ reported record low-temperature mobility of ∼2700 cm²/V s in the β-(Al_xGa_1−x)₂O₃/Ga₂O₃ heterostructure. Furthermore, Okumura et al.¹³ demonstrated β-(Al_xGa_1−x)₂O₃ metal–semiconductor field effect transistors (MESFETs). However, most of these power devices are lateral devices where the currents flow laterally, and voltages are handled laterally. These lateral devices usually underperform compared with their material limits. In commercial Si and SiC power devices, vertical architecture dominates, especially for high-voltage high-power applications, due to larger current and voltage handling capability, avalanche capability, no surface-related issues, better heat dissipation, and smaller chip area.

To date, there are very few reports of vertical β-(Al_xGa_1−x)₂O₃ devices. One of the major challenges is growing high-quality β-(Al_xGa_1−x)₂O₃ layers with high Al contents [e.g., >20% on (010) β-Ga₂O₃ substrates].¹³ This is because β-Ga₂O₃ crystallizes in a monoclinic structure, and Al₂O₃ prefers a conundrum structure, leading to phase separation at high Al contents.²⁰ Furthermore, due to the lattice mismatch with sufficiently high Al composition, epitaxial growth of β-(Al_xGa_1−x)₂O₃ on β-Ga₂O₃ is challenging. Moreover, Schottky and Ohmic contact behavior on β-(Al_xGa_1−x)₂O₃ needs to be further understood comprehensively. However, Ohmic and Schottky contact behavior on β-Ga₂O₃ is extensively investigated in the past few years.^21,22 Jadhav et al.²³ investigated temperature-dependent barrier height inhomogeneity in β-Ga₂O₃ Schottky barrier diodes (SBDs). Ahmadi et al.²⁰ found Schottky barrier heights of Ni to β-(Al_xGa_1−x)₂O₃ with different Al compositions, which was attributed to the lateral fluctuation of Al alloy composition. Furthermore, β-(Al_xGa_1−x)₂O₃ power devices suffer from low breakdown voltages and high leakage current. A systematic investigation of the leakage mechanism and the temperature-dependent characteristics of β-(Al_xGa_1−x)₂O₃ devices are still lacking. In this work, we demonstrate vertical β-(Al_xGa_1−x)₂O₃ (x = 0.21) SBDs on free-standing (edge-defined film-fed grown) highly doped (010) β-Ga₂O₃ substrates and systematically investigate their temperature-dependent forward and reverse electrical characteristics. Different models have been used to comprehensively understand the leakage mechanisms of the vertical β-(Al_xGa_1−x)₂O₃ SBDs. This work can serve as an important reference for the design of high-voltage high-power vertical β-Al_x(Ga_1−x)₂O₃ power devices.

200 nm β-(Al_xGa_1−x)₂O₃ (x = 0.21) layer was grown using molecular beam epitaxy (MBE) on the edge-defined film-fed grown (010) β-Ga₂O₃ substrate (Fig. 1) by Novel Crystal Technology, Inc, Japan. During the MBE growth, Ga and Al are evaporated from effusion cells in RF-generated oxygen plasma to form β-(Al_xGa_1−x)₂O₃ thin films.^24,25 The Al composition of the grown film can be estimated by the shift of β-Ga₂O₃ and β-(Al_xGa_1−x)₂O₃ (020) peak from XRD spectra.²⁶ More details about the MBE growth and Al content determination can be found elsewhere.^24–26 The β-Ga₂O₃ substrate is heavily doped with [Sn] = 3.1 × 10¹⁸ cm⁻³, while Si doping concentration in β-(Al_xGa_1−x)₂O₃ layer was estimated to be 2.0 × 10¹⁷ cm⁻³. Atomic force microscopy (AFM) suggested a film surface RMS roughness of 2.6 nm [Fig. 1(d)], and x-ray diffraction (XRD) confirmed the (020) β-(Al_xGa_1−x)₂O₃ peak [Fig. 1(b)] of the film. The device fabrication started with sample cleaning using acetone, isopropyl alcohol (IPA), and distilled water. Then, a 200 nm Ni hard mask was deposited by electron beam (E-beam) evaporation on the film using standard photolithography and liftoff. This Ni hard mask protects the etching of β-(Al_xGa_1−x)₂O₃ during mesa-isolation of the devices. Next, SF₆ inductive-coupled plasma reactive ion etching (ICP-RIE) was performed at 400 W until a mesa depth of 300 nm was obtained. The Ni hard mask was removed using a Ni etchant, followed by sample cleaning using HF and H₂SO₄ to remove the etching damage induced by the ICP-RIE dry etching. Then, Ti/Au (20/130) nm cathode (Ohmic contact) was deposited at the back side of the β-Ga₂O₃ substrate using E-beam evaporation followed by 500 °C rapid thermal annealing (RTA) in N₂ environment. Finally, Pt/Ti/Au (20/10/120) nm anode (Schottky contact) was deposited by E-beam evaporation and formed using standard photolithography and liftoff. Figure 1(a) shows the schematic of the fabricated vertical β-(Al_xGa_1−x)₂O₃ SBDs on the β-Ga₂O₃ substrate. The diameter of the SBD (ϕ) is 100 μm. Current density-voltage (J–V) measurements of the fabricated devices were measured using a probe station with a hotplate and a Keithley 2470 source meter. Capacitance-voltage (C–V) measurements were performed on a Hewlett-Packard 4275A LCR meter.

Figures 2(a) and 2(b) show the forward characteristics of the vertical β-(Al_xGa_1−x)₂O₃ SBD at room temperature. The device exhibited a turn-on voltage of ∼1.5 V, a specific on-resistance of 3.4 mΩ cm² at +5 V, and an on/off ratio of ∼10⁹. The C–V measurements were performed at room temperature using 1 MHz frequency. Figure 2(c) indicates a carrier concentration of 2.8 × 10¹⁷ cm⁻³ in the β-(Al_xGa_1−x)₂O₃ film, which is close to the nominal Si doping. The temperature-dependent forward J–V characteristics of the device are presented in Fig. 2(d). The measured electrical characteristics are quite stable and reproducible among many devices across the wafer. The devices after high-temperature testing retain the initial J–V curves even after cooling down to room temperature. Using the diode thermionic emission (TE) model, the Schottky barrier height $(φb)$ and ideality factor $(n)$ of the vertical β-Al_x(Ga_1−x)₂O₃ SBD can be calculated. For $V>3kT$⁠, the TE model can be expressed as²⁷ 

where J is the current density, $Js$ is the saturation current density, $A∗$ is the Richardson constant, T is the temperature in kelvin, q is the electron charge, $φeff$ is the effective Schottky barrier height, n is the ideality factor, k is the Boltzmann constant, $m∗$ is the effective electron mass, and h is the Planck constant.

Figure 3 shows the Schottky barrier heights and ideality factors of the vertical β-(Al_xGa_1−x)₂O₃ SBD calculated using the TE model. It should be noted that the Richardson constant of 37.8 A/cm²K² was calculated using the reported effective electron mass of 0.313m₀ (Ref. 3) for β-(Al_xGa_1−x)₂O₃. With increasing temperature, $φeff$ varied from 0.91 to 1.18 eV, while n changed from 1.8 to 1.1 [Fig. 3(a)]. There is a clear temperature dependence of both parameters, which stems from the inhomogeneous metal/semiconductor interface.^28,29 In Fig. 3(b), a linear correlation between $φeff$ and n was observed, which is a well-known phenomenon in the presence of an inhomogeneous Schottky contact. In the metal/semiconductor interface, there are regions with low and high Schottky barrier heights. At low temperatures, electrons can only pass through low Schottky barrier height regions, whereas at high temperatures, electrons gain momentum to cross high Schottky barrier height regions. As a result, the Schottky barrier height increased with temperature. To further investigate this behavior, the Schottky barrier height can be considered a Gaussian distribution of potential with a mean barrier height $φb¯$ and a standard deviation $σ$⁠, and the barrier is linearly dependent on voltage as follows:

where $φb0$ and $σ0$ are the values at zero bias, and the coefficients $γ$ and $ξ$ represent the voltage-induced deformation of the Schottky barrier distribution.³⁰ Substituting Eqs. (5) and (6) into Eq. (4) and combining Eqs. (1) and (2), the ideality factor can be written as^31–33 

Therefore, Eq. (7) implies ideality factor becomes temperature-dependent, and its value can exceed unity. The voltage dependence of the Schottky barrier height and ideality factor was attributed to the interfacial states at the metal/semiconductor interface. These states become more negative with applied forward bias, leading to an increase in the Schottky barrier height with bias and ideality factor greater than unity.³² This voltage dependency of the Schottky barrier height can be interpreted as image force shifting the Schottky barrier maxima away from the metal–semiconductor into the semiconductor as the forward bias increases.³³ Furthermore, theoretical derivations suggest that both $φeff$ and $(n−1−1)$ are linear functions of inverse temperature $(1/T)$⁠, which is in good agreement with the experimental results in Figs. 3(c) and 3(d). The extracted $φb0¯$ and $σ0$ were 1.81 and 0.18 eV, respectively. It is reported that Pt on (010) β-Ga₂O₃ has an ideal Schottky barrier height of up to 1.93 eV.³⁴ This work shows the mean Schottky barrier height at zero bias is 1.81 ± 0.18 eV, which is consistent with the ideal value.

It should be noted that the C–V measurements did not correctly estimate the barrier height from Fig. 2(c). This discrepancy is likely due to two reasons. First, there is frequency dispersion in the C–V measurements in WBG semiconductors. Due to this, the frequency that uses for the C–V measurements may not be the ideal frequency to measure the barrier height. At a particular frequency, some impurity states or donor states respond slowly to the applied AC electric field. To study this effect, frequency dispersion C–V needs to be measured, which is out of the scope of this study. Second, the interfacial states between the metal and the semiconductor are insensitive to C–V measurements at low voltages. The inhomogeneity at the metal/semiconductor interface lowers the accuracy of the C–V measurements, which increases the uncertainty of the measured barrier height. However, barrier height measured from the J–V measurements are quite reliable as it represents the current flowing through the inhomogeneous Schottky barrier.

Figure 4(a) shows the temperature-dependent reverse J–V characteristics of the vertical β-(Al_xGa_1−x)₂O₃ SBD. The reverse leakage current increased with increasing temperature. Figure 4(b) represents the current density as a function of 1/T at different reverse voltages. Different gradients in Fig. 4(b) corresponded to different leakage mechanisms. Figure 4(c) shows potential leakage mechanisms for SBDs. Different temperature regimes activate different processes inside the semiconductor, which can be investigated from the reverse J–V measurements. Due to the high Schottky barrier height of >1 eV in the vertical β-(Al_xGa_1−x)₂O₃ SBD, TE or thermionic field emission (TFE) is unlikely to be a major contributor to the reverse leakage of the device. The possible candidates for the vertical β-(Al_xGa_1−x)₂O₃ SBD include Poole–Frenkel emission (PFE), trap-assisted tunneling (TAT), Fowler–Nordheim tunneling (FNT), field emission (FE), and variable range hopping (VRH). More details about these processes can be found elsewhere.^35–41 To identify the dominant process, fitting the reverse leakage data using the mathematical expression of each model is widely used. It was found that two dominant mechanisms were PFE and TAT, while the other mechanisms played a minor role.

The PFE is a trap-mediated transport mechanism where the carrier density depends exponentially on the activation energy of the traps, and the current density due to PFE is given by⁴¹ 

where E is the electric field in the β-(Al_xGa_1−x)₂O₃ layer, $φt$ is the barrier height for electron emission from a trap state, $εs$ is the high-frequency relative dielectric permittivity, $ε0$ is the permittivity of free space, C is a proportionality constant, and k is the Boltzmann constant. It should be noted that the high-frequency (optical) dielectric constant, rather than the static one, should be used in the PFE equation.⁴¹ Electrons can move slowly through an insulator or a semiconductor in the presence of a large electric field. Initially, electrons are in a localized or trap state and cannot move freely. With a high electric field, these localized electrons can be promoted to the conduction band and contribute to leakage currents. These electrons can move through the crystal before relaxing into another localized state. In other words, the PFE model describes an electric-field enhanced emission from a trap state which increases reverse leakage. From Eq. (8), $ln⁡(JE)$ is a linear function of $E$⁠,

Figure 5(a) indicates the PFE plot for the vertical β-(Al_xGa_1−x)₂O₃ SBD between 373 and 473 K. The transport model based on the PFE in Eq. (9) shows a good agreement with the experimental data in this temperature regime with consistent Schottky barrier height and dielectric constant. Figure 5(b) shows the temperature-dependent slope $m(T)$ and intercept $b(T)$ extracted from Fig. 5(a). Both $m(T)$ and $b(T)$ are linear functions against inverse temperature, which is expected in the PFE model. The extracted dielectric constant $εs$ and the emission barrier height $φt$ for the device were $εs=8.2$ and $φt=1.06eV$⁠, which are consistent with experimental results.^1,14,42 The obtained $φt$ is comparable with the extracted values from the TE model. These results indicate that the PFE mechanism is dominant at high temperatures (>373 K).

Below 373 K, the leakage current of the vertical β-(Al_xGa_1−x)₂O₃ SBD deviated from the PFE model and leaned toward the TAT model. In the TAT model, an electron in the metal could be activated to a trap state at the metal/semiconductor interface and then tunnel to the semiconductor side.^43,44 This model can be expressed by

where $φt$ is the barrier height for electron emission from a trap state, $m∗$ is effective electron mass, C is a proportionality constant, and $ℏ$ is the reduced Planck's constant. The equation can be rearranged to find the $φt$ from the measured reverse leakage current,

Figure 5(c) shows the measured and theoretical TAT plots for the vertical β-(Al_xGa_1−x)₂O₃ SBD between 298 and 353 K. The extracted barrier height for electron emission from a trap state $(φt)$ was between 0.92 and 1.1 eV. At low temperatures, electrons can tunnel through the Schottky barrier height with the assistance of traps. With enough thermal energy at high temperatures, they can escape from the trap levels and transport under high electric fields (i.e., the PFE model). For high-voltage applications, growing thick β-(Al_xGa_1−x)₂O₃ is needed and demands further research and development.

We demonstrated vertical β-(Al_xGa_1−x)₂O₃ SBDs on free-standing (010) β-Ga₂O₃ substrates. The device exhibited excellent forward rectifying behaviors with a high on/off ratio of ∼10⁹, a turn-on voltage of 1.5 V, and an on-resistance of 3.4 mΩ cm². Temperature dependence of the Schottky barrier height and ideality factor was due to the inhomogeneous metal/semiconductor interface. This interface inhomogeneity was explained by considering the Schottky barrier height as a Gaussian distribution with a mean Schottky barrier height of 1.81 eV at zero bias with a standard deviation of 0.18 eV. Comprehensive reverse leakage analysis indicated that PFE and TAT mechanisms were the main contributors to the reverse leakage currents of the device. The extracted physical parameters from the PFE and TAT models are consistent with experimental results. This work can serve as an important reference for the future development of β-(Al_xGa_1−x)₂O₃ based electronics and photonics for high-power, high-voltage, and ultraviolet (UV) photonic applications.

Research supported as part of the ULTRA, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0021230 (computational study) and by the National Science Foundation (NSF) under Award No. 2302696 (experimental study and data analysis).

The authors have no conflicts to disclose.

Dinusha Herath Mudiyanselage: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Dawei Wang: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Validation (equal). Houqiang Fu: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead).

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