Leakage Current by Poole–Frenkel Emission in Pt Schottky Contacts on () β-Ga₂O₃ Grown by Edge-Defined Film-Fed Growth

Two pieces of () β-Ga₂O₃ substrates were prepared from a bulk crystal grown by the EFG method in this study. The Ga₂O₃ powder 99.995% in purity was used as the source material. The crystal was grown in the <010> direction, with a growth rate adjusted to 6–10 mm/h, in the atmosphere mixture of argon and carbon dioxide. After cutting the substrates about 1 mm in thickness and 10 × 10 mm² in size, a high temperature annealing at 1500 °C was performed in air for 48 hours to reduce residual stress in the crystal and improve their crystalline quality. And the surfaces of the substrates were treated by a double-side chemical mechanical polishing (CMP) process. Vertical SBDs were fabricated using one piece of the substrates. First, the substrate was cleaned with acetone and isopropanol, followed by a 4-cycle deionized (DI) water rinse and N₂ blow drying. After that, ohmic metal was deposited on back side of the sample by blanket evaporation of Ti/Au (50 nm/250 nm). To facilitate the formation of a good ohmic contact between Ti and β-Ga₂O₃, a rapid thermal annealing at 850°C for 30 seconds in a N₂ ambient was performed. Then, a Pt/Ti/Au (50 nm/50 nm/150 nm) metal stack was evaporated on the front side of the sample and patterned using a liftoff process, serving as the Schottky electrodes. Fig. 1 schematically illustrates the device structure of the fabricated SBDs. The diameter of the circular Schottky contacts was 200 μm. The sample was attached onto a copper plate by using conductive silver paste and a Keithley 4200 parameter analyzer was employed for the current–voltage (I-V) and capacitance-voltage (C-V) characterization. The I-V-T measurements were performed under a vacuum of ∼ 10⁻⁴ Pa.

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Fig. 2 shows the typical I-V characterization of a fabricated Pt/β-Ga₂O₃ SBD at 300 K. The device exhibited a good rectification characteristic with a reverse leakage current density of ∼10⁻³ A/cm² at a reverse bias of −20 V and a forward current density reaching 320 A/cm² at a forward bias of 3.7 V. The ideality factor n_s, the Schottky barrier height ϕ_B, and the series resistance R_S were extracted from the forward I-V curve by using the following thermal emission (TE) model.

where S is the area of the Schottky barrier contact, A^* is effective Richardson's constant (33.7 A cm⁻² K⁻²),¹⁵ q is the electron charge. The n_s, ϕ_B, and R_S were estimated to be 1.81, 1.27 eV, and 5.56 mΩ·cm², respectively. The observed Schottky barrier height was lower than the theoretical value based on the electron affinity of Ga₂O₃ ∼ 4.00 eV¹⁵ and the work functions of Pt ∼ 5.93 eV.¹⁶ Besides, the ideality factor was much larger than unity. These could be due to the interface traps within the Schottky contacts and the barrier inhomogeneities.^15,17 Fig. 3 shows the C-V characteristics for the fabricated devices measured at 100 kHz under 300 K. The effective donor concentration (N_d – N_a) in the sample was extracted to be ∼ 4.03 × 10¹⁷ cm⁻³ from the linear fitting curve in the inset of Fig. 3. Apart from the shallow donor impurities like Si and Sn, it has been reported that plenty of oxygen vacancies usually exist within the β-Ga₂O₃ crystals and contribute to their n-type conductivity.^8,18 The built-in voltage was extracted to be 2.42 V, which was much higher than the I-V determined schottky barrier height. This behavior was resulted from the existence of the defects in Ga₂O₃ and the barrier inhomogeneities in a noideal diode. Similar phenomenon was also observed by Yao et al.,¹⁹ which was associated with the observed large ideality factor in previous I-V results.

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In order to reveal the crystal defects near the surface of () β-Ga₂O₃ substrates, we carried out a wet etching process using the other piece of sample and observed its etch pits. The sample was first immersed in a 30% KOH solution at 90°C for 1 h. Then the etched surface was characterized by scanning electron microscopy (SEM). As shown in Fig. 4, etch pits with a distinctive shape can be clearly observed. The defects density of the () β-Ga₂O₃ substrates used in this study was estimated to be ∼ 2 × 10⁵ cm⁻². The KOH etched pits in our study were slightly different from those etched by H₃PO₄.^9–11 We considered that these high-density defects must give rise to the reverse leakage current and the inhomogeneous barrier heights in the fabricated SBDs.

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Fig. 5a shows the reverse I-V-T characteristics of the Pt/β-Ga₂O₃ SBD measured in a temperature range of 300 K to 425 K. The leakage current was observed to increase rapidly with the increase of both bias voltage and temperature, indicating an electric-field-enhanced thermal emission of the electrons within the reverse-biased Pt/β-Ga₂O₃ SBDs. We employed a PFE model to analyze the leakage mechanisms in the device. The PFE refers to the emission of electrons via a trap state into a continuum of electron states, which could be associated with the presence of defects.^20–23 The PFE-governed leakage current density is given by

where E_b is the electric field in the semiconductor barrier at the metal-semiconductor interface, ϕ_t is the barrier height of electron emission from the trap states, ε_r is the high-frequency relative dielectric constant, and C is a constant. As discussed in Ref. 22, r is the degree of compensation ranging from 1 to 2 depending on the position of Fermi level. Fig. 5b plots the log(J/E_b) versus for the Pt/β-Ga₂O₃ SBD measured at various temperatures. The linear dependence of log(J/E_b) on is a proof for the PFE mechanism of the leakage current in the devices, as expressed by

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The m(T) and b(T) are plotted as functions of q/kT in Fig. 6. As defined in Eqs. (3c) and (3d), ε_r and ϕ_t can be calculated from the slop of m(T) and b(T) versus q/kT, respectively. Considering the β-Ga₂O₃ substrates in the experiment are relatively defective, it is fairly safe to choose r = 1 in the calculation.²³ The obtained ε_r is 4.42, in good agreement with the reported value 3.91 for β-Ga₂O₃.²⁴ From Fig. 6b, ϕ_t is calculated to be 0.7 V, suggesting that the trap states are probably located at ∼0.7 eV below the conduction band in the () β-Ga₂O₃ substrates. Quite similarly, deep-level defects located at ∼ 0.8 eV below the conduction band have been recently revealed in the EFG-grown unintentionally-doped β-Ga₂O₃ by a steady-state photo-capacitance spectroscopy.^25,26 These results further evidence the validity of using PFE model to describe the leakage current in our study. Therefore, it can be concluded that emission of electrons from metal into the defects-related trap states should be the dominant leakage mechanism in the Pt/β-Ga₂O₃ SBDs in the temperature range of 300 K to 425 K.

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In summary, we fabricated Pt/β-Ga₂O₃ SBDs on an EFG-grown () substrate and investigated the leakage current transport mechanism across the Schottky contacts through an I-V-T measurement. The fabricated SBDs showed a higher Schottky barrier height extracted by C-V measurement than that by I-V measurement, and a much larger ideality factor than one, indicating the existence of interface traps and the distribution of defect-induced barrier inhomogeneities of the devices. In the temperature range of 300 K to 425 K, the reverse leakage current could be well described by the PFE model, indicating a dominant leakage mechanism of the Pt/β-Ga₂O₃ SBDs by the emission of electrons via the detect-related trap states that located near the metal-semiconductor interface. The energy level of the defect-related trap states was deduced to be ∼0.7 eV below the conduction band for the EFG-grown () β-Ga₂O₃ substrates.

This work was supported in part by the Frontier and Key Technological Innovation Foundation of Guangdong Province under grant No. 2017A050506039, the International Science and Technology Cooperation Program of Guangzhou under grant No. 201807010093 and the National Natural Science Foundation of China under grant 11505140, 11375144 and 61621001.

Leidang Zhou 0000-0003-3052-5556

Xing Lu 0000-0001-5808-9552