Anisotropic electrical properties of NiO_x/β-Ga₂O₃p-n heterojunctions on (01), (001), and (010) crystal orientations

There has been substantial recent interest in ultra-wide bandgap (UWBG) semiconductors, such as gallium oxide (β-Ga₂O₃), ¹⁾ aluminum nitride, ²⁾ diamond, ³⁾ and boron nitride ⁴⁾ for power electronics due to their large bandgaps and high critical field. These properties can result in higher operating voltages, larger currents, increased efficiencies, and smaller device footprint compared to devices based on traditional semiconductors such as silicon and wide bandgap semiconductors such as silicon carbide and gallium nitride. ⁵⁾ As an emerging UWBG material, β-Ga₂O₃ has attracted much attention for electronic and photonic device applications. ¹⁾ However, a significant challenge for β-Ga₂O₃ is its lack of p-type conductivity. Theoretical predictions indicate a difficulty in obtaining holes due to the high activation energy (>1 eV) of acceptors for β-Ga₂O₃. ⁶⁾ Moreover, due to the flat valence band maximum, the heavy hole effective mass leads to low hole mobility ⁷⁾ while holes tend to be localized in β-Ga₂O₃ as polarons due to lattice distortion. ⁸⁾ Thus, most reported β-Ga₂O₃ devices, such as field effect transistors ⁹⁾ and Schottky barrier diodes, ¹⁰⁾ are unipolar. The demonstration of p-n junctions in β-Ga₂O₃ is critical for the development of bipolar devices and advanced Ga₂O₃-based electronic devices.

Recently, p-NiO_x has emerged as a popular choice for the formation of β-Ga₂O₃ p-n heterojunctions due to its easy deposition and extensive use as a hole contact in high-efficiency solar cells. ^11,12) Kokubun et al. ¹³⁾ demonstrated the first NiO_x /β-Ga₂O₃ p-n heterojunction with Li-doped NiO_x epitaxial layer. Several NiO_x /β-Ga₂O₃ heterojunctions, including p-n diodes ^14–16) and junction barrier Schottky diodes ^17–19) have been demonstrated with excellent electrical characteristics, such as low on-resistance, high on/off ratio, and large reverse blocking voltage. Moreover, NiO_x /β-Ga₂O₃ heterojunctions are versatile with a wide range of applications, including edge terminations in β-Ga₂O₃ power diodes ²⁰⁾ and all-oxide-based UV photodetectors. ²¹⁾

The low crystal symmetry of monoclinic β-Ga₂O₃ results in highly anisotropic material with a direct impact on several key physical and electronic properties, such as dielectric constant, ²²⁾ thermal conductivity, ²³⁾ and electron mobility ²⁴⁾ which are different along different crystallographic directions. This anisotropy poses challenges for device fabrication and results in discrepancies in device performance. Fu et al. ²⁴⁾ compared Schottky contacts on $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(010)$ β-Ga₂O₃ planes and observed that the $(010)$ orientation had higher barrier height and lower reverse leakage. Sasaki et al. ²⁵⁾ reported that the rate of epitaxial growth on the $(100)$ plane was slower compared to the $(010)$ plane due to the low adhesion energy on $(100)$ terraces. Jang et al. ²⁶⁾ found that the etch rate and ability to form Ohmic contacts on $(\mathop{2}\limits^{\unicode{x00305}}01)$ plane was higher compared to $(010)$ plane owing to the higher density of oxygen dangling bonds. However, the anisotropic properties of the widely used NiO_x /β-Ga₂O₃ heterojunctions are not well understood. In this work, a systematic comparative analysis of NiO_x /β-Ga₂O₃ p-n heterojunctions with $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ substrate orientations has been carried out. Temperature-dependent electrical measurements, reverse recovery characteristics, and capacitance–frequency (C–f) measurements, were performed to provide a better understanding of the anisotropic nature of NiO_x /β-Ga₂O₃ p-n heterojunctions.

Figure 1(a) shows the crystal structure of β-Ga₂O₃ and the corresponding planes used as substrates for this study. These β-Ga₂O₃ planes are widely used for β-Ga₂O₃ devices. Previous literature has shown clear differences between $(\mathop{2}\limits^{\unicode{x00305}}01)$ [or $(001)$] and $\left(010\right)$ plane dangling bond densities, which were calculated to be 2.68 × 10¹⁵ [or 2.69 × 10¹⁵] and 1.74 × 10¹⁵ cm^–2, respectively. ²⁷⁾ Edge-defined film-fed grown $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ β-Ga₂O₃ substrates from Novel Crystal Technology were used for this study. ²⁸⁾ The substrates had similar n-type [Sn] doping concentrations of ∼5 × 10¹⁸ cm⁻³, similar thickness, and good crystalline quality, as verified by XRD measurements. To prepare the substrates, a standard cleaning procedure was implemented, which included cleaning with acetone, isopropyl alcohol, and deionized water, aided by sonication. The back contacts of Ti/Au (20/130 nm) were deposited using electron beam (E-beam) evaporation. followed by rapid thermal annealing at 500 °C in an N₂ environment. All back contacts showed very low contact resistance of <0.01 mΩcm². Standard photolithography was then performed to define circular patterns for the deposition of NiO_x and the anode (diameter of 300 μm). 200 nm NiO_x and the anode Ni/Au (20/130 nm) were deposited using E-beam evaporation, followed by a lift-off process. The fabricated device structure and device dimensions are shown in Fig. 1(b). The anode, cathode, and NiO_x layers were deposited simultaneously for all samples to avoid any inconsistencies in fabrication. All NiO_x layers were highly doped with a similar hole density of >2 × 18 cm^–3, and the Ohmic contacts to NiO_x layers had a similar contact resistance of ∼0.3 mΩcm². After device fabrication, all samples were annealed at 350 °C in N₂ ambient for 1 min. This annealing step was expected to improve the device performance by forming an Ohmic contact between the Ni/NiO_x interface and reducing the number of interface states at the NiO_x /β-Ga₂O₃ heterojunction. ²⁹⁾

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Electrical characterization was conducted using a probe station equipped with a controllable thermal chuck, Keithley 4200-SCS parameter analyzer, and ultra-fast pulse measurement units. Cross-sectional transmission electron microscope (XTEM) images were taken for all samples. The TEM samples were prepared using a Thermo Fisher Helios 5UX Dualbeam system with final thinning in a Gatan precision ion-polishing system. The milling started with a Ga-focused ion beam at 30 keV, followed by thinning at 5 and 2 keV, and subsequent Ar-ion thinning at 2 and 1 keV. Devices with $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ β-Ga₂O₃ substrate normals were imaged along their respective [010], [100] and [001] zone axes. High-resolution TEM (HRTEM) images were taken using a Philips CM 200 operated at 200 kV and an image-corrected FEI Titan 80–300 operated at 300 kV. Figure 1(c) shows an XTEM image of the full diode structure consisting of the top electrode (Au, Ni), NiO_x, and β-Ga₂O₃ substrate. Figures 1(d)–1(f) show HRTEM images of the NiO_x /β-Ga₂O₃ interface for samples grown on $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001)$ and $(010)$ substrates, respectively. The polycrystalline nature of NiO_x layers was evident in HRTEM images, and abrupt NiO_x /β-Ga₂O₃ interfaces were clearly visible.

Figure 2(a) shows I–V curves for the three NiO_x /β-Ga₂O₃ p-n diodes, where the turn-on voltages were 2.09, 2.22, and 2.50 V for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ substrates, respectively. Devices on $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ planes had excellent rectification ratios of ∼10¹⁰ at ±3.75 V. However, $(010)$ devices showed a smaller on/off ratio of about ∼10⁹ at ±3.75 V. Furthermore, devices on $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ planes exhibited specific on-resistances of 2.92 and 1.55 mΩcm², while the $(010)$ device showed a specific on-resistance of 6.50 mΩcm². Ideality factors were 1.95, 2.03, and 2.13 for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ planes, respectively. These large ideality factors indicate that the current recombination in the heterojunction is dominant compared to diffusion currents.

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The C–V measurements were performed at a frequency of 100 kHz [Fig. 3(a)], and the devices showed built-in potentials of 2.72, 2.74, and 2.63 V on $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ devices, respectively [Fig. 3(b)]. The built-in voltages were comparable in all three devices since there is no current transport through the devices in C–V measurements. The built-in voltages determined by I–V and C–V measurements showed some discrepancies. In general, C–V measurements are mainly affected by the doping concentration of NiO_x and β-Ga₂O₃, as well as the charges from the interface states. However, they do not provide information about the current conduction through the interface. Conversely, extraction of built-in voltage through I–V measurements is influenced by the crystal anisotropy and interface states. The effective carrier concentration (${N}_{d}-{N}_{a}+{N}_{{t}}$ ) ³⁰⁾ calculated from the C–V measurements was 4.7 × 10¹⁸, 4.5 × 10¹⁸, 1.6 × 10¹⁸ cm^–3 for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ devices, respectively, where ${N}_{d}$ is the ionized donor concentration, ${N}_{a}$ is the ionized acceptor concentration, and ${N}_{t}$ is the equivalent charge concentration of traps. Since the β-Ga₂O₃ and NiO_x film in the three samples had similar carrier concentrations, the observed variation in the effective carrier concentrations is likely related to the different NiO_x /β-Ga₂O₃ heterojunction interfaces caused by the crystal anisotropy, which is verified by C–f measurements.

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Figures 3(c)–3(e) show C–f measurements for the devices on $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ substrates to evaluate the interface trap state density (${D}_{{\rm{it}}}$). The C–f measurements are fitted using the equations below, assuming the interface states are distributed in two energy levels. ^31,32)

$$\begin{eqnarray}&&C={C}_{{\rm{sc}}}+\frac{{C}_{{\rm{it}}-1}}{{(1+2\pi f{\tau }_{1})}^{2}}+\frac{{C}_{{\rm{it}}-2}}{{(1+2\pi f{\tau }_{2})}^{2}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{D}_{{\rm{it}}}={C}_{{\rm{it}}}/{q}^{2}A\end{eqnarray} \tag{ 2 }$$

where ${C}_{{\rm{sc}}}$ is the capacitance of the space charge region, and ${C}_{{\rm{it}}-1}$(${C}_{{\rm{it}}-2}$) is the capacitance of the first state (second state) with their corresponding relaxation time ${\tau }_{1}$ (${\tau }_{2}$). ${C}_{{\rm{it}}-1}$ represents an energy level that corresponds to interface states closer to the conduction band with a smaller relaxation time, and ${C}_{{\rm{it}}-2}$ represents a deep energy level with a considerably larger relaxation time. A similar ${C}_{{\rm{it}}-2}$ of ∼2 × 10⁻¹² F was observed with a relaxation time of about ∼8 μs for all devices. This may represent deep-level states (e.g., vacancies) with relaxation time much larger than the interface states. However, ${C}_{{\rm{it}}-1}$ varied significantly for devices on different crystal orientations. The relaxation time for ${C}_{{it}-1}$ was 0.64, 0.43, and 0.34 μs for $(201),$ $(001),$ and $(010)$ devices, respectively, which are consistent with previous reports. ^31,32) ${C}_{{\rm{it}}-1}$ changed with crystal orientation, while ${C}_{{\rm{it}}-2}$ remained relatively constant. It should be noted that the exact nature of the defect states in NiO_x /β-Ga₂O₃ diodes is still unclear and demands further investigation. The extracted interface trap densities (${D}_{{\rm{it}}-1}$) from ${C}_{{\rm{it}}-1}$ were 4.3 × 10¹⁰, 7.4 × 10¹⁰, and 1.6 × 10¹¹ eV^–1cm^–2 for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ devices, respectively. ^29,31,32) The interface states derived from ${C}_{{\rm{it}}-1}$ are much closer to the conduction band, and thus may play an important role in the device performance. Table I summarizes all the parameters extracted through C–f curve fitting.

Table I. Interface state parameters extracted from C–f curve fitting.

Orientation	${C}_{{\rm{it}}-1}$ (F)	${C}_{{\rm{it}}-2}$ (F)	${\tau }_{1}$ (s)	${\tau }_{2}$ (s)	${D}_{{\rm{it}}-1}$ (eV–1cm–2)	${D}_{{\rm{it}}-2}$ (eV–1cm–2)
$(\mathop{2}\limits^{\unicode{x00305}}01)$	4.80 × 10–12	2.50 × 10–12	0.64 × 10–6	8.69 × 10–6	4.3 × 1010	2.2 × 1010
$(001)$	8.36 × 10–12	2.27 × 10–12	0.43 × 10–6	8.57 × 10–6	7.4 × 1010	2.0 × 1010
$(010)$	1.79 × 10–11	1.62 × 10–12	0.34 × 10–6	8.02 × 10–6	1.6 × 1011	1.4 × 1010

The differences in electrical properties of NiO_x /β-Ga₂O₃ p-n heterojunctions can be attributed to several factors. First, the difference in interface states may be significantly promoted by the density of dangling bonds. If the number of dangling bonds is high, then the adhesion of the NiO_x layer is promoted, exhibiting fewer interface states. Due to the higher dangling bond density in $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ plane, it is easier to form better-quality NiO_x /β-Ga₂O₃ heterojunction with high surface energy. ²⁷⁾ This is analogous to the fact that forming Ohmic contacts on $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ planes is easier than on $(010)$ plane. ²⁶⁾ Second, different doping concentrations can be induced in the heterojunction due to interface states. The interface states can have a big impact on net charge density. It is likely that there are lower compensating trap states in $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ NiO_x /β-Ga₂O₃ p-n heterojunctions as indicated by the C–f measurement, contributing larger net charge densities. This is further evidenced by the different gradients in the 1/C² –V plot. The observed differences are primarily influenced by the presence of interface states, considering three NiO_x and β-Ga₂O₃ in the three samples had similar carrier concentrations. As discussed later, a difference in reverse recovery time (${t}_{{\rm{rr}}}$) of the devices was observed, indicating that carrier recombination on different planes is affected by the crystal anisotropy.

The temperature-dependent forward characteristics of three NiO_x /β-Ga₂O₃ p-n diodes are presented in Figs. 4(a)–4(c). The observed temperature-dependent behavior was stable and reproducible, and the initial I–V curves were retained even after heating and cooling down, indicating excellent thermal stability of the heterojunction. ^16,29) The device ideality factor and turn-on voltage were extracted as a function of temperature, as shown in Figs. 4(d)–4(f). The turn-on voltage decreased linearly with the temperature, which can be attributed to the reduction of depletion width facilitating diffusion of holes. ³³⁾ The ideality factor varied between 1.95–3.77, 2.03–2.95, and 2.13–4.47 in $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ devices, respectively. This behavior of turn-on voltage and ideality factor is consistent with previous reports. ^29,33) The ideality factor of $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ devices remained almost constant under high temperatures. However, the ideality factor in $(010)$ devices first increased and then decreased. This behavior can be attributed to the fact that there are 10 times more interface trap states in $(010)$ heterojunction compared to $(\mathop{2}\limits^{\unicode{x00305}}01)$ and $(001)$ heterojunctions. With increasing temperature, the carrier emission from interface traps is enhanced, affecting the ideality factor.

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The ${t}_{{\rm{rr}}}$ of the diode is defined as the time it takes to reach 0.25${I}_{M}$ after switching off, where ${I}_{M}$ is the maximum current during the reverse recovery period. The ${t}_{{\rm{rr}}}$ of the diodes is affected by several factors, including the doping concentration, the width of the depletion region, crystal anisotropy, and the applied voltage. In this work, all three samples were subject to voltages of ±5 V to observe the reverse recovery of the diode. The $\left(\mathop{2}\limits^{\unicode{x00305}}01\right)$ and $(001)$ devices had a ${t}_{{\rm{rr}}}$ of 68 ns, while (010) devices took 62 ns to recover [Fig. 5(a)]. The shorter reverse recovery time for $(010)$ is likely due to larger interface defect densities that promote electron/hole recombination with a faster recovery time and mobility variation along different crystal orientations. All devices had a peak current of about 86 mA and showed temperature independence ³³⁾ in reverse recovery time, as shown in Fig. 5(b), where the y-axis is offset for clarity. This indicates that the junction capacitance and stored charges in the depletion region are independent of temperature. The forward current during the reverse recovery test was ∼6 mA. Additionally, the ${di}/{dt}$ of three samples for the reverse recovery characteristics was 3.95 A μs⁻¹, which is comparable to previously reported values. ³³⁾ The reverse recovery charge was 4.47, 4.54, and 4.26 nC for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ devices, respectively. The different ${t}_{{\rm{rr}}}$ in different crystal orientations indicate carrier recombination is influenced by the interface states. Table II summarizes the device parameters of the three NiO_x /β-Ga₂O₃ p-n heterojunctions, where ${D}_{{\rm{it}}}$ of the devices is based on the dominant ${D}_{{\rm{it}}-1}$ values.

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Table II. Electrical properties of the NiO_x /β-Ga₂O₃ p-n diode heterojunctions grown on $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ substrates.

Orientation	Von(I–V) (V)	Vbi(C–V) (V)	Rsp-on(mΩcm2)	on/off ratio	η	${t}_{{\rm{rr}}}$ (ns)	${D}_{{\rm{it}}}$ (eV–1cm–2)
$(\mathop{2}\limits^{\unicode{x00305}}01)$	2.09	2.74	2.92	1010	1.95	68	4.3 × 1010
$(001)$	2.22	2.72	1.55	1010	2.03	68	7.4 × 1010
$(010)$	2.50	2.63	6.50	109	2.13	62	1.6 × 1011

In conclusion, NiO_x /β-Ga₂O₃ p-n heterojunctions fabricated on $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ substrates showed considerable differences in electrical properties in terms of turn-on voltages, ideality factor, on-resistance, and reverse recovery time. The (010) device exhibited the highest turn-on voltage of 2.50 V, the highest ideality factor of 2.13, the largest on-resistance of 6.50 mΩcm², and the lowest recovery time of 62 ns. The C–f measurements indicate an interface trap density of 4.3 × 10¹⁰, 7.4 × 10¹⁰, and 1.6 × 10¹¹ eV^–1cm^–2 for $(\mathop{2}\limits^{\unicode{x00305}}01),$ $(001),$ and $(010)$ plane devices, respectively. All devices were fabricated simultaneously and exhibited excellent rectifying behaviors with a high on/off ratio of ≥10⁹ and high-quality interfaces between NiO_x and β-Ga₂O₃, as confirmed by HRTEM. These differences in device electrical properties are attributed to the different atomic configurations, the density of dangling bonds, and interface trap state densities. These results indicate the anisotropic nature of β-Ga₂O₃ in heterojunction-based p-n diodes and should serve as a valuable reference for future development of Ga₂O₃ heterojunction bipolar devices.

Acknowledgments