Electrical Characterizations of Planar Ga₂O₃ Schottky Barrier Diodes

Abstract

In this work, a Schottky barrier diode (SBD) is fabricated and demonstrated based on the edge-defined film-fed grown (EFG) Ga₂O₃ crystal substrate. At the current stage, for high resistance un-doped Ga₂O₃ films and/or bulk substrates, the carrier concentration (and other electrical parameters) is difficult to be obtained by using the conventional Hall measurement. Therefore, we extracted the electrical parameters such as on-state resistance (R_on), Schottky barrier height (${\varphi }_B$), the ideal factor (n), series resistance (R_s) and the carrier concentration (N_d) by analyzing the current density–voltage (J–V) and capacitance–voltage (C–V) curves of the Ga₂O₃-based SBD, systematically. The detailed measurements and theoretical analysis are displayed in this paper.

1. Introduction

Owing to the suitable energy band gap (E_g) of ~4.9 eV, a high Baliga’s figure of merit (FOM) of more than 3200, a high Huang’s material FOM of 279, Johnson’s FOM of 2844, and a high theoretical breakdown field (E_BR) of ~8 MV/cm, gallium oxide (Ga₂O₃) has been widely employed to construct optical detectors and power electronics along with low direct current losses and stable operations [1,2,3]. Till now, Ga₂O₃-based Schottky barrier diodes (SBDs) have achieved high breakdown voltages of 2300 V in a vertical edge-terminated SBD [4] and 3000 V in a lateral field-plated (FP) SBD [5], suggesting strong competitiveness superior to GaN and SiC. Owing to the low dark current and fast response speed [6], the Ga₂O₃-based Schottky diode photodetectors also have drawn much attention for high performances. For instance, the high photo responsivity (R), high external quantum efficiency (EQE), large specific detectivity (D*), and short response time in Ni/β-Ga₂O₃ [7], Pt/ε-Ga₂O₃ [8], graphene/β-Ga₂O₃ [9], and MXenes/β-Ga₂O₃ [10] photodiodes are realized.

In electronic devices, the electrical parameters, such as carrier concentration, are key issues that affect the device design, construction, and operation. For doped Ga₂O₃ and/or the flakes exfoliated from the bulk single crystal, the electron concentrations are reported as 10¹⁶–10²⁰ cm⁻³ [11,12,13,14], while in fact, the un-doped Ga₂O₃ has a high resistance due to the large E_g, thus it is very hard to obtain some electrical parameters via the conventional Hall measurement. Additionally, a systematic and comprehensive study for electrical characterizations such as on-state resistance (R_on), Schottky barrier height (${\varphi }_B$), the ideal factor (n), series resistance (R_s) and the carrier concentration (N_d) of Ga₂O₃ Schottky devices is less reported. Therefore, to solve this problem, we fabricated a Ga₂O₃-based SBD, and then performed the electrical characterizations through the J–V, H(J)–J, and C–V characteristic curves.

2. Experimental Section

The Ga₂O₃ crystal substrate was grown by the edge-defined film-fed grown method, whose scale is 10 mm $\times$ 10 mm. For fabricating the Schottky diode, photolithography, lift-off, and electron beam vapor techniques were used to finish the Ni/Au (Schottky, 30 nm/100 nm) and Ti/Au (Ohmic, 30 nm/100 nm) electrode patterns as shown in Figure 1b. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and scanning electron microscopy (SEM) were performed to verify the quality of the Ga₂O₃ crystal substrate. The electrical test was executed with Keithley 4200 analysis equipment in the air at room temperature. The area of the electrode pattern is 2.4 $\times$ 10⁻³ cm². Figure 1a is the schematic of the planar Ga₂O₃ SBDs.

3. Results and Discussion

As shown in Figure 2a, the XRD pattern of the edge-defined film-fed (EFG)-grown Ga₂O₃ substrate is displayed, showing (201), (400), (401), (402), and (601) orientations. The prepared Ga₂O₃ crystal is polycrystalline β-Ga₂O₃. The SEM image of the surface of the Ga₂O₃ substrate is portrayed in Figure 2a inset, suggesting a decent crystallization with well-defined boundaries and uniform claviform grains. In Figure 2b, the binding energies of Ga 2p_1/2, Ga 2p_3/2, and O 1s are determined to be 1144.7 eV, 1117.9 eV, and 530.6 eV by XPS, they are similar to the reported values as shown in

Table 1. Comparison of the binding energies of Ga 2p_1/2, Ga 2p_3/2, and O 1s.

Ga 2p1/2 (eV)	Ga 2p3/2 (eV)	O 1s (eV)	Reference
1144.7	1117.9	530.6	This work
1145.18	1118.28	531.18	[15]
1145	1120	530.7	[16]
1145.5	1118.5	531.4	[17]

, verifying the formation of the Ga₂O₃ semiconductor.

In Figure 3a, current density–voltage (J–V) curves of the Ni/Ga₂O₃/Ti Schottky diode are shown in linear-scale and semi-log scale, respectively. The output current density is 3.04 $\times$ 10⁻² A/cm² and 1.25 $\times$ 10⁻⁷ A/cm² at 2 V and −2 V, respectively, translating to a high rectifying ratio of 2.44 $\times$ 10⁵; the fabricated device is on-state at forward voltages while off-state at reverse voltages. By extrapolating the linear region of the log-scaled J–V curve in Figure 3a (red line) to obtain its slope, the on-state resistance (R_on) is estimated to be 51.5 Ω cm². Furtherly, we use the thermionic emission (TE) model to describe the Ni/Ga₂O₃/Ti Schottky diode [18]:

$$J=J_s\left(e^{\frac{qV}{nkT}}-1\right)$$

(1)

$$J_s=A^{*}{T}^2{e}^{-\frac{{\varphi }_B}{kT}}$$

(2)

$${\varphi }_B=\frac{kT}{q}\ln \left(\frac{A^{*}{T}^2}{J_s}\right)$$

(3)

and

$$A^{*}=\frac{q{m}^{*}{k}^2}{2{\pi }^2{\hslash }^3}$$

(4)

where $q$ is the electron charge, V is the applied voltage, $J_s$ is the reverse saturation current, n is the ideal factor, k is the Boltzmann constant, T is the thermodynamic temperature, ${\varphi }_B$ is the Schottky barrier height, and $A^{*}$ is the Richardson constant. For Ga₂O₃, its effective electron mass $m^{*}=0.342 m_0$, with $m_0$ the mass of the free electron, thus the $A^{*}$ of Ga₂O₃ is calculated to be 41.07 A/cm² K² [19].

As displayed in Figure 3b, with the TE model described in Equations (1)–(4), the n, ${\varphi }_B$ and turn-on voltage (V_on) are determined to be 1.34, 0.93 eV, and 0.52 V, respectively. In Figure 3b inset, the $J_s$ of the Schottky diode is 9.35 $\times$ 10⁻¹⁰ A/cm². The n value between 1 and 2, nearer to 1, indicates a decent Schottky electrical behavior in the fabricated device. The V_on suggests a built-in potential difference (V_bi) of 0.52 eV. In fact, the work function of Ni (W_m) is 5.15 eV [20], and the electron affinity of Ga₂O₃ (${\chi }_s$) is 4.00 eV [21]. The Ni-Ga₂O₃ energy band diagram before they make contact is shown in Figure 4a. According to the Schottky–Mott rule [22,23], the Ni-Ga₂O₃ interface barrier is about 1.15 eV, i.e., the difference between W_m and ${\chi }_s$. After they make contact, as given Figure 4b, the conduction and valence energy band edge (E_c and E_v) bend up, owing to the electron transferring to the electrode. The formation of the ${\varphi }_B$ indicates a barrier for electron transport in the device, thus the device has a V_on and rectifying effect.

For the device, the series resistance (R_s) is a key parameter affecting the performances of the Schottky diode, modeled by a combination of a capacitance (C_j) and a resistor (R_j) as shown in Figure 2a inset. When the current flow is in the diode, it has a relationship with voltages applied on the device [24]:

$$V_D=V-JA{R}_s$$

(5)

where $V_D$ is the voltage on the two sides of the diode, V is the applied voltage, and A is the area of the electrode. Other than the homojunction device, in the Schottky junction similar to the heterojunction, the key role in determining the electrical behavior could not be told by diffusion current model. When $V_D>3kT/e$, the current in diode could be described by the thermionic electron model:

$$J=J_s\exp \left[e\left(V-JA{R}_s\right)/nkT\right]$$

(6)

Thus,

$$V=A{R}_{s}J+n{\varphi }_B+\frac{nkT}{e}\ln \left(\frac{J}{A^{*}{T}^2}\right)$$

(7)

$$dV/dlnJ=A{R}_{s}J+\frac{nkT}{e}$$

(8)

moreover, H(J) is defined as

$$\mathrm{H}\left(\mathrm{J}\right)=\mathrm{V}-\frac{e}{nkT}\ln \left(\frac{J}{A^{*}{T}^2}\right)=A{R}_{s}J+n{\varphi }_B$$

(9)

based on Equation (8), through the linear fitting ($dV/dlnJ$)-$J$ curve shown in Figure 5a (blue dot-line curve), the n and R_s of the Schottky diode are estimated to be 1.67 and 45.5 Ω cm². Then, according to the Equation (9), ${\varphi }_B$ and R_s of the Schottky diode could be obtained as 0.86 eV and 46.6 Ω cm², by fitting the H(J)-J curve displayed in Figure 5a (green dot-line curve). In addition, according to the energy band diagram in Figure 3, ${\varphi }_B$ can be demonstrated as ${\varphi }_B=e{V}_{bi}+\left(E_c-E_f\right)$ [18], where $E_c$ and $E_f$ are the conduction minimum and Fermi level of the Ga₂O₃. $E_c-E_f=kTln\left(\frac{N_c}{N_d-N_a}\right)$, where $N_c$ is effective state density at conduction band, expressed as $N_c=2{\frac{2\pi m^{*}kT}{h^2}}^{3/2}$, thus the electron concentration of the Ga₂O₃ can be calculated to be 1.04 $\times$ 10¹⁹ cm⁻³ [25]. What’s more, based on the Norde’s method [26], a function F(V) is defined as:

$$\mathrm{F}\left(\mathrm{V}\right)=\frac{V}{2}-\frac{kT}{e}\ln \left(\frac{J\left(V\right)}{A^{*}{T}^2}\right)$$

(10)

so, ${\varphi }_B$ and R_s could be expressed as:

$${\varphi }_B=F\left(V_0\right)+\frac{V_0}{2}-\frac{kT}{e}$$

(11)

and

$$R_s=\frac{kT}{eJ\left(V_0\right)A}$$

(12)

where $V_0$ is the voltage at the rock bottom of this function, $F\left(V_0\right)$ and $J\left(V_0\right)$ are the corresponding functions of $V_0$. As shown in Figure 5b, the $V_0$ has been marked as 0.45 V. On the basis of Equations (10)–(12), ${\varphi }_B$ and R_s of the Schottky diode could be obtained as 1.04 eV and 112.1 Ω cm².

The Schottky barrier region in a Schottky diode could be regarded as a planar capacitance, which can be shown as $C=\frac{{\epsilon }_s{\epsilon }_{0}A}{W}$ [25,27], where W is the width of the depletion, ${\epsilon }_s$ and ${\epsilon }_0$ are the permittivity of Ga₂O₃ (${\epsilon }_s$~10) and vacuum permittivity (8.85 $\times$ 10⁻¹² F/m). Based on Poisson’s equation, it can be described as:

$$\frac{1}{C^2}=\frac{2}{q{N}_d{\epsilon }_s{\epsilon }_0{A}^2}\left(V_{bi}-V-\frac{kT}{q}\right)$$

(13)

As shown in Figure 6a, the capacitance–voltage (C–V) and $\frac{1}{C^2}$-V curves are displayed with a frequency (f) of 100 kHz, and it can be clearly seen that the C decreases from 1.75 $\times$ 10⁻¹⁰ F to 1.27 $\times$ 10⁻¹⁰ F, with a gradual slowing rate. With Equation (13), the N_d could be fitted through the $\frac{1}{C^2}$-V curve to be 4.36 $\times$ 10¹⁷ cm⁻³. In addition to Figure 6b, the C is almost unchanged with different frequencies, due to the fact that the current in a Schottky diode is caused by the entrance of a majority carrier into the metal side instead of the charge accumulation, i.e., there is no storage effect, thus no diffusion capacitance. Such characterization is beneficial in constructing high-frequency devices for Ga₂O₃.

Table 2. Basic performance parameters of some reported Ga₂O₃ Schottky diodes in 2019 and 2020.

Substrate	Anode Metal	$$\begin{gathered} {\mathit{V}}_{\mathit{b}\mathit{r}} \\ \left(\mathbf{V}\right) \end{gathered}$$	$\frac{{\mathit{I}}_{\mathit{o}\mathit{n}}}{{\mathit{I}}_{\mathit{o}\mathit{f}\mathit{f}}}$	n	$$\begin{gathered} \mathit{q}{\mathit{V}}_{\mathit{b}\mathit{i}} \\ \left(\mathbf{eV}\right) \end{gathered}$$	$$\begin{gathered} \mathit{q}{\mathit{\varphi }}_{\mathit{B}} \\ \left(\mathbf{eV}\right) \end{gathered}$$	$$\begin{gathered} {\mathit{N}}_{\mathit{d}} \\ \left({\mathbf{cm}}^{-3}\right) \end{gathered}$$	${\mathit{R}}_{\mathit{o}\mathit{n}}$ $(\mathbf{m}\mathbf{\Omega }·\mathbf{c}{\mathbf{m}}^2)$	${\mathit{R}}_{\mathit{s}}$ $(\mathbf{m}\mathbf{\Omega }·\mathbf{c}{\mathbf{m}}^2)$	Ref
Wafer (100)	Ni	-	2.44 $\times$ 105	1.34	0.52	0.93	$4.36\times {10}^{17}$	51.5	45.5	This work
Epi layer (001)	Ni	261	-	1.21	0.74	-	$1.77\times {10}^{16}$	77.3	-	[27]
Wafer $\left(\overline{2}01\right)$	Ni	23	$2\times {10}^{11}$	1.21		1.31–1.64	$1.96\times {10}^{18}$	1.54	-	[28]
Film (100)	Mo	260	-	-	-	1.55	$2\times {10}^{17}$	-	-	[29]
Wafer $\left(\overline{2}01\right)$	Ni/Pt	-	-	1.14	1.3	1.37	$1.45\times {10}^{18}$	-	-	[30]
Epi layer (001)	Ni	-	$1\times {10}^{10}$	1.17	-	1.02	$6.9\times {10}^{15}$	40	-	[31]

lists and compares the basic electrical parameters of some Ga₂O₃ SBDs in the past two years. From the table, we comprehensively discussed and calculated the basic electrical parameters by different analysis methods of J–V and C–V.

4. Conclusions

In this work, an EFG-grown Ni/Ga₂O₃/Ti Schottky diode is fabricated and characterized. By different analysis methods of J–V and C–V, its electrical parameters such as on-state resistance (R_on), Schottky barrier height (${\varphi }_B$), the ideal factor (n), series resistance (R_s) and the carrier concentration (N_d) are obtained and discussed, systematically and comprehensively. The further investigation of Ga₂O₃ materials and devices is in inherent demand due to its excellent properties and the prospect of applications.