Ultrawide bandgap (UWBG) semiconductors represent a growing new area of research including materials, physics, technologies, and applications. This new semiconductor class is promising for future generation devices especially the devices used in harsh-environment applications. Among these UWBG are AlGaN, AlN, diamond and Ga₂O₃. Compared with other UWBG semiconductors, Ga₂O₃ has a bandgap of about 4.8 eV with a high breakdown electrical field^{[1, 2]}. In contrast to the other UWBG, Ga₂O₃ is directly obtainable from melt by scalable growth methods such as Czochralski^[3], optical floating zone^[4] and vertical Bridgman^[5] etc. therefore, Ga₂O₃ is comparatively low cost^[2]. The monoclinic β-Ga₂O₃ is the most thermodynamically stable^{[2, 6]} in comparison with other polymorphs (α, β, γ, δ, ε, and k)^[2]. Currently β-Ga₂O₃ is therefore mainly used in unipolar devices while p–n heterojunctions require different semiconductors because of the challenge to obtain stable p-type β-Ga₂O₃^[7]. For Schottky barrier diode (SBD) formation with β-Ga₂O₃, different metals are used such as Au^[8], Ni^[9], Pt^[8] and W^[10]. Interpreting and understanding the temperature dependant β-Ga₂O₃ SBD characteristics and the dominate conduction mechanisms are very important for improving SBD performance^[11]. The most important transport mechanism for this type of SBD is the thermionic emission (TE) current^{[12, 13]}. However, at low temperature other transport mechanisms dominate such as tunneling^[11] and tunneling via dislocations^[14]. Labed et al.^[11] have demonstrated the domination of tunneling at low temperature for Ni/β-Ga₂O₃ SBD and with increasing temperature, the tunneling current decreases. Fillali et al.^[15] also demonstrated this fact for GaAs/AlGaAs MQW SBDs. Arslan etal.^[14] showed the domination of tunnelling via dislocations current in the depletion region at low temperatures for an (Ni/Au)/AlInN/AlN/GaN SBD. β-Ga₂O₃ power-switching devices performance and reliability depend in great part on dislocations, therefore, their presence in β-Ga₂O₃ materials have to be reduced. Dislocations are induced by the substrate’s surface state and its polishing and etching, or dislocations that directly originate from stacking faults in the substrate^[16]. In addition to their negative effects on leakage current and breakdown^{[14, 17]}, dislocations may act as nucleation sites for other types of defects^[17] and their density may be as high as 1 × 10⁵ cm^{–2 [17, 18]}. Yao et al.^[17] estimated the dislocation density in the range of 6 × 10⁴–1 × 10⁶ cm^–2 for bulk β-Ga₂O₃. Yang et al.^[19] fabricated Schottky barrier diodes on β-Ga₂O₃ substrates with dislocation density of about 1 × 10⁶ cm^–2. The dislocation density is affected by interfacial traps, plasma and diffusion of metal atoms into the surface of β-Ga₂O₃^{[1, 9]}. Therefore, tunneling via dislocation is expected to dominate at this type of device, especially at low temperature. Furthermore, in the last few years there is a high interest for tungsten (W) for Schottky contact with β-Ga₂O₃^{[20, 21]}. This interest is related to several reasons: it has a high thermal stability, a lower temperature-dependent contact characteristics with β-Ga₂O₃, and a work function of 4.5 eV so that a modest barrier height with potentially better temperature endurance is anticipated. Furthermore, tungsten is at a lower cost with comparison with gold and platinum.

In this work, the W/β-Ga₂O₃ Schottky barrier diode (SBD) deposited by CMFS is studied and analyzed in a temperature domain from 100 to 300 K to unveil the conduction mechanism at low temperatures. The aim is to study the possibility of tunneling via dislocation transport mechanism and to extract the interfacial dislocation density.

The active layer of the SBD is a Si-doped β-Ga₂O₃ film, grown by halide vapor phase epitaxy on the Sn-doped β-Ga₂O₃ substrate at 1 × 10¹⁸ cm^–3. The edge-defined film-fed growth (EFG) is used to prepare the substrate, which has an orientation of (001), by Novel Crystal (Japan). The donor concentration in the β-Ga₂O₃ epitaxial film is 3 × 10¹⁶ cm^–3. The ohmic contacts, consisting of Ti/Au electrodes (10 nm/40 nm), were then deposited by E-beam evaporation. A tungsten (W) film (300 nm) is used for the Schottky contact, and is deposited on the Si-doped β-Ga₂O₃ active layer by confined magnetic field based sputtering method (CMFS). The fabricated SBD was annealed at 400 °C. An SEM cross section image of the fabricated β-Ga₂O₃ SBD is shown in Fig. 1.

The W/β-Ga₂O₃ semi-logarithmic temperature dependent J–V characteristics are shown in Fig. 2(a). The forward bias of the structure current is an exponential function of the applied bias voltage only for temperatures higher than 180 K. However, for temperatures lower than 180 K, double regions were observed which can be clearly seen in Fig. 2(b). The double regions at low voltage domain are believed to a non-negligeable tunneling current contribution to the total current^[11]. The leakage current, at room temperature (300 K) at –2 V, is of about ~10⁻⁶ A/cm² and is nearly independent on temperature. The forward current is about 192 A/cm² at 2 V forward bias at room temperature and is also nearly independent on temperature.

Schottky barrier height ( ϕb(T) ), serie resistance ( Rs ) and ideality factor (η) were extracted as presented in Fig. 3. ϕb(T) and Rs versus temperature are determined by the Sato and Yasumura method^[22] in which, from the current–voltage equation, a function F(V,T) is defined as^[22]:

1F(V,T)=V2−KBTqlnJA*T2=ϕb+JRsn+V(1η−12).

From Eq. (1), it can be shown that the barrier height ϕb(T) and R_s are given by^[22]:

2ϕb(T)=Fmin(V,T)−(2η−1)KBTq+V(Fmin)(1η−12),

3Rs=(2−η)KBTqJ(Fmin),

where J(F_min) is the current when F(V,T ) is at its minimum at a fixed temperature.

The slope of the linear region of the ln(J–V ) plot at low voltage is proportional to the ideality factor η. This relation is expressed as^[23]:

4η=qKBTdVd(ln(J)).

With increasing temperature from 100 to 300 K, η decreases from 2.1 to 1.05. The high value at low temperature is often related to the tunneling current^[11]. The decreasing η is due to the effect of thermionic emission transport process. The Schottky barrier height (SBH) ( ϕb ) increased from 0.54 to 1.03 eV with increasing temperature from 100 to 200 K, then a saturation in ϕb for temperatures higher than 200 K. This behavior of η and ϕb could be due to barrier inhomogeneity at the W/β-Ga₂O₃ interface^{[19, 24]}. Furthermore, for temperatures lower than 200 K, low energy electrons can be transferred to tungsten by tunnelling through the barrier. When the temperature increases from 200 K, other electrons at higher energies surmount the barrier using a thermionic emission mechanism and the barrier appears to be higher and the band diagram extracted using Silvaco TCAD at different temperatures explains the increasing in ϕb with increasing temperature as shown in Fig. 4. Clearly, a high ϕb at room temperature was obtained when tungsten is deposited by CMFS. This result may be related to high tungsten workfunction or to the β-Ga₂O₃ electron affinity being lower than 4 eV. The first maybe due to the tungsten atom diffusion into the surface of β-Ga₂O₃, which is similar to Nickel diffusion^[1].

Finally, as shown in Fig. 3, R_s and R_on decreased with increasing temperature. These decreases are related to the β-Ga₂O₃ resistivity decrease which could be due to the excitation and transition of electrons under the influence of lattice thermal vibration, as the operating temperature increases^[24]. A high ideality factor and a high leakage current indicate the domination of tunneling current at 100 K. Among the expected tunneling mechanisms are tunneling via dislocation and traps (oxygen and gallium vacancies) assisted tunneling. In most publications, a high dislocation density is observed in bulk β-Ga₂O₃^{[19, 25]}. In addition, one of the expected dislocation source is vacancy condensation^[26]. In addition, the diffusion of tungsten into the surface of β-Ga₂O₃ and the formation of the Ga–W–O ternary compound at the W/β-Ga₂O₃ interface after annealing is expected^[27]. The formation of this compound leads to a lattice mismatch between the Ga–W–O ternary compound and β-Ga₂O₃ and the result is the formation of an interfacial dislocation in addition to bulk β-Ga₂O₃ dislocation which will affect the W/β-Ga₂O₃ SBD performance and transport mechanism.

Generally, the tunneling current through a barrier is given by^{[11, 14]}:

5JTu=Jt{exp[q(V−RsJ)E0]−1},

where J_t is the tunneling saturation current and E₀ is the tunneling parameter. E₀ can be defined as^{[11, 28]}:

6E0=E00cothE00KBT.

With the consideration of the domination of tunneling via dislocations, the saturation current Jt is given by^{[14, 29]}:

7Jt=qDdisνDexp(−qVk/E0),

where D is the dislocation density, νD≈ 3.024 × 10¹² s⁻¹ is the Debye frequency for β-Ga₂O₃^[30] and qVk≈ϕb^[14].

Using Eq. (5), Jt and E0 are determined from measured J–V characteristics of Fig. 2 and knowing qVk (0), the dislocation density can be extracted from the following equation^[14]:

8Ddis=Jt(0)qνDexpqVk(0)E0(0),

where Jt(0) and E0(0) can be obtained by polynomial extrapolation of Jt(T) and E0(T) to 0 K. The polynomial fitting equations are given in the legend of Fig. 5. The value of qVk(0) approximate to ϕb(0) which is obtained by extrapolation of ϕb to zero. The dislocation density for W/Ga-W-O/β-Ga₂O₃ SBD is extracted by using J_t(0) =1.78 × 10⁻⁷ A/cm², E₀(0) = 25.83 meV, and qV_k(0) = 0.47 eV. A dislocation density of about ~ 3.56 × 10⁷ cm⁻² is obtained. In Ga₂O₃, two types of dislocation, which are screw and edge are expected^[31]. The high dislocation demonstrates the possibility of tunneling via dislocation dominated transport mechanism especially at low temperatures.

In conclusion, the parameters of W/β-Ga₂O₃ Schottky barrier diode (SBD), deposited by CMFS, were extracted and analyzed at different temperatures. The ideality factor decreases from 2.1 to 1.05 with increasing temperature from 100 to 300 K. The high ideality factor is interpreted by the tunneling current domination at low temperature. The barrier height increased from 0.54 to 1.03 eV with increasing temperature. These variations are related to the Gaussian distribution of ϕb in the interfacial layer. The high ϕb value at room temperature when CMFS used for tungsten deposition may be related to the high tungsten workfunction. R_s and R_on decreased with increasing temperature which was related to β-Ga₂O₃ resistivity. Finally, a 3.56 × 10⁷ cm⁻² dislocation density was extracted from the tunneling current. This high density demonstrated the domination of tunneling, via dislocation, transport mechanism especially at low temperatures.