1 Introduction

As an emerging semiconductor, β-Ga2O3 has attracted significant interest as next-generation high-power devices due to its wide bandgap (~ 4.85 eV) and theoretical critical field strength of 8 MV/cm [1]. High-performance power devices have been demonstrated in the form of Schottky barrier diodes [2,3,4] and field effect transistors (FTEs) [5,6,7]. Enhancing the device performance further as theoretically predicted requires high-quality epitaxial layer with low compensating defects and low background doping. In addition, β-Ga2O3 has been applied to other devices such as solar blind ultraviolet photodetectors [8], electroluminescent devices [9], window materials for optoelectronic devices [10], transparent conductive oxides [11], and hydrogen gas sensors [12].

Because of the highly asymmetric monoclinic crystal structure, β-Ga2O3 has known to have anisotropic material properties. Guo et al. found that thermal conductivity along the [010] direction is approximately three times larger than along the [100] direction [13]. Anisotropic nonlinear optical properties in β-Ga2O3 have been reported [14, 15]. Liu et al. grew β-Ga2O3 epilayers on r- and c-plane sapphire substrates and showed that β-Ga2O3 epilayers on r-plane revealed higher UV responsivity and detectivity [16]. Wong et al. reported an electron mobility anisotropy in β-Ga2O3 FETs, associated with the anisotropic carrier scattering [17]. Zhang et al. investigated the anisotropic etching behavior of β-Ga2O3 and showed that the wet etching in hot phosphoric acid could effectively reduce the sidewall roughness caused by plasma dry etching [18]. Jang et al. found that (\(\overline{2 }\) 01) Ga2O3 had higher etch rates and could form ohmic contacts more easily than (010) Ga2O3, which was correlated with the higher density of oxygen dangling bonds on the (\(\overline{2 }\) 01) plane [19]. Sasaki et al. found that the epitaxial growth rate for (100) plane was lower than (010) plane because of the low adhesion energy on the terraces for (100) surface [20]. Fu et al. comparatively investigated Schottky contact to (\(\overline{2 }\) 01) and (010) β-Ga2O3 interfaces and found higher barrier height, lower reverse leakage current, and larger breakdown voltage for (010) orientation [21]. Bhattacharyya et al. fabricated Schottky contacts to (010), (\(\overline{2 }\) 01) and (100) β-Ga2O3 substrates and found that the barrier heights for (010) orientation are highest among three orientations [22]. These anisotropic material properties definitely give a significant impact on the β-Ga2O3 based device performance.

Metal–semiconductor (MS) Schottky contacts are utilized to investigate the nature of defects and their impact on the material quality and the electrical characteristics. MS contacts are classified into two categories, namely, Schottky and ohmic contacts. The barrier height in a metal contact to an n-type semiconductor is given by ΦB = ΦM – χ, where ΦM and χ are the metal work function and the electron affinity of the semiconductor (4.0 eV for β-Ga2O3 [1]), respectively [23]. The work functions for various metals are available in Ref. [24]. Electrical properties of metal/β-Ga2O3 contacts according to the β-Ga2O3 crystal orientation have been investigated. For example, Yao et al. investigated the Schottky metal dependent electrical properties of Schottky diodes on (\(\overline{2 }\) 01) and (010) β-Ga2O3 [25]. Schottky barrier heights from current–voltage (I–V) and capacitance–voltage (C–V) methods of the five metals revealed little dependence on the metal work function. Lyle et al. fabricated Ti contacts on (010) and (001) β-Ga2O3 and observed higher barrier height for (010) plane [26]. Further research on MS contacts can enhance the performance of β-Ga2O3-based devices. In this paper, recent studies on the control and understanding of metal contacts to β-Ga2O3 single crystals has been reviewed.

2 Material properties of β-Ga2O3

Among different crystalline phases of Ga2O3, the monoclinic phase β-Ga2O3 has the best thermal stability, while other four phases (α-, γ-, δ-, and ε-Ga2O3) are metastable and can be transformed to β-Ga2O3 at high temperatures [1]. Hence, most studies are focused on β-Ga2O3. Figure 1a shows a schematic draw of the unit cell of β-Ga2O3 and Fig. 1b shows the (010) and (\(\overline{2 }\) 01) planes which are most commonly used for device applications [19]. Table 1 summarizes the material characteristics of β-Ga2O3, GaN, 4H-SiC, diamond and Si. Except diamond, the bandgap and breakdown field of β-Ga2O3 are larger than other semiconductors. The Baliga’s figure of merit (BFOM) for β-Ga2O3 is larger than GaN and 4H-SiC, highly beneficial to fabricate high-power electronic devices. However, relatively low thermal conductivity can cause self-heating effects. Excessive heat accumulation will degrade the performance and stability of the devices. Relatively low mobility also has a negative effect on the device characteristics.

Fig. 1
figure 1

a β-Ga2O3 crystal structure and b (010) and (\(\overline{2 }\) 01) β-Ga2O3 surfaces [19]

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Table 1 Material properties of β-Ga2O3 in comparison with those of GaN, 4H-SiC, Diamond and Si (Baliga’s figure of merit: BFOM) [1]
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Bulk Ga2O3 single crystals can be grown using the following methods: edge-defined film-fed growth (EFG) [27], Czochralski (CZ) [28, 29], Floating zone (FZ) [30] and vertical Bridgman (VB) [31]. Using the EFG method, Kuramata et al. [27] obtained a large and high-quality β-Ga2O3 single crystals up to 4 inches, with no twin boundaries and the dislocation density of ~ 103 cm−2. Galazka et al. reported a two-inch-diameter cylindrical β-Ga2O3 single crystal grown by CZ method [29]. FZ method is utilized to grow β-Ga2O3 rod with a typical growth rate of 6 mm/h and a diameter of 10 mm [30]. VB method provides some advantage such that β-Ga2O3 single crystals are easily released after growth. Using VB method, Hoshigawa et al. obtained a 25-mm-diameter β-Ga2O3 single crystal [31]. Among these methods, the EFG method is considered to be the most promising technique to grow bulk β-Ga2O3, because of the capability of achieving large size and high quality bulk β-Ga2O3 for future high-volume production [32, 33]. Unintentionally doped (UID) n-type β-Ga2O3 single crystals are normally obtained due to the incorporation of Si and Ir atoms from the β-Ga2O3 seed and crucible. Hence semi-insulating crystals are achieved by Mg or Fe doping acting as deep acceptors [32, 33].

Low-resistivity β-Ga2O3 substrates can be obtained by intentional doping, which are necessary to achieve better ohmic contacts and lower threshold voltages. For n-type dopants, Sn, Si, and Nb have been employed. Ohira et al. investigated the effect of the annealing process at 1100 °C on the material properties of Sn-doped β-Ga2O3 grown by the FZ method and found that their properties changed marginally [34]. Zhang et al. studied the effect of Sn doping in FZ-grown β-Ga2O3 crystals and reported an increase in the absorption coefficient with the Sn doping and a reduction in the absorption coefficient after annealing, associated with the decrease of free carriers [30]. VÍllora et al. obtained Si-doped β-Ga2O3 grown by the FZ method with the Si concentrations of 1016 ~ 1018 cm−3 and showed that the conductivity can be intentionally controlled over three orders of magnitude by Si doping [35]. Based on the result, they suggested that electrical conductance of β-Ga2O3 is mainly governed by Si impurities and the contribution of oxygen vacancies, if any, is not significant. Zhou et al. grew Nb-doped β-Ga2O3 by the FZ method and could achieve the carrier concentration from 9.55 × 1016 to 1.8 × 1019 cm−3 [36]. In the case of p-type doping, Mg has been used as a dopant. Onuma et al. grew Mg-doped β-Ga2O3 crystals by the FZ method and observed the semi-insulating behavior for Mg concentration of 4 × 1018 –2 × 1019 cm−3 [37]. Based on the first-principles calculations, Dong et al. showed that N serves as a deep acceptor with an energy level of 1.33 eV above the valence band maximum, which is not effective as a p-type dopant [38]. Hence the achievement of p-type doped β-Ga2O3 remains a big challenge.

3 Schottky barrier diodes

Schottky barrier diodes can be electrically characterized using I–V and C–V methods to obtain Schottky barrier heights (SBHs). Assuming the thermionic emission (TE) model, the forward bias I–V characteristics of a Schottky diode are analyzed using the following equation [23]

$$J = A^{**} T^{2} \exp ( - q\phi_{B} /kT)[\exp \{ q(V - IR_{S} )/nkT\} - 1]$$
(1)

where A** is the effective Richardson constant (41.1 cm−2 K−2 for n-Ga2O3), qϕB is the effective SBH, RS is the series resistance, and n is the ideality factor. Both the barrier height and ideality factor are calculated from the linear part in ln(I)–V curves. The flat-band barrier height is obtained from the C–V characteristics under reverse bias condition. The capacitance in the Schottky diodes satisfies the following equation [23]

$$\frac{{A^{2} }}{{C^{2} }} = 2\left( {\frac{{V_{b} - V - kT/q}}{{qN_{D} \varepsilon_{S} \varepsilon_{0} }}} \right)$$
(2)

where Vb is the built-in potential, ND is the carrier concentration, and εS the dielectric constant of semiconductor, and ε0 is the vacuum permittivity. The carrier concentration is calculated from the slope of A2/C2 versus V plot. The barrier height is obtained from \(q\phi_{B}^{(C - V)} = qV_{0} + qV_{n} + kT\), where V0 is the intercept of A2/C2 with the voltage axis, and \(qV_{n} = E_{C} - E_{F}\). The SBH from C–V method is generally higher than that from I–V method. This is due to the nonuniform interfacial layer and the distribution of interfacial defects at the MS interface [39]. The obtained capacitance during the C–V measurement at high frequency is not sensitive to potential fluctuations for length scales smaller than the depletion width. In this case, the capacitance is the average value over the SBH values. In addition, the effect of image force lowering and tunneling on the current conduction is negligible under the flat-band condition because electric field in the semiconductor is zero. Thus, the SBHs determined from the C–V method are observed to be higher than those determined from the I–V method. The flat-band barrier heights can also be obtained using the ideality factor and the effective SBH obtained from the TE model [40]

$$\phi_{FB} = n\phi_{TE} - (n - 1)\frac{kT}{q}\ln \left( {\frac{{N_{C} }}{{N_{D} }}} \right)$$
(3)

where NC is the density of states at conduction band. In identically prepared diodes on the same semiconductor, there exists normally a linear relationship between the effective SBH and the ideality factor. After obtaining the straight lines by fitting to the effective SBH versus ideality factor plots, laterally homogeneous Schottky barrier height (qϕBhom) can be obtained from an extrapolation of these straight lines to the image-force controlled ideality factor nif [41].

Analyses on the temperature dependent I–V characteristics can also be carried out, which are required for clarifying the origin of non-idealities in the Schottky barrier and attaining the detailed knowledge on the current transport mechanism and the properties of defects and the mechanism of barrier formation. One of the non-idealities is the temperature dependence of electrical parameters. For example, an increase in barrier height and a decrease in ideality factor are observed from the temperature dependent I–V characteristics, which are associated with the laterally inhomogeneous Schottky barrier [42]. A Gaussian distribution of barrier heights over the Schottky contact area is assumed in this model, where the effective SBH (\(q\phi_{B}\)) related with a zero-bias mean SBH (\(q\overline{\phi }_{B}\)) and a standard deviation (σ0) is given by [42]

$$q\phi _{B} = q\bar{\phi }_{B} - q^{2} \sigma _{0} ^{2} /2kT$$
(4)

Then, the modified Richardson plot can be obtained as follows

$$\ln \left( {\frac{{I_{0} }}{{T^{2} }}} \right) - \frac{{q^{2} \sigma_{0}^{2} }}{{2k^{2} T^{2} }} = \ln (AA^{**} ) - \frac{{q\phi_{B} }}{kT}$$
(5)

Using Eq. (5), the modified Richardson constant (A**) is calculated.

Li et al. reported an increase in barrier height with the temperature in Ni Schottky contacts to β-Ga2O3 [43]. Although they provided the SBH values at different temperatures, the Schottky barrier inhomogeneity was not examined using the modified Richardson plots. By taking the SBHs at different temperatures from their work [43], the characteristics of Schottky barrier in β-Ga2O3 were analyzed in this article. Based on the linear fit to the plot of \(q\phi_{B}\) versus1/2kT shown in Fig. 2a, the value of \(q\overline{\phi }_{B}\) = 1.42 eV and \(\sigma_{0}\) = 0.143 V were obtained. From the linear fitting to the modified Richardson plot of \(\ln (I_{0} /T^{2} ) - q^{2} \sigma_{0}^{2} /2k^{2} T^{2}\) versus 1/kT shown in Fig. 2b, the Richardson constant was calculated to be 35.7 Acm−2 K−2. This is similar to the theoretical value of 41.1 Acm−2 K−2 for n-Ga2O3, indicating that the temperature dependence of barrier heights can be explained by the inhomogeneous Schottky barrier with a Gaussian distribution of barrier heights. Li et al. also showed that the forward I–V characteristics follow the thermionic field emission (TFE) model rather than TE [43]. The obtained barrier heights from TFE model were about 1.32 ~ 1.40 eV, which are similar to the \(q\overline{\phi }_{B}\) value of 1.42 eV, assuring again the inhomogeneous Schottky barrier for the forward current characteristics. The inset in Fig. 2(a) shows a schematic diagram of inhomogeneous Schottky barrier.

Fig. 2
figure 2

taken from Li et al. [43]. The inset in a shows a schematic band diagram of inhomogeneous Schottky barrier

a Plot of barrier height versus 1/2kT and b modified Richardson plot. The barrier heights at different temperatures were

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4 Metal contacts to β-Ga2O3

4.1 Schottky contacts to β-Ga2O3

Normally Schottky contacts to β-Ga2O3 single crystals have been fabricated in vertical structure, in which Schottky and ohmic contacts are formed on the front and back surfaces of the samples, respectively. A β-Ga2O3 epitaxial layer was used in some studies (denoted as n-epi/n-bulk), while other studies used bulk β-Ga2O3 (denoted as n-bulk). Note that most of the research results were obtained by analyzing only one or two contact metals and a comprehensive investigation using various metal contacts to the same β-Ga2O3 layer is still lacking. Owing to the different material quality of β-Ga2O3 layer, carrier concentration, surface/interface states, and surface treatment, direct comparison between each work can result in incorrect conclusions. Hence, research results including multiple metals within the same study were discussed mainly in this article.

Table 2 shows the research results in the literature obtained from Schottky contacts to (\(\overline{2 }\) 01) β-Ga2O3. The reported barrier heights for Ni and Pt contacts are in the range of 0.9 ~ 1.6 eV. Investigation of Schottky diodes using multiple metal contacts were performed by Yao et al. [25] and Hou et al. [56]. The Schottky metal contacts for these two works were formed on EFG-grown Sn-doped (\(\overline{2 }\) 01) β-Ga2O3 single crystals. Based on the reported SBHs, the relationships between barrier height and metal work function in Schottky contacts to (\(\overline{2 }\) 01) β-Ga2O3 were obtained, which are shown in Fig. 3a. The barrier heights show little dependence on metal work function, indicating significant Fermi-level (FL) pinning. Such FL pinning was associated with native defects or interface states located at ~ 1.3 eV below the conduction band (EC) [56]. Higher density of oxygen dangling bonds on the (\(\overline{2 }\) 01) plane was suggested as an origin of strong FL pinning. Hou et al. also reported that barriers heights of oxidized Schottky contacts were to be higher than their unoxidized metal counterparts [56]. However, the oxidized contacts also showed little correlation between barrier height and metal work function. The barrier heights of the oxidized Schottky contacts were pinned by another deep-level defect close to EC–2.0 eV.

Table 2 Summary of Schottky contacts to (\(\overline{2 }\) 01) β-Ga2O3 reported in the literature
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Fig. 3
figure 3

taken from Yao et al. [25] and Hou et al. [56] and b (001) β-Ga2O3 Schottky contacts using the barrier heights taken from Lingaparthi et al. [76]. The metal work functions were taken from ref. [24]

Plots of barrier height versus metal work function for a (\(\overline{2 }\) 01) β-Ga2O3 Schottky contacts using the barrier heights

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Table 3 shows the research results in the literature obtained from Schottky contacts to (001) β-Ga2O3. Si-doped epitaxial layers grown on Sn-doped β-Ga2O3 substrates were mainly examined in this orientation. Lingaparthi et al. explored the surface states on halide vapor phase epitaxy (HVPE) grown (001) β-Ga2O3 epilayers by determining the SBHs for different metal contacts using Cr, Cu, Ni, and Au [76]. Figure 3b shows the plots of barrier height versus metal work function using the data taken from Lingaparthi et al. [76]. For epi-1 sample (HVPE-grown Si-doped epitaxial layer with the carrier concentration of 2.5–3.2 × 1016 cm–3), the barrier height was found to be nearly pinned at 1.2 ~ 1.35 eV, closely matched with the energy level of the oxygen vacancy [VO(III)] state (EV + 3.57 eV) in β-Ga2O3. Based on this result, they suggested that FL pinning is due to VO-related surface states on (001) oriented β-Ga2O3 epitaxial layers. In contrast, the FL was observed to be weakly pinned on the bulk and epi-2 (improved Si-doped epitaxial layer with the concentration of 5.3–7.2 × 1016 cm–3) (001) β-Ga2O3. The density of surface states for epi-1 sample was found to be higher than those for bulk and epi-2 samples, indicating the presence of higher density of VO-related states on the β-Ga2O3 surface for epi-1 sample. In another work [77], they showed by simulation that deep donor type surface states (probably VO) are responsible for lowering the barrier height and increasing the reverse leakage current. Based on the results they suggested that the oxygen vacancy generated in (001) β-Ga2O3 epitaxial layer during the HVPE growth process affected on the SBH and the electrical properties of (001) β-Ga2O3 based devices.

Table 3 Summary of Schottky contacts to (001) β-Ga2O3 reported in the literature
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Tables 4 and 5 show the research results in the literature obtained from Schottky contacts to (100) and (010) β-Ga2O3, respectively. Studies on these orientations are rather sparse. Lyle et al. investigated six different Schottky metals to (100) β-Ga2O3 substrates [78]. Near-ideal average ideality factors (1.05–1.15) were found for Ti, Mo, Co, and Ni contacts, whereas higher ideality factors (∼1.3) were observed for Pd and Au contacts. The electrical behavior of the Pd and and Au contacts were associated with the presence of spatially inhomogeneous Schottky barriers. Figure 4a shows the plots of barrier height versus metal work function using the data taken from Lyle et al. [78], revealing a strong correlation between the calculated barrier heights and the metal work functions. Similarly, Fig. 4b shows the plots of barrier height versus metal work function for (010) β-Ga2O3 Schottky contacts, where the data were taken from Yao et al. [25] and Farzana et al. [88]. The barrier height is observed to be dependent on the metal work function, suggesting that metal contacts to (010) β-Ga2O3 are not fully pinned. According to the comparative studies on the Schottky contact to (\(\overline{2 }\) 01) and (010) β-Ga2O3 interfaces by Fu et al. [21] and Bhattacharyya et al. [22], barrier heights were found to be higher for (010) orientation compared to (\(\overline{2 }\) 01) orientation. Figures 5a and b show the temperature-dependent I–V characteristics for (\(\overline{2 }\) 01) and (010) β-Ga2O3 Schottky diodes, respectively, reported by Fu et al. [21]. The obtained barrier heights in Figs. 5c and d show the higher values for (010) orientation. These works indicate that the crystalline anisotropy of β-Ga2O3 can affect the electrical properties of Schottky contacts and needs to be taken into account for device design.

Table 4 Summary of Schottky contacts to (100) β-Ga2O3 reported in the literature
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Table 5 Summary of Schottky contacts to (010) β-Ga2O3 reported in the literature
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Fig. 4
figure 4

taken from Lyle et al. [78] and b (010) β-Ga2O3 Schottky contacts using the barrier heights taken from Yao et al. [25] and Farzana et al. [88]. The metal work functions were taken from ref. [24]

Plots of barrier height versus metal work function for a (100) β-Ga2O3 Schottky contacts using the barrier heights

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Fig. 5
figure 5

Temperature-dependent I–V characteristics for a (\(\overline{2 }\) 01) β-Ga2O3 Schottky diode and b (010) β-Ga2O3 Schottky diode, c ideality factor and SBH as a function of temperature, and d SBH versus ideality factor [21]

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Surface treatment prior to metallization is an important factor in determining the SBH and the device stability. Yao et al. investigated the effect of five different wet chemical treatments on the electrical properties of Ni/(\(\overline{2 }\) 01) β-Ga2O3 Schottky diodes and found that rinsing in an organic solvent, cleaning with HCl and H2O2, and rinsing with deionized water showed the best results [25]. Based on the results they concluded that unpassivated surface states and/or bulk/near-surface defects are more dominant in determining the electrical behavior of these diodes compared to the choice of different Schottky metals. Yang et al. characterized the effect of various surface treatments such as gaseous (ultraviolet/O3), liquid (HCl, buffered oxide etch), or plasma (CF4 and O2) on the properties of Ni/(001) β-Ga2O3 Schottky diodes [94]. Standard chemical cleaning involving UV/O3 or acid was found not to degrade the near-surface electrical properties whereas plasma treatment induced surface damage acting as generation-recombination centers. To date, however there is limited work on such systematic investigation using various surface treatments for the same β-Ga2O3 surface.

According to the review on Schottky contacts to β-Ga2O3, we can summarize the following points. (1) Significant FL pinning is observed for the Schottky contacts to (\(\overline{2 }\) 01) β-Ga2O3 due to presence of surface and/or near surface defects. The possible origin of such defects is suggested to be oxygen vacancy-related defects. (2) Correlations between the barrier height and metal work function are observed for (001), (100) and (010) β-Ga2O3, suggesting that metal work function affects the barrier height on these orientations. (3) Compared to (\(\overline{2 }\) 01) β-Ga2O3, (010) β-Ga2O3 revealed higher barrier height, associated with the larger surface band bending [21]. (4) When the surface defects are generated during the epitaxial growth, the FL pinning can occur [76]. Therefore, optimizing growth conditions for β-Ga2O3 epitaxial layer is pivotal to improve the device performance. (5) Mostly Schottky metals were deposited by using e-beam evaporation. For other semiconductors (e.g., GaN [95]), different barrier heights were obtained according to the deposition methods. This point needs to be explored for β-Ga2O3 Schottky diodes more thoroughly.

As a modulating method for diode characteristics, an interfacial layer (IL) between metal and β-Ga2O3 was proved to yield useful results. He et al. formed about 4 nm thick Al2O3 IL between Ni/Au and (\(\overline{2 }\) 01) β-Ga2O3 substrate by annealing the sputtered Al layer at 300 °C in O2 atmosphere [96] and observed the improved diode characteristics, with respective to the sample without IL. Further, they showed that this Al-reacted IL exhibited better performance than the sample with the Al2O3 IL prepared by atomic layer deposition (ALD). Harada and Tsukazaki deposited PdCoO2 layer on (\(\overline{2 }\) 01) β-Ga2O3 substrate by pulsed laser deposition (PLD) and fabricated the stacked Schottky contacts composed of various metals (Pt, Ni, Cr, and Ti) [97]. As shown in Fig. 6, they found that the barrier height systematically increased from 0.7 to 1.9 eV with the increase in the thickness of PdCoO2 from 0 to 20 nm by selecting suitable combination of top metal and thickness of PdCoO2. The PdCoO2 layer consisted of alternatingly stacked ionic Pd+ and [CoCo2]– sublattices, which spontaneously induced interface dipoles that increased the SBH in β-Ga2O3 Schottky diodes. Bhattacharyya et al. deposited about 3 nm thick SiO2 IL by ALD on (010), (\(\overline{2 }\) 01) and (100) β-Ga2O3 substrates and observed the increase in barrier height for all orientations [22]. Especially, the Schottky contacts to (100)-oriented substrates exhibited a dramatic increment in barrier height and a reduction in reverse leakage current. These works suggest a strong potential of IL as a method to modulate the diode characteristics, however, these kinds of works are hardly observed.

Fig. 6
figure 6

Plots of barrier height versus metal work function for metal/β-Ga2O3 contacts with an PdCoO2 interlayer (IL). With increasing the thickness d of PdCoO2 IL from 0 to 20 nm, the barrier height was found to increase. The inset shows the possible band diagram with a PdCoO2 (IL). (Reprinted from ref. 97, under the terms of the Creative Commons CC BY 4.0 license)

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The strong light absorption of metal contacts can limit the development of β-Ga2O3 Schottky-junction-based photonic devices. Due to the excellent properties such as high optical transmittance, large electrical conductivity, and a tunable work function, graphene is a good alternative for transparent electrodes. Graphene/β-Ga2O3 contacts has been studied for the applications of photosensors [9, 98,99,100,101,102]. Graphene/β-Ga2O3 Schottky contacts have also been applied for other devices. The graphene/β-Ga2O3 contact in the double graphene-gate β-Ga2O3 metal − semiconductor FET (MESFET) operated in the enhancement-mode were found to have a barrier height of ~ 0.62 eV and an ideality factor of 1.5 [100]. Yan et al. reported the high critical breakdown field of 5.2 MV/cm in β-Ga2O3 perpendicular to the (100) crystal plane using a vertical graphene/β-Ga2O3 heterostructure [101]. Kim et al. examined high-performance solar-blind photodetectors based on mechanically exfoliated β-Ga2O3 flakes and found that their photoresponsivity was enhanced significantly with UV-transparent graphene electrodes [102]. They also suggested that the high optical transparency of graphene gate prevents the shadowing effect under UV–C illumination, enabling carriers to be generated at the graphene/β-Ga2O3 junction. Using the first-principles calculations, Yuan et al. suggested the following points in graphene/β-Ga2O3 contacts [103]: (1) the small n-type Schottky barrier of ~ 0.07 eV is irrespective of the interface stacking arrangement and the intrinsic electronic property of Ga2O3 hardly alters in the interface, (2) the n-type Schottky barrier to ohmic contact transition can be obtained by shorting the interlayer distance, or increasing the graphene layers or applying a negative external electric field, and (3) applying a large positive external electric field can realize the p-type Schottky barrier to ohmic contact transition. These results will expand the application of graphene/β-Ga2O3 based devices further.

4.2 Ohmic contacts to β-Ga2O3

In order to realize high performance devices, it is essential to obtain good ohmic contact with low resistance and high thermal stability/reliability. High quality ohmic contact to β-Ga2O3 can be formed when the Schottky barrier is low and/or the β-Ga2O3 layer is heavily doped for the carriers to tunnel through the barrier. In general, the specific contact resistivity (ρC), typically expressed in Ω∙cm2, is used as a parameter to assess the quality of ohmic contacts [104, 105]. The most common ohmic contacts to β-Ga2O3 are composed of Ti/Au metallization with post deposition annealing. Table 6 shows the research results on ohmic contacts to β-Ga2O3 in the literature.

Table 6 Summary of ohmic contacts to β-Ga2O3 reported in the literature
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As a way of improving ohmic contact properties, Si-ion implantation was employed to create a heavy doped n+-region that facilitates electron tunneling across the junction [106,107,108, 110, 111]. However, this process requires high temperature annealing (> 900 °C) to electrically activate Si donors. Ozone molecular beam epitaxy (MBE) was also used to grow highly doped epitaxial layer [112]. Meanwhile, Yao et al. reported that the contact resistance of Ti/Au metallization is associated with the limited interfacial reactions between the metal and β-Ga2O3 [113]. They observed that Ti began to react with the Ga2O3 at annealing temperatures above 400 °C and formed an insulating oxide layer, increasing the contact resistance. In addition, they investigated the ohmic properties of nine metals (Ti, In, Ag, Sn, W, Mo, Sc, Zn and Zr) with an Au capping layer and concluded that metal work function is not dominant in determining ohmic contact to β-Ga2O3 but interfacial reaction gives a significant effect on the morphology and electrical behavior. Li et al. could suppress the contact resistance between Ti and Ga2O3 by annealing in Ar ambient [114]. However, they also observed the degraded contact property when annealed above 500 °C. This was associated with the formation of a thicker TiOx non-/low conductive layer [115]. Therefore, most works utilized the annealing temperature between 400 and 500 °C for the Ti/Au ohmic contact. Lee et al. carried out a study on the interdiffusion and interfacial reactions of the ohmic contact between Ti/Au and β-Ga2O3 [116]. As shown in Fig. 7, they could observe a defective β-Ga2O3 layer, a Ti–TiOx layer, and an intermixed Au–Ti layer containing Ti–rich nanocrystalline products after annealing. After in-situ annealing with O pressure of 100 Pa at 800 °C for 2 h, Guo et al. observed that the contact exhibited a conversion from ohmic behavior to Schottky behavior, associated with the decrease of concentration of oxygen vacancies [117]. The instability of the Ti/β-Ga2O3 interface using Ti/Au metal scheme needs to be improved with enhanced thermal stability. Hence, more comprehensive understanding of interfacial reactions can increase the potential of Ti based ohmic contacts.

Fig. 7
figure 7

a High-angle annular dark field and b bright field scanning transmission electron microscopy (STEM) images of Ti/Au metallization on Sn-doped β-Ga2O3 after annealing at 470 °C for 1 min. Insets are the field of view in low magnification. The images show, from the bottom to top, the Ga2O3 substrate, a defective Ga2O3 region, a Ti-TiOx region, an Au rich layer, Ti- or TiOx-rich nanoparticles, and Au-Ti intermixed layer. c Schematic illustrations of the evaluation of the Ti/Au metallization layers on Sn-doped β-Ga2O3 by thermal annealing. (Reprinted from ref. 116, under the terms of the Creative Commons CC BY 4.0 license)

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Including Si ion implantation, plasma bombardment and reactive ion etching (RIE) has also been studied as other pretreatments prior to the metallization. Higashiwaki et al. showed that the Schottky-like Ti/Au contacts became ohmic-like with the RIE process, which were associated with the generation of oxygen vacancies resulted from the out-diffusion of the oxygen atoms [118]. Zhou et al. also demonstrated that Ar plasma bombardment for 30 s could reduce the contact resistance by enhancing surface n-type doping [119]. Using both RIE and Si ion implantation, the specific contact resistance was reported to be 8.1 × 10–6 Ω∙cm2 [120]. This suggests that the ohmic contact properties can be enhanced by using both RIE and Si ion implantation. Surface defects are introduced at the β-Ga2O3 surface during the RIE etching and ion bombardment. Then, these defects can act as carrier recombination centers after metallization, reducing contact resistance. As another method to heavily dope β-Ga2O3, Zeng et al. employed spin-on-glass (SOG) method with a high-temperature diffusion drive-in process at 1200 °C for 5 min to obtain heavy Sn-doped β-Ga2O3 [121]. The specific contact resistance was found to be ~ 2.1 × 10–5 Ω∙cm2. Xia et al. reported a contact resistance of ~ 1.5 Ω∙mm by using a recess and MBE regrown Si delta doping with a carrier concentration of ~ 2 × 1020 cm −3 [122]. Based on the reported results, it is speculated that a heavily doped β-Ga2O3 layer can be obtained by various doping techniques, resulting in the specific contact resistance of 10–5 ~ 10–6 Ω∙cm2.

As shown in Table 6, some works employed indium tin oxide (ITO) and aluminum zinc oxide (AZO) as an IL between ohmic metals and β-Ga2O3 layer [107, 108]. This ohmic contact scheme can be realized with a relatively low doping concentration (~ 1017 cm−3) of β-Ga2O3 by post-annealing alone and maintain their ohmic property even after annealing above 1150 °C [108]. These are advantageous compared to Ti-based electrodes, simplifying the device fabrication process and realizing high-temperature operating devices. As shown in Fig. 8, no bubbling was observed on the surface of ITO/Ti/Au contacts while a bubble was observed after annealing at 500 and 600 °C, resulted from the out-diffusion of oxygen atoms into the upper metal layers [110]. Thus, it is required to cap ITO layers with different metal layers to prevent the degradation of surface morphology.

Fig. 8
figure 8

Optical micrographs of metal patterns on Au/Ti/ITO/Ga2O3 for a as-deposited, b after 500 °C annealing, and c 600 °C annealing [110]

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Recently, Lyle et al. fabricated Ti/Au metal contacts on (010) and (001) β-Ga2O3 layers and investigated the interfacial characteristics as a function of annealing temperature [26]. They observed significant differences in the chemical and electrical properties of the Ti/(010) β-Ga2O3 and Ti/(001) β-Ga2O3 interfaces: 1) larger amounts of Ti-oxidation observed on the (001) surface, 2) higher barrier heights on the (010) surface, and 3) changes in the barrier heights for higher temperature annealing and the increase in Ti-oxidation with increasing the temperature. Based on these results, they suggested that the electrical properties of Ti-based contacts depend on the orientation of β-Ga2O3 layer. However, such comparison between different crystal orientations is still lacking and thus more systematic study on the orientation-dependent ohmic contact properties is necessary.

To develop the ohmic contact properties further for n-type β-Ga2O3, the work function of contact metal should be close or smaller than the electron affinity of β-Ga2O3 (4.0 eV [1, 83]). Accordingly, low work function metals such as Hf (work function 3.9 eV), Sc and La (both 3.5 eV) and Gd (2.9 eV) and bilayers of these with Au can be considered as alternatives to Ti/Au [123]. Shi et al. investigated the ohmic contact properties using Mg/Au metallization [124], where the work function of Mg is 3.66 eV [24].

Like Schottky contact, the transport mechanisms for ohmic contact make us to understand the electrical properties of ohmic contacts to β-Ga2O3 thoroughly. According to TE, thermionic field emission (TFE), and field emission (FE) models, the specific contact resistivities are described as [104, 105]

$$\rho_{C} \propto \frac{1}{T}{\text{exp}}\left( {\frac{{q\phi_{B} }}{kT}} \right),{\text{ for TE}}$$
(6)
$$\rho_{C} \propto {\text{exp}}\left( {\frac{{q\phi_{B} }}{{E_{00} }}} \right),{\text{ for TFE }}\& {\text{ FE}}$$
(7)

Here, \(E_{00} = q\hbar /2(N_{D} /m_{e} \varepsilon_{S} )^{1/2}\) is the energy parameter, where me is the electron effective mass. The current transport mechanism is different according to the E00 value, such as TE for E00/kT <  < 1, TFE for E00/kT ~ 1, and FE for E00/kT >  > 1 [104]. When no significant temperature dependence of the contact resistance is observed, it would imply that the FE model is dominant. In spite of the importance, clarifying the current transport mechanism in β-Ga2O3 ohmic contact has rarely been done. As an example, Shi et al. [125] investigated the carrier transport mechanism of Mg/Au ohmic contact to lightly doped (\(\overline{2 }\) 01) β-Ga2O3. They found that the basic mechanism of current transport is dominated by TE model with the effective barrier height of 0.1 eV.

To summarize this section, following points are suggested to be investigated further. Ion implantation requires a high-temperature annealing process to activate the implanted donor, which may cause incomplete activation and surface roughening. Epitaxial growth can produce a high quality of epitaxial layer, but it has some drawbacks such as high expense and low throughput. Hence further studies are necessary to optimize the heavy doping process of β-Ga2O3. Though Ti/Au metallization is widely used for ohmic contacts, other metallization can be investigated. For GaN, Ti/Al/X/Au (X = Ti, Ni, Pt…) multilayers were reported to be good ohmic contacts [126]. Some materials such as TiO2, ITO and AZO reveal the negative conduction band offset (ΔEC) with β-Ga2O3 [127]. When such materials are used as an IL, current can flow through the IL without obstruction under the forward bias while electrons can tunnel through the triangular barrier at the IL/β-Ga2O3 interface under the reverse bias, increasing the current values [127]. Therefore, ohmic contact properties with an optimized IL is expected to reduce the ohmic contact resistance further. Like dry plasma etching, wet etching can also affect the ohmic contact properties. Studies on the effect of wet etching on β-Ga2O3 ohmic contacts are lacking, requiring further investigations.

5 Reverse leakage current in β-Ga2O3

When the defects are present in the semiconductor, they can increase the reverse leakage current and decrease the breakdown voltage. Recently, much research has been done to clarify the relationship between defects and reverse leakage current in β-Ga2O3 Schottky diodes. Based on the analysis on the leakage current in Schottky diode array formed on (010) β-Ga2O3, Kasu et al. [89] found that the dislocation defects along the [010] direction acted as leakage current sources while Si doping concentration was not associated with the leakage current. In another work, Kasu et al. [128] observed following etch pits on the (\(\overline{2 }\) 01) β-Ga2O3 surface: (1) line-shaped etch pattern originated from a void defect and (2) arrow-shaped etch pit and gourd-shaped etch pit originated from a dislocation. Further, they suggested that there is no relationship between the defects and the leakage current in vertical Schottky diodes, unlike the case for the (010) surface. Although the etch pit density on the (\(\overline{2 }\) 01) surface was higher than that on the (010) surface, the number of Schottky diodes with a high leakage current was much lower for the (\(\overline{2 }\) 01) surface compared to the (010) surface.

Sdoeung et al. utilized ultra-high sensitive emission microscopy to investigate the origin of reverse leakage current for EFG-grown (001) β-Ga2O3 Schottky barrier diodes [129]. They observed that the reverse leakage current is associated with the partially appearing voids on the surface but could not observe clear relationship between the leakage current path and the dislocations by synchrotron X-ray topography. Oshima et al. found in Schottky diodes on (001) β-Ga2O3 that the electrical properties such as barrier height, ideality factor and leakage current revealed almost no correlation with the density of the line-shaped voids [130]. Stacking faults, one of the killer defects, were considered to be responsible for the leakage current in Schottky contacts to HVPE-grown (001) β-Ga2O3 [131]. These works indicate that the leakage current sources would be different according to the growth methods and crystal orientations.

The transport mechanisms to explain the reverse leakage current include TE, TFE, and FE models. In general, the dominant transport mechanism depends on the doping concentrations: TE for ND < 1 × 1017 cm−3, TFE for 1 × 1017 < ND < 1 × 1019 cm−3, and FE for ND > 1 × 1019 cm−3. When the image-force barrier lowering is present, it can also affect the revere leakage current. According to TE and TFE models, following equations can be used to analyze the reverse I–V characteristics [23, 132, 133]

$$J_{{}}^{TE} = A^{**} T^{2} \exp \left( { - \frac{{q\phi_{B} }}{kT}} \right)$$
(8)
$$J^{TFE} = \frac{{A^{**} T}}{k}\sqrt {\pi E_{00} q\left[ {V_{R} + \frac{{\phi_{B} }}{{\cosh^{2} (E_{00} /kT)}}} \right]} \times \exp \left( { - \frac{{q\phi_{B} }}{{E_{0} }}} \right)\exp \left( { - \frac{{qV_{R} }}{\varepsilon ^{\prime}}} \right)$$
(9)
$$\varepsilon ^{\prime} = \frac{{E_{00} }}{{E_{00} /kT - \tanh (E_{00} /kT)}},E_{0} = E_{00} \coth (E_{00} /kT)$$
(10)

where \(\xi = \sqrt {2qN_{D} /\varepsilon_{S} (V_{R} + V_{b} - kT/q)}\) is the electric field at the MS interface, and VR is the reverse bias voltage. The reverse leakage current in Schottky diodes for wide band-gap semiconductors such as GaN, SiC, and diamond is generally explained by TFE rather than TE, in which the relatively large barrier height hinders thermal emission over the Schottky barrier but renders tunneling through the barrier [69]. This explanation can also be considered for β-Ga2O3 Schottky diodes.

When the defects are involved with the leakage current, Poole–Frenkel (PF) emission, one-dimensional variable range hopping (1D-VRH), and trap assisted tunneling (TAT) may contribute to the current conduction [134,135,136]. Fowler–Nordheim (FN) tunneling is another possible transport mechanism, which becomes dominant when the barrier is thin enough (< 10 nm) [135]. The PF emission is associated with the electron emission via a trap state into a continuum of electron states [134, 135]. When the PF emission is the dominant transport mechanism, the reverse current is described by the following equation

$$J \propto \xi \exp \left[ { - \frac{{q(\phi_{PF} - \sqrt {q\xi /\pi \varepsilon_{0} \varepsilon_{S}^{h} } )}}{kT}} \right]$$
(11)

where ϕPF is the electron emission energy from the trap and \(\varepsilon_{S}^{h}\) is the relative dielectric permittivity at high frequencies. The 1D-VRH model describes a thermal activation current transport from the metal into the semiconductor occurring along the defect states related with a threading dislocation near or below the Fermi level [47]. The conductivity of the device is given by [136]

$$\sigma = \sigma_{0} \exp [ - (T_{0} /T)^{0.5} ]$$
(12)

where T0 is the characteristic temperature. When TAT is dominant, the reverse current is expressed as follows [137]

$$J \propto \exp \left( {\frac{{ - 8\pi \sqrt {2qm_{e} } }}{3h\xi }\phi_{T}^{3/2} } \right)$$
(13)

where ϕT is the electron trap energy. The strong electric field within the depletion region reduces the lateral distance between the traps and the available states in the conduction band, substantially increasing the probability of electron tunneling [137]. Figure 9 shows the schematic band diagram of possible reverse leakage current transport mechanisms in β-Ga2O3 Schottky diodes.

Fig. 9
figure 9

Schematic band diagram of possible reverse leakage current transport mechanisms in β-Ga2O3 Schottky diodes

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Zhou et al. demonstrated in Pt/(\(\overline{2 }\) 01) β-Ga2O3 Schottky contacts that the reverse leakage current is governed by the PF emission with the trap emission energy of ~ 0.7 eV [134]. Yang et al. showed in lateral Pt/(\(\overline{2 }\) 01) β-Ga2O3 Schottky diodes that two models including the TAT and 1D-VRH play important roles in the reverse leakage current [47]. Xu et al. reported in Ni/(\(\overline{2 }\) 01) β-Ga2O3 Schottky contacts that the TFE and TAT models are dominant at low and high reverse biases, respectively, associated with the deep-level traps at the MS interface [138]. According to the comparative analysis on the Pt/ β-Ga2O3 Schottky contacts on (\(\overline{2 }\) 01) and (010) substrates, Fu et al. showed that the reverse current for both samples were explained by the TAT and 1D-VRH models [21].

Lingaparthi et al. observed high reverse leakage current in Ni/(001) β-Ga2O3 Schottky diodes [77]. Based on the comparison between experimental and simulation data, they concluded that the thin surface barrier formed by high density of oxygen vacancies near the surface caused tunneling to occur easily. Further, they could reduce the leakage current after annealing in an oxidative environment. Xu et al. showed in Au/β-Ga2O3 based metal–semiconductor-metal solar blind photodetectors that the dark reverse leakage current is dominated by the TFE at low electric field and the PF emission from a deep trap level of 0.42 eV at high field, respectively [139]. Xia et al. found in Ni/(001) β-Ga2O3 Schottky diodes that the reverse leakage current showed a good fit to the TFE model when the reverse voltage was less than 80 V, and it was dominated by the tunneling effect at higher voltage [67]. They also observed that at high reverse voltage, a large number of electrons are injected into the drift region, and the current follows a trap-assisted space-charge-limited conduction (SCLC) mechanism. Li et al. analyzed the reverse leakage current of Ni/(\(\overline{2 }\) 01) β-Ga2O3 Schottky diodes using the numerical reverse leakage model [45]. As shown in Fig. 10(a), they could explain the reverse leakage current, with including both the image-force lowering (IFL) and doping effects. They also observed that the linearity in the FN plot shown in Fig. 10(b) deviated with the temperature, indicating that not FE but TFE is strongly involved. Furthermore, they observed that the barrier height from the reverse leakage model is consistent with those from the forward I–V and C–V methods. Based on the analysis, they suggested the possibility of achieving the intrinsic breakdown electric field in β-Ga2O3 Schottky diodes with a high barrier height of 2.2 ~ 3 eV, without developing p-n homojunction in Ga2O3 [45]. To data, however, the analysis on the reverse leakage current in β-Ga2O3 Schottky diodes is limited in the literature. Therefore, the development of various β-Ga2O3 based devices requires to clarify the exact transport mechanisms in metal/β-Ga2O3 contacts.

Fig. 10
figure 10

a Temperature-dependent reverse leakage current density, with the numerical reverse leakage model. The contribution from thermionic emission (TE) with image force lowering (IFL) is also shown. b Fowler–Nordheim (FN) plot with the fitting results using the numerical reverse leakage model [45]

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Using CF4 plasma treatment, Luo et al. reported the suppression of reverse leakage current by four orders of magnitude in Ni/ β-Ga2O3 Schottky diodes [140]. Okumura and Tanaka performed wet and dry etchings for β-Ga2O3 and investigated various acid and alkali solutions to remove the plasma-induced damage [141]. By immersing the plasma etched samples in hot phosphoric acid solution, they could find the differential on resistance and the ideality factor of (001) β-Ga2O3 Schottky diodes with mesa termination to be 0.91 mΩcm–2 and 1.03, respectively, and could explain the reverse current by TFE model. Xia et al. comparatively investigated the effects of downstream plasma exposure with O2, N2 and CF4 on (001) β-Ga2O3 substrate and observed that the changes are much less than caused by exposure to hydrogen-containing plasmas [142]. While fabricating Ga2O3 based devices, plasma treatments are used in deep etching for patterning, surface cleaning, resist/dielectric layer removing. In those cases, the plasma-induced damage is unavoidable, which degrades the device performance [48, 58, 143, 144]. Thus, an additional process for minimizing the plasma-induced surface damage is crucial to realize suitable device performance. Yang et al. employed thermal annealing at 450 °C to remove the near-surface damage caused by inductively coupled plasma (ICP) discharges of BCl3/Ar [145]. To reduce the surface damage of dry etched β-Ga2O3, Lee et al. performed the wet etching processes using tetramethyl ammonium hydroxide (TMAH) solution and sulfuric peroxide mixture (SPM) solution [146]. Tang et al. reported high performance β-Ga2O3 trench Schottky diodes with the employment of a novel etching technique called self-reactive etching (SRE) [147]. These works suggest that the development of etching and the post etching methods is another important issue in fabricating β-Ga2O3 based devices.

Because the thermal stability is critical in the performance of β-Ga2O3 based devices, the temperature-dependent I − V measurements were mainly performed at elevated temperatures [42, 50, 72, 78, 79, 87]. But this does not provide full information about the conduction mechanism and the properties of the barrier formation. The low-temperature dependent I − V characteristics enable us to understand the different aspects of the transport mechanisms. For instances, Reddy et al. investigated the current characteristics of Au/Ni/β-Ga2O3 Schottky diodes in the temperature range of 100 ~ 400 K [65]. Sheoran et al. also characterized the I − V properties of Au/Ni/β-Ga2O3 Schottky diodes in the temperature range of 78 ~ 350 K [74]. For both works, higher ideality factor than unity at low temperatures was explained by the inhomogeneous Schottky barrier. Meanwhile, Labed et al. examined the I − V characteristics of Ni/β-Ga2O3 Schottky contacts in the temperature range of 100 ~ 300 K and concluded that tunneling is reduced while TE is increased with increasing temperature [148]. At low temperatures, tunneling effect becomes more significant in the current conduction [23]. However, there is little research on the low temperature electrical characterization [57, 149], which needs to be considered for future works.

6 Surface and deep-level defects in β-Ga2O3

Because the density of surface/interface states plays an important role in determining the effective SBH, passivating these states is essential to improve the diode performance. Therefore, the nature of surface electronic behavior is also an important factor for metal contacts and gas sensing devices. In n-type semiconductors, the FL is pinned at the charge neutrality level (CNL) at the surface due to surface states, in which the surface barrier height is given by [150]

$$q\phi_{B} = E_{g} - E_{V}$$
(14)

where EV is the valence band maximum (VBM) measured with respect to the FL. Using X-ray photoemission spectroscopy (XPS) measurements, Fu et al. obtained the surface barrier heights of 1.14 and 1.63 eV for the (\(\overline{2 }\) 01) and (010) β-Ga2O3 surfaces, respectively. The conduction bands were bent upward, implying the presence of negatively charged surface states and defects near the surfaces [21]. CNL is located near the middle of the band gap in conventional semiconductors such as Si and GaAs, where the metal induced gap states (MIGS) change from a donor-like to an acceptor-like nature [151, 152]. As shown in Fig. 11, the CNLs for ZnO, CdO, In2O3, and SnO2 are located at 0.5, 0.4, 0.7, and 0.6 eV above the conduction band minimum (CBM), respectively, which can be understood by the relatively low energy of CBM formed by the low-lying metal s orbitals [153]. Therefore, the surface states tend to be positively charged donor-like, causing electrons to be accumulated near the surface and a downward band bending is observed. The CNL for Ga2O3 is located at 0.6 eV below the CBM, causing both surface electron depletion and upward band bending [154].

Fig. 11
figure 11

Band lineups of oxide semiconductors and other conventional semiconductors [153]

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Hong et al. performed post deposition annealing at 200 °C for Ni/Au Schottky contacts to (001) β-Ga2O3 substrate and found the lower interface trap density and higher reverse breakdown voltage compared to the as-grown sample, which was explained by the NiO formation due to the Ni diffusion into Ga2O3 [155]. Hu et al. employed a floating metal ring (FMR) edge termination structure in Ni/Au contacts to β-Ga2O3 and found that the interface trap density was in the range of 1.24 × 1012 cm−2 eV−1 to 1.71 × 1013 cm−2 eV−1 [80]. Yatskiv et al. investigated the electrical properties of graphite/β-Ga2O3 Schottky junctions formed on two different (\(\overline{2 }\) 01) and (010) β-Ga2O3 orientations and found better diode performance for (\(\overline{2 }\) 01) orientation, associated with a lower density of interface states and their shorter trapping/detrapping time constants [156]. Ingebrigtsen et al. observed the lower reverse leakage current and the lower ideality factor in the (010) samples compared to the (\(\overline{2 }\) 01) ones. Using deep level transient spectroscopy (DLTS), they found that the E2 concentration (EC–0.82 eV) in the (\(\overline{2 }\) 01) samples is higher compared to that in the (010) samples, associated with the different band bending at the two β-Ga2O3 surfaces [157]. The barrier heights of the oxidized Schottky contacts were 0.5 ~ 0.8 eV higher than their plain metal counterparts, associated with the passivation of interfacial oxygen vacancies and an increase in the work function of the oxidized metals [56]. With the oxygen annealing, Lingaparthi et al. observed the passivation of surface states and the reduction of the net carrier concentration, lowering the reverse leakage of β-Ga2O3 Schottky diodes [158]. These results indicate that the surface/interface states affect the electrical properties of metal/ β-Ga2O3 contacts and the passivation effect of these states would be investigated further.

Using DLTS and deep-level optical spectroscopy (DLOS) measurements, Zhang et al. investigated the deep-level defects in EFG-grown (010) β-Ga2O3 [159]. They reported that the three traps at EC–0.62, 0.82, and 1.00 eV are similar to traps in CZ-grown β-Ga2O3 observed by Irmscher et al. [160]. It was predicted that Sn on Ga sites (SnGa) or oxygen vacancy may be related with the defects at EC–0.82 eV [159, 161]. According to the temperature-dependent van der Pauw and Hall-effect measurements for the samples grown by various methods, including EFG, CZ, MBE, and low-pressure chemical vapor deposition (LPCVD), Neal et al. reported that the donor energy of Si and Ge is 30 meV, while the acceptor energies for Fe and Mg are 860 meV and 1.1 eV, respectively [162]. Farzana et al. reported in Ge-doped (010) β-Ga2O3 grown by plasma assisted MBE that the dominant deep-level states are in the middle and lower half parts the bandgap, with the highest concentration for energy levels at EC –2.00 eV, EC–3.25 eV, and EC–4.37 eV [163]. This is contrary to the results reporting much higher concentrations of defects within the upper bandgap region [159, 160]. Figures 12(a) and (b) show the summary of the energy distribution of deep level defects for EFG-grown β-Ga2O3 (010) substrate and Ge-doped β-Ga2O3 (010) MBE epitaxial layers, respectively, by Farzana et al. [163]. Very low concentration of relatively shallow levels in the range of EC–0.1 eV to EC–0.2 eV was observed in PAMBE-grown Ge-doped (010) β-Ga2O3 epitaxial layers, suggesting high potential for future devices where defect levels in the upper regions are responsible for device degradation mechanisms.

Fig. 12
figure 12

Summary of the distribution (energy levels and concentrations) of deep-level defects for a EFG-grown (010) β-Ga2O3 substrate and b MBE-grown Ge-doped (010) β-Ga2O3 epitaxial layers. The horizontal bars represent the concentration of each trap state, drawn to the scale of 1 × 1016 cm–3 as indicated by the black line (NT) [163]

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Studies on irradiated samples is also beneficial for identifying and explaining electrically active defects. Ingebrigtsen et al. investigated the impact of proton irradiation on the charge carrier concentration and electrically active defects [164]. Polyakov et al. investigated the effect of hydrogen plasma on deep-level spectra and suggested that hydrogen plasma exposure could produce surface damage in the near-surface region and compensate shallow donors [165]. Ghadi et al. investigated the deep-level defects in metal organic chemical vapor deposition (MOCVD)-grown β-Ga2O3 [166]. As a p-type dopant, Mg acceptor levels in MOCVD-grown β-Ga2O3 has also been investigated [167]. According to the growth methods, there may exist various deep-level defects in the epitaxial Ga2O3 layer. As comprehensively reviewed by Wang et al. [168] and Tadjer et al. [169], the origin of deep-level defects is an important electrical component to be studied. These defects can act as electron traps, affecting the current conduction significantly.

Chen et al. investigated the emission kinetics of a single-trap in (\(\overline{2 }\) 01) β-Ga2O3 Schottky diodes and reported that the deep level E1 (EC–0.63 eV) observed by DLTS is related with the PF emission [170]. Based on the temperature-dependent Hall-effect measurements, Oishi et al. found that the dominant scattering mechanisms are ionized impurity and optical phonon scatterings for the low- and high-temperature regions, respectively [171]. Gong et al. fabricated β-Ga2O3 Schottky diodes terminated with p-NiO field limiting rings and reported that the reverse leakage mechanism is identified to be PF emission through localized traps with an energy level of EC–0.72 eV [172], similar to the energy level of gallium vacancies (VGa) in β-Ga2O3 determined by DLTS method [173]. Armstrong et al. observed the strong photoconductive gain in β-Ga2O3 Schottky photodiodes and associated it with self-trapped hole formation near the Schottky diode, lowering the effective Schottky barrier in reverse bias and producing photoconductive gain [174]. Qian et al. employed fluorine plasma treatment in Ga2O3-based solar-blind photodetectors and found the enhanced device performance due to the passivation of local oxygen vacancies and the suppression of surface chemisorption [175]. However, the detailed mechanism explaining the effect of each defect on the current transport mechanisms is unsatisfactory. Therefore, clarifying the correlation between surface/deep level-defects and current transport mechanisms more thoroughly is suggested for another future work.

7 Summary

Many published review papers regarding β-Ga2O3 single crystals in the literature are roughly categorized as follows: 1) growth and material properties of bulk β-Ga2O3 [168, 169, 176,177,178,179,180,181], bulk β-Ga2O3-based power/photonic devices [8, 9, 182,183,184,185] and their combination [1, 186,187,188,189,190]. Studies on metal contacts are essential to understand the electrical behavior of β-Ga2O3-based devices and the material properties of Ga2O3. To data, reviews of metal contacts to β-Ga2O3 single crystals are still lacking [191, 192]. This review suggests the following further research for metal/ β-Ga2O3 contacts: (1) clarifying the correlation between various defects and current transport mechanisms based on the temperature-dependent electrical properties, (2) nanoscale electrical investigation to explain the macroscale electrical properties, (3) controllable n-type heavy doping and thermally stable metallization for ohmic contacts. Resultantly, the importance of studies on the metal contacts to β-Ga2O3 (both bulk and epitaxial layers) will increase continuously.