1.
Introduction

Beta gallium oxide (β-Ga₂O₃), with a large band gap of about 4.8 eV and a high theoretical breakdown electric field of 8 MV/cm^{[1, 2]}, has gained prominent attention to be applied as an adequate material for high power electronic devices. The Baliga’s ?gure of merit for β-Ga₂O₃ is about ten times larger than that of 4H-SiC and four times larger than that of GaN^[3]. Another important advantage of β-Ga₂O₃ is that larger-area single-crystal substrates can be synthesized by several conventional melt growth methods, commonly employed are Czochralski (CZ)^{[4, 5]}, floating-zone (FZ)^{[6, 7]}, and edge-defined film-fed growth (EFG)^[8–10]. In addition, carrier concentration of n-type β-Ga₂O₃ can be controlled by doping with Sn/Si in range of 10¹⁵–10¹⁹ cm^{?3[11, 12]}.



The metal oxide semiconductor field-effect transistors (MOSFET) and schottky barrier diodes are two critical power electronics application of β-Ga₂O₃. Low resistance ohmic contacts are essential for β-Ga₂O₃ devices to reduce devices’ conduction loss. Several groups^[13–15] have employed heavily doping by ion implantation technique and an intermediate semiconductor layer between metal and semiconductor to form ohmic contact. However, both of them were either expensive or complex. Additionally, in spite of the resistance of ohmic contacts per unit area being as low as 4.6 × 10^-6 Ω·cm², the mechanism of current transport in β-Ga₂O₃ ohmic contacts has received a little attention and is reported rarely. The current transport mechanism is vital for improving performance of β-Ga₂O₃-based powder devices to understand the basic electrical characteristic of ohmic contact on β-Ga₂O₃ surface, including Schottky barrier height and the carrier transport mechanism.



Up till now, four leading model of current flow in the metal–semiconductor ohmic contact are developed, namely, the thermionic emission theory (TE), field emission (FE), thermal-field emission theory (TFE), and metallic shunts model^[16]. The E₀₀ is defined as qh/4π[N/(m^*ε_s)]^1/2. Here, h is the Plank constant, N is carrier concentration in the semiconductor, ε_s is the permittivity of the semiconductor, q is the elementary charge, and m^* is the effective mass of electron in the semiconductor. (Ⅰ) For thermionic emission theory, ${
ho _ {
m{c}}}T propto {
m{exp}}left( {displaystylefrac{{q{varphi _ {
m{b}}}}}{{kT}}}
ight)$, the specific contact resistance (ρ_c) of the ohmic contact decreases with increasing temperature and rises exponentially with an increase in φ_b between metal and semiconductor. Here, k is Boltzmann constant and φ_b is the effect barrier height between metal and semiconductor. (Ⅱ) For field emission theory, ${
ho _ {
m{c}}} propto {
m{exp}}left( {displaystylefrac{{{varphi _ {
m{b}}}}}{{{E_{00}}}}}
ight)$, ρ_C increases with φ_b and decrease with increasing carrier concentration of uncompensated impurities in a semiconductor, and is virtually independent of the temperature. (Ⅲ) For thermal-field emission theory, ${
ho _ {
m{c}}} propto {
m{exp}}{left( {displaystylefrac{{{varphi _ {
m{b}}}}}{{{E_{00}}{
m coth}left( {q{E_{00}}/kT}
ight)}}}
ight)_ {
m{b}}}$, ρ_c should increase with an increase in φ_b and weakly decreases with an increase of temperature. (Ⅳ) For metallic shunts model, ρ_C increases with temperature. In addition, there is another criterion for judging in which current transport model is dominant: when qE₀₀/kT < 0.5, the thermal emission mechanism is dominant; when qE₀₀/kT > 5, the field emission is dominant; when 0.5 < qE₀₀/kT < 5, the thermionic field emission is dominant.



In this letter, Mg/Au is used to prepare ohmic contact with lightly doped β-Ga₂O₃ because of its low work function, high humidity resistance, oxygen resistance, and corrosion resistance^{[17, 18]}. The Mg/Au stacks exhibit excellent ohmic contact properties on lightly doped β-Ga₂O₃ after annealing at 400 °C. To investigate current transport mechanism on β-Ga₂O₃, the dependence of current–voltage on measuring temperature was performed, followed by an analysis based on TE model.

2.
Experimental

The Sn lightly doped ($overline 2$01)-oriented β-Ga₂O₃ substrate with 680 μm thickness was used by cutting into 5 × 5 mm² pieces. The carrier concentration of single crystal β-Ga₂O₃ substrate was about 4.94 × 10¹⁷ cm^?3. Prior to metal deposition, the substrate was cleaned in methanol, acetone, methanol, and deionized water (DIW) by ultra-sonication for 5 minutes, respectively. Next, the substrates were dipped in Piranha solutions (DIW (30 %) : H₂O₂ (96%) : H₂SO₄ = 1 : 1 : 4) solution for 5 min. Then, the substrates were dipped in DIW at 90 °C for 5 min, later cooled down to room temperature. Finally, the substrate was rinsed in HF (> 40%) for 5 h. Metal deposition was performed by conventional thermal evaporation method. The Mg metal (99.999%) was evaporated with the thickness of 820 nm, followed by 600 nm thick Au metal film coating. Then metal electrodes were annealed at an optimum temperature of 400 °C for 2 min in a quartz tube under Ar gas protection. The contact metal pads for transmission line method (TLM) testers were formed by standard lithography process with space of 0.15, 0.2, 0.25, 0.3, and 0.4 mm. The dimensions of contact metal pads are 0.4 × 1.2 mm².



The current–voltage characteristics were measured using Keithley 2611A semiconductor characterization system in the range of 300–375 K. The ρ_c was extracted using the transmission line method (TLM). Hall Effect 5500 PC measurement system was employed to determine the carrier concentration of bulk β-Ga₂O₃.

3.
Results and discussion

Fig. 1 shows the current–voltage characteristics of as-deposited and annealed Mg/Au/β-Ga₂O₃ contacts samples, as measured from adjacent contact pads with a gap spacing of 0.15 mm. For the as-prepared sample, the I–V curves showed nonlinear behavior, while sample annealed at 400 °C showed the linear behavior of current–voltage curve, which indicates that thermal annealing can lead to the formation of ohmic contacts.






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Figure1.
(Color online) I–V curves for as-prepared and 400 °C annealed samples. The insert is the schematic structure of the Mg/Au/β-Ga₂O₃ contact.




Suzuki et al.^[19] reported that the barrier height of Au/β-Ga₂O₃ contact decreased with an increase in the annealing temperature. Similarly, in our experiment, the annealing results in lowing the barrier height between Mg/Au and β-Ga₂O₃ interfaces and formed ohmic contact to show linear I–V characteristic.



Fig. 2(a) shows the dependence of the experimentally measured total resistance (R_T) on distance (d) between two adjacent contact pads for the annealed sample at different measuring temperatures. The R_T can be represented by equation:

${R_ { m{T}}} = 2{R_ { m{C}}} + displaystylefrac{{d{R_{ m SH}}}}{W} = 2{R_ { m{C}}} + frac{d}{{qN{mu _ { m{n}}}S}}. $

Here, R_C and R_SH are contact resistance and sheet resistance, respectively. The d, W, q, N, μ_n and S are the distance of adjacent electrodes, width of electrodes, element charge, carrier concentration, carrier mobility and electrode area, respectively. The intercept of line with the ordinate axis corresponds to double R_C and its slope is proportional to the R_SH. The dependence of R_T on d is linear at each measuring temperature, as shown in Fig. 2(a). Fig. 2(b) shows that the R_C decreases from 0.96 to 0.8 Ω and R_SH increases from 0.3 to 0.56 Ω/□ as measuring temperature rise from 300 to 375 K. As we know, the carrier mobility is affected by temperature and it decrease with increasing measuring temperature at high temperature. Thus, the reason of the increase of R_SH with increasing the testing temperature could be attributed to the decrease of electron mobility.






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class="figure_img" id="Figure2"/>



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Figure2.
(Color online) (a) Resistance of Mg/Au-β-Ga₂O₃ structure with two adjacent ohmic contacts versus the distance at different temperatures. (b) Contact resistance and sheet resistance of the ohmic contact Mg/Au-β-Ga₂O₃ versus measuring temperatures.




In order to investigate the current transport mechanism of Mg/Au ohmic contact for annealed sample, the ρ_c was extracted as a function of measuring temperature. The ρ_c decreased slightly from 4.3 × 10^?4 to 1.59 × 10^?4 Ω·cm² in the measuring temperature range from 300 to 375 K, as shown in Fig. 3. According the model of current flow in the metal semiconductor ohmic contact, TFE and FE model may be the basic theories of current transport at the Mg/Au-β-Ga₂O₃ ohmic contact interface. However, judging from E₀₀, it is calculated to be 0.007 V and qE₀₀/kT (T = 300 K) is 0.27 < 0.5. Where, the m* is 0.28m_e^[20], ε_S is 10 for β-Ga₂O₃, with N is 4.94 × 10¹⁷ cm^?3 measured by Hall Effect 5500 PC measurement system. Consideration with the lightly doped β-Ga₂O₃, it is reasonable to conclude that the mechanism of current transport is dominated by thermionic emission theory in the present system rather than thermal-field emission theory.






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Figure3.
(Color online) Specific contact resistance of the ohmic contact Mg/Au-β-Ga₂O₃ versus measuring temperatures.




For FE theory, ${
ho _ {
m{c}}}T propto {
m{exp}}left( {displaystylefrac{{q{varphi _ {
m{b}}}}}{{kT}}}
ight)$, the dependence of ρ_cT on 1/T should be linear on a semi-logarithmic scale with the slope of this dependence proportional to the barrier height φ_b. Fig. 4 gives the experimental and theoretical relationships between ρ_cT and 1/T. It is fitted well between them, which means that the current transport mechanism of Mg/Au/β-Ga₂O₃ ohmic contact is FE consistent with the previous discussion. In addition, the effective barrier height is calculated to be 0.1 eV from the slope of the fitting curve. The effective barrier height between Mg/Au and β-Ga₂O₃ is sufficiently low which is responsible for the formation of the low contact resistance.






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Figure4.
(Color online) The dependence of ln (ρ_cT) on 1/T graph about Mg/Au-β-Ga₂O₃ ohmic contact for the annealed sample, experimental data (point) and TE model fitting (line).

4.
Conclusion

In summary, ohmic contact has been successfully realized on β-Ga₂O₃ using low work function Mg/Au stacks after annealing at 400 °C and the current transport mechanism was investigated. The temperature dependence of specific contact resistance of the Mg/Au-β-Ga₂O₃ ohmic contact decreased with increasing the measuring temperature from 300 to 375 K and qE₀₀/kT is 0.27 < 0.5. Therefore, the current transport mechanism is dominant thermionic emission theory. The effective barrier height extracted is 0.1 eV by fitting experiment data with thermionic emission model. Further investigation will be carried out on the heavily doped β-Ga₂O₃.

?

Acknowledgements



This work was supported by the National Key R&D Plan (Nos. 2016YFB0400600, 2016YFB0400601)，the National Science Foundation of China (Nos. 11675198, 61376046, 11405017, 61574026), the Fundamental Research Funds for the Central Universities (Nos. DUT15LK15, DUT15RC(3)016, No. DUT16LK29), the Liaoning Provincial Natural Science Foundation of China (Nos. 2014020004, 201602453, 201602176), the China Postdoctoral Science Foundation Funded Project (No. 2016M591434), the Open Fund of the State Key Laboratory on Integrated Optoelectronics (Nos. IOSKL2015KF18, IOSKL2015KF22).