Control of Schottky barrier height in metal/$β$-Ga₂O₃ junctions by insertion of PdCoO₂ layers

Schottky junctions composed of metals and wide-bandgap semiconductors are essential elements for power electronics.¹ Among the various wide-bandgap semiconductors,² such as GaN, SiC, diamond, and Ga₂O₃, an oxide semiconductor Ga₂O₃ has significant advantages including a wide bandgap close to 5 eV, ability to fabricate high-quality single crystals by a mass-production-compatible melt-growth technique, and controllable conductivity.³ Schottky junctions on Ga₂O₃ substrates have been investigated using various contact electrodes such as elemental metals,^4–10 partially oxidized metals,^11–13 and crystalline oxide metals,¹⁴ some of which are promising structures with sufficient rectification properties for switching device applications. The current density–voltage (J–V) property of a Schottky junction is characterized by a forward threshold voltage V_F and reverse leakage current density J_R, which are governed by a SBH.¹ A smaller V_F and lower J_R are preferable for the minimization of the power dissipation by Joule heating during repeated device operation. However, V_F and J_R normally exhibit a trade-off relationship: a smaller V_F with higher J_R or a larger V_F with lower J_R. To meet the requirements of operation conditions such as operation temperature, voltage, frequency, and duty cycle, it is necessary to optimize the SBH for minimization of the total power dissipation in on-state $PLon=δSJFonVF$⁠, off-state P_L(off) = (1 − δ)SJ_RV_R, turn-off transient $PLturn-off=0.5τoffSJFonVRf$⁠, and turn-on transient $PLturn-on=0.5τonSJFonVRf$⁠.¹ Here, S is the junction area, J_F^on is the on-state forward current density, V_R is the reverse bias voltage, δ is the duty cycle, $τon(off)$ is the turn-on (off) transient duration, and f is the operation frequency. As predicted by the Schottky–Mott relation for an ideal Schottky junction, an n-type SBH is determined by the difference between the work function ϕ_m of the contact metal and the electron affinity χ_s of the semiconductor.¹⁵ However, it is well known that the SBH in a realistic device often does not follow the Schottky–Mott relation due to the extrinsic origin of Fermi-level pinning, even when the contact metal is properly selected to control the SBH.¹⁶ As alternative approaches, rather than just replacing the contact metals, atom implantation,¹⁷ alloying,¹⁸ bilayer structures,¹⁹ and the interface dipole effect^20,21 have been studied in conventional semiconductor devices. In this study, we exploit the interface dipole effect by insertion of the ionic layered metal PdCoO₂ to control SBHs in β-Ga₂O₃ Schottky junctions [Fig. 1(a)]. At the interface of PdCoO₂/β-Ga₂O₃, owing to ionic layer stacking {… Pd⁺/[CoO₂]⁻/Pd⁺/[CoO₂]⁻ …[Fig. 1(a)]},²² large interface dipoles (∼1.1 eV) are naturally formed.¹⁴ By inserting ultrathin PdCoO₂ between various metals (Pt, Ni, Cr, and Ti) and β-Ga₂O₃, we demonstrate the systematic control of SBHs in a wide range of 0.7 eV–1.9 eV by tuning the PdCoO₂ thickness.

For precise evaluation of the Schottky barrier height, avoiding defect formation during the device patterning is important. Here, we chose a lift-off process using water-soluble sacrificial templates to fabricate the Schottky junctions with the diameter D = 200 µm, following our previous works.^14,23 This process is free from a high-energy plasma bombardment that could generate deep trapping sites in β-Ga₂O₃.²⁴ Commercially available unintentionally n-type doped β-Ga₂O₃ (−201) substrates of nominal electron concentration n = 6.2 × 10¹⁷ cm⁻³ (Novel Crystal Technology, Inc.) were cleaned by an acidic solution [water:(30%–35.5% H₂O₂):(95% H₂SO₄) = 1:1:4] for 5 min and then rinsed with water. The LaAlO₃/BaO_x sacrificial templates were patterned on the β-Ga₂O₃ substrates using conventional photolithography and pulsed-laser deposition (PLD) at room temperature. The c-axis-oriented PdCoO₂ thin films were grown by PLD at a substrate temperature of 700 °C under an oxygen pressure of 150 mTorr.²⁵ The thickness of PdCoO₂ (d) was controlled by the number of ablation laser pulses. A growth rate (nm/pulse) was estimated by the Laue fringes in the x-ray diffraction pattern of a PdCoO₂ reference sample grown on c-Al₂O₃.²⁵ The 40-nm top metals (Pt, Ni, Cr, and Ti) were deposited independently with a shadow mask on different regions of one sample, as shown in Fig. 1(b). The Ni, Cr, and Ti layers were deposited by electron-beam evaporation, and the Pt layer was deposited by sputtering. After the deposition of the top metals, the samples were immersed in de-ionized water under ultrasound to remove the LaAlO₃/BaO_x water-soluble template together with the unnecessary part of the top metal/PdCoO₂ layers. To obtain Ohmic contacts, Al wires were wedge-bonded directly to the top surface of the β-Ga₂O₃ substrate. The bonded Al wires were then covered by mechanically pressed In, which gives the contact resistance in the order of 10 $Ω$⁠. Two-probe J–V characteristics were measured at 298 K using an Agilent 4155C semiconductor parameter analyzer and triaxial needle probers. As shown in Fig. 1(a), the forward direction corresponds to a positive bias applied to the top metal and ground connection with the In/Al Ohmic contact. We characterized J–V properties of approximately 10 devices for each combination of a top metal material and a different PdCoO₂ thickness d. The triangular domains with smooth surface terraces in PdCoO₂ thin films give thickness inhomogeneity with the root-mean-square (rms) roughness below 1 nm (Fig. S1). Capacitance vs voltage (C–V) characteristics were measured by using an Agilent E4980A precision LCR meter using 1-kHz AC modulation voltage with an amplitude of 0.1 V.

The ideal SBHs for J–V ϕ_b0^JV and the SBHs for C–V ϕ_b^CV are plotted against d in Figs. 4(a) and 4(b). For all the top metals except for Cr, ϕ_b0^JV gradually increases with d to the maximum value of about 1.9 eV that agrees well with that of the bare PdCoO₂/β-Ga₂O₃ (gray diamonds). This indicates that the saturated ϕ_b0^JV for the thickest limit d = 20 nm is dominated by the PdCoO₂/β-Ga₂O₃ interface; the work function of the top metal plays a less decisive role in the determination of ϕ_b0^JV because of the sufficient separation from the interface. We speculate that the smaller ϕ_b0^JV ∼ 1.6 eV observed for Cr/PdCoO₂ (20 nm)/β-Ga₂O₃ might originate from the interfacial reaction between Cr and PdCoO₂, which could affect the work function of PdCoO₂. In fact, the ideality factor of the all the Cr junctions for d = 20 nm (Fig. S2) is apparently worse than that for other junctions. By contrast to the behavior of the ϕ_b0^JV in Fig. 4(a), the ϕ_b^CV of metal/PdCoO₂/β-Ga₂O₃ reaches the saturation value around d = 4.7 nm, approaching the ϕ_b^CV of PdCoO₂/β-Ga₂O₃ (gray line) [Fig. 4(b)]. As ϕ_b^CV generally reflects the areal mean value of SBHs in the junction area S and ϕ_b0^JV is dominated by the lowest SBH in the junction,³² the different thickness dependences between ϕ_b^CV and ϕ_b0^JV suggest the existence of the in-plane inhomogeneity of the SBH for small d. This inhomogeneity could originate from the difference in PdCoO₂ thickness and/or difference in electrostatic screening length between the inside and the boundary regions of the triangular PdCoO₂ domains (Fig. S1). For small d, as the effect of top metals is not completely screened by the PdCoO₂ layer, the interface area would consist of the inside of PdCoO₂ domains generating high SBHs and the boundary regions generating low SBHs. Such in-plane fluctuation of SBHs is known to be smoothed by the band-bending effect that occurs in the length scale ∼W_d.²⁷ Because the typical size of the boundary regions (the purple dotted line and the gray lines and arrows in Fig. S1) is smaller than the depletion layer width W_d = 60–100 nm, the low-SBH regions would be pinched-off by the neighboring high-SBH regions, as a result of the band-bending effect.^16,27,33 This pinch-off effect would result in the gradual increase in ϕ_b0^JV with an increase in d, as in Fig. 4(a).

The controllable range of ϕ_b0^JV by the insertion of the PdCoO₂ layer is summarized in Fig. 5, where ϕ_b0^JV is plotted against the work function of the top metal.^28,29 By selecting the suitable combination of top metal and d, ϕ_b0^JV can be controlled in the range of 0.7 eV–1.9 eV. The wide-range controllability would be beneficial to tune the optimal balance between V_F and J_R, depending on various types of Schottky diode applications. The possible energy band diagram is presented in the inset of Fig. 5. At the interface of the top metal and PdCoO₂ (ϕ_PCO = 4.7 eV¹⁴) layers, the vacuum-level shift between the metal and PdCoO₂ (Δ_m) is expected to compensate the difference in work function. Usually, the interface resistance caused by Δ_m is negligible, owing to the short potential screening lengths that allow electrons to pass through the interface by tunneling. In contrast, the dipole at the PdCoO₂/β-Ga₂O₃ metal–semiconductor interface (Δ = 1.1 eV) effectively contributes to the large SBH ϕ_b0^JV and ϕ_b^CV of ∼1.9 eV.¹⁴ 

Based on the possible band diagram, the systematic reduction in ϕ_b0^JV and ϕ_b^CV with a decrease in d can be discussed assuming the two dipoles, Δ_m and Δ at the top and bottom of the PdCoO₂ layer. To consider the mechanism, the characteristic length scale d_c was determined by a fitting curve for the average SBH ϕ_b^CV vs d (Fig. S6), assuming an exponential decaying function. We employed the ϕ_b^CV vs d plot for the determination of d_c because it is less affected by the in-plane inhomogeneity of the SBH. The obtained d_c values were 1.2 ± 0.2 nm for Pt, 1.5 ± 0.5 nm for Ni, 4.0 ± 1.4 nm for Cr, and 2.4 ± 0.8 nm for Ti, where the error bars represent the standard deviations of the fittings. As a relevant length scale to d_c, the Thomas–Fermi screening length of the electrostatic potential should be taken into account, which is formulated as $rTF=1/2aBohr3/n3D1/6$⁠, where the Bohr radius a_Bohr is 0.53 Å and n_3D is the charged carrier density in the metal. Using n_3D of a PdCoO₂ bulk single crystal²² (∼2.45 × 10²² cm⁻³), r_TF was estimated to be ∼0.07 nm. The experimentally obtained d_c values were considerably larger than r_TF ∼ 0.07 nm that was calculated by assuming the homogeneous carrier distribution n_3D in PdCoO₂. In the layered crystal structure of PdCoO₂, mobile electrons exist mainly in the Pd⁺ sublattices, while the electrons in [CoO₂]⁻ sublattices are localized.³⁴ Thus, it is expected that charge screening occurs effectively in the Pd⁺ layer, but not in the insulating [CoO₂]⁻ layer. Considering the insulating nature of [CoO₂]⁻ layers, the effective screening length is expected to be in the order of the inter-Pd-layer distance (∼0.6 nm), which is much longer than r_TF ∼ 0.07 nm. The estimated screening length of ∼0.6 nm, accompanied with the finite rms interface roughness < 1 nm (Fig. S1), would explain the observed d_c values for Pt (d_c = 1.2 ± 0.2 nm) and Ni (d_c = 1.5 ± 0.5 nm). The longer d_c observed for Cr (d_c = 4.0 ± 1.4 nm) and Ti (d_c = 2.4 ± 0.8 nm) might be due to an interfacial layer that may form between Cr (Ti) and PdCoO₂. Further studies are necessary to understand the atomic-scale band diagram of the Schottky junction having a PdCoO₂ insertion layer thinner than d_c.

In summary, we have fabricated the stacked Schottky contacts composed of various metals (Pt, Ni, Cr, and Ti) and PdCoO₂ thin films on n-type β-Ga₂O₃ (−201) substrates. The SBH systematically increased with the increase in the thickness of PdCoO₂, thanks to the contribution of the interface dipole effect. The characteristic length d_c for a change in the average SBH ϕ_b^CV is likely to be determined by the electrostatic screening in the layered metal PdCoO₂ that has mobile electrons dominantly in Pd⁺ layers. The wide-range controllability of the SBH, from 0.7 eV to 1.9 eV, demonstrates that the insertion of the PdCoO₂ layer is useful for the development of high-performance Schottky diodes based on Ga₂O₃ with optimized properties.

See the supplementary material for the surface morphology of a PdCoO2/β-Ga2O3 thin film, additional datasets of the Schottky junction properties, and the determination of the characteristic length dc.

The authors thank K. Fujiwara for the experimental help with sputtering and NEOARK Corporation for the use of a maskless lithography system PALET. This work was performed under the Inter-university Cooperative Research Program of the CRDAM-IMR, Tohoku University (Proposal No. 18G0407). This work was partly supported by a Grant-in-Aid for Scientific Research (A) (Grant No. 15H02022) and a Grant-in-Aid for Early-Career Scientists (Grant No. 18K14121) from the Japan Society for the Promotion of Science (JSPS), JST CREST (No. JPMJCR18T2).