Electric dipole effect in PdCoO2/β-Ga2O3 Schottky diodes for high-temperature operation

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Science Advances  18 Oct 2019:
Vol. 5, no. 10, eaax5733
DOI: 10.1126/sciadv.aax5733


High-temperature operation of semiconductor devices is widely demanded for switching/sensing purposes in automobiles, plants, and aerospace applications. As alternatives to conventional Si-based Schottky diodes usable only at 200°C or less, Schottky interfaces based on wide-bandgap semiconductors have been extensively studied to realize a large Schottky barrier height that makes high-temperature operation possible. Here, we report a unique crystalline Schottky interface composed of a wide-gap semiconductor β-Ga2O3 and a layered metal PdCoO2. At the thermally stable all-oxide interface, the polar layered structure of PdCoO2 generates electric dipoles, realizing a large Schottky barrier height of ~1.8 eV, well beyond the 0.7 eV expected from the basal Schottky-Mott relation. Because of the naturally formed homogeneous electric dipoles, this junction achieved current rectification with a large on/off ratio approaching 108 even at a high temperature of 350°C. The exceptional performance of the PdCoO2/β-Ga2O3 Schottky diodes makes power/sensing devices possible for extreme environments.


Recent requirements for Schottky junctions are demanding, particularly for switching/sensing device applications under harsh operating conditions, including high current densities, frequencies, and temperatures (1, 2). However, conventional Si-based Schottky diodes suffer from serious current leakage at more than 200°C because of the small Schottky barrier height (~0.9 eV) limited by the narrow bandgap of Si (~1.1 eV) (1). To realize a higher-temperature operation, alternative Schottky interfaces with a large Schottky barrier height should be developed on the basis of wide-bandgap semiconductors. The energy barrier height ϕb is shown in an ideal band diagram for a metal-semiconductor Schottky interface (Fig. 1A) according to the Schottky-Mott relation: ϕb = ϕm − χs, where ϕm is the work function of a metal and χs is the electron affinity of the semiconductor (3). The typical rectifying current-voltage characteristics of a Schottky junction, schematically shown in Fig. 1B, can be formulated by a simple thermionic emission model, as in Eq. 1.J=A**T2e(ϕb/kBT)[e(qV/nkBT)1](1)where J is the current density, A** is the effective Richardson constant, T is the absolute temperature, q is the elementary charge, kB is the Boltzmann constant, n is the empirical ideality factor, and V is the applied bias voltage. The ideal reverse current density Js (J is for V < 0) is defined as the saturation value Js = A**T2e−(ϕb/kBT), as highlighted in Fig. 1B, providing the fundamental lower bound of the reverse current density achievable at a given temperature (1). The benchmark for high-temperature operation of Schottky diodes is exemplified by the temperature dependence of Js at ϕb = 1.0, 1.4, and 1.8 eV (Fig. 1C). For high-temperature operation, the thermally excited Js must be suppressed by a large barrier height to achieve a large on/off ratio together with high forward current. For example, a ϕb >1.4 eV is required to maintain Js below 10−6 A/cm2 at 250°C, which is a typical temperature in automobile engines.

Fig. 1 Schottky junctions based on a layered PdCoO2 and β-Ga2O3 for high-temperature operation.

(A) Energy band diagram of a metal-semiconductor interface with a Schottky barrier of ϕb. ϕm, work function of metal; χs, electron affinity of semiconductor; Evac, vacuum level; EF, Fermi energy; EC, conduction band minimum; V, bias voltage. The electron is depicted as a red circle. (B) Typical current-voltage characteristic of Schottky junction showing the current rectification behavior under forward (on-state) or reverse (off-state) bias voltage. The saturation current density Js is noted in red. (C) Temperature dependence of the saturation current density Js with Schottky barrier heights of 1.0 eV (blue), 1.4 eV (green), and 1.8 eV (red) calculated by the thermionic emission model using the Richardson constant of β-Ga2O3, A** = 41.1 A/cm2 (24). (D) Schematic image for the characterization of the PdCoO2/−β-Ga2O3 Schottky junction. (E) HAADF-STEM image of the PdCoO2/β-Ga2O3 interface. The crystal orientation is represented by arrows. (F) Enlarged image of the HAADF-STEM image of the PdCoO2/β-Ga2O3 interface. The anisotropic Ψd-s orbital proposed for the conduction band of PdCoO2 is schematically shown (20). Right: Corresponding crystal model. The alternating Pd+ and [CoO2] charged layers are shown based on the nominal ionic charges in the bulk PdCoO2. The actual charge state at the interface can be modified by electronic reconstruction with screening charges.

Semiconductors that are capable of realizing a high ϕb, beyond 1.4 eV, include wide-bandgap materials, such as SiC, GaN, and Ga2O3 (4). In particular, Ga2O3 devices have recently attracted considerable attention owing to their wide bandgap of approximately 5 eV, the high-temperature stability of the material, and commercial availability of large single crystals (5). Diode operation has been demonstrated in Schottky junctions, composed of polycrystalline Pt (6, 7) and Ni (6, 810) and oxidized metals (1113) (see table S1 for polycrystalline metals and table S2 for oxidized metals). The finite range of available work functions in elemental metal electrodes, 4.0 to 5.6 eV (14), limits the achievable Schottky barrier height in the Schottky-Mott framework: ϕb = ϕm − χs. For stable operation, choosing a thermally stable Schottky contact is crucial to avoid interfacial reactions and maintain the ϕb value at high temperature (15).

Rather than using the polycrystalline electrodes, we chose a crystalline interface, where a metal is rigidly integrated with a semiconductor. To achieve a large Schottky barrier height beyond the limitation of the Schottky-Mott rule, we used a polar interface of oxide heterostructures, combining Ga2O3 with a polar layered metal PdCoO2 (Fig. 1D). The layered delafossite structure of PdCoO2 with alternating Pd+ and [CoO2] sublattices has two remarkable features (16, 17): an out-of-plane polarity and high in-plane conductivity (1820). The out-of-plane polarity, given by the alternating charged Pd+ and [CoO2] sublattices of PdCoO2, has recently been revealed to modulate the surface physical properties of PdCoO2 bulk single crystals (21, 22). This polar ionic stacking can effectively induce an electric dipole layer that enhances the Schottky barrier height at the interface. The high in-plane conductivity of PdCoO2, comparable to that of Au, supports its applicability as a Schottky contact metal. The hexagonal lattice oxygen atoms on the surface of PdCoO2 (0001) match those of β-Ga2O3 (−201), which makes it possible to form a functional interface that leverages the polar nature of PdCoO2.


We fabricated heterostructures of 20-nm-thick PdCoO2/β-Ga2O3 (a commercial n-type substrate with a nominal donor density of 7.8 × 1017 cm−3) by pulsed-laser deposition. The c axis–oriented growth was observed in typical x-ray diffraction patterns (fig. S1A). The lattice arrangement at the interface was imaged with a high-angle annular dark-field scanning transmission electron microscope (HAADF-STEM), as shown in Fig. 1 (E and F). The layered crystal structure of PdCoO2 was seen, and no threading dislocations were apparent (Fig. 1E), indicating an epitaxial relationship of PdCoO2 [0001]//β-Ga2O3 [−201], although the in-plane lattice mismatch was large at approximately 3%, as estimated from the O-O distances of 2.83 Å for PdCoO2 and 2.93 Å for β-Ga2O3 (fig. S2). An enlarged HAADF-STEM image (Fig. 1F) shows that the [CoO2] layer corresponds to the initial layer of PdCoO2 on the β-Ga2O3. The wave function of the Pd+ conducting layer is depicted in the inset of Fig. 1F, producing a polar interface between PdCoO2/β-Ga2O3 and the highly anisotropic in-plane conductivity in PdCoO2. The in-plane conductivity of the PdCoO2/β-Ga2O3 is approximately 6.3 × 104 S/cm at room temperature (fig. S1B), the value of which is high enough to achieve sufficient current spreading in the contact pad. Here, only the polarity originating from the PdCoO2 layer is considered, because the β-Ga2O3 (−201) surface is likely to be reconstructed to a stable nonpolar structure before the PdCoO2 deposition. The abrupt interface of PdCoO2/β-Ga2O3 provides a suitable platform for exploiting interfacial dipole effects with minimized extrinsic contributions, i.e., defects.

To investigate the Schottky characteristics of the PdCoO2/β-Ga2O3 junctions, we patterned the PdCoO2 thin films into circle-shaped devices using a water-soluble templating process (23). Typical J-V characteristics (Fig. 2A) showed clear rectification with a resistance ratio >109 and a reverse current density as low as the measurement limit of 10−8 A/cm2 at 220°C (blue). Applying Eq. 1 to the forward-bias region made it possible to evaluate the Schottky barrier height ϕb (the symbol ϕbJV is used to specify the measurement technique: J-V measurement) and the ideality factor n, which were approximately 1.85 eV and 1.04, respectively, at 220°C, using the A** = 41.1 A/cm2 of β-Ga2O3 (24). These values are close to the corresponding values of 1.78 eV and 1.06 characterized at room temperature. Such rectifying properties were maintained at 350°C (Fig. 2A, red) together with a large on/off ratio of approximately 108 and a reverse current density of 10−6 A/cm2. Moreover, the weak temperature dependences of ϕbJV (inset of Fig. 2A) and the ideality factor (fig. S3A) indicate the homogeneous Schottky barrier height at the interface (see Materials and Methods for a detailed discussion). The value of ϕbJV is mainly dominated by the activation process across the lowest-energy barrier region. The reverse current density (V = −20 V) at high temperature (Fig. 2B) is compared with the ideal Js lines (Fig. 1C) and data from previous studies (2530). Owing to the large ϕbJV, the value of |J−20V| at the PdCoO2/β-Ga2O3 junction (Fig. 2B, red squares) is suppressed at the measured high temperatures. We compare our ϕbJV values with metal/β-Ga2O3 junctions of previous studies (table S1), where ϕbJV is plotted as a function of the metal work function ϕm (Fig. 2C). The large deviation of the reported ϕbJV values for the specific metal/β-Ga2O3 junctions probably arises because of the differences in interface quality, e.g., a partial Fermi-level pinning at the surface that can occur (31), even when the same metal contacts are used. As measured by ultraviolet photoelectron spectroscopy (fig. S4), the PdCoO2 film is plotted at a work function of 4.7 eV in Fig. 2C. The ϕbJV value of 1.8 eV for PdCoO2/β-Ga2O3 is located above the empirical trend of the reported values in the elemental metal/β-Ga2O3 junctions (gray dotted line), whose barrier height lies in the range of 1.0 to 1.5 eV (table S1). Although partial oxidation of metals is known to increase ϕbJV (1113), the work function and crystal structures/orientations are unknown for the oxidized states of the polycrystalline film. The plot shown in Fig. 2C, which is based on the experimentally determined values of ϕbJV and ϕm, indicates that ϕbJV of PdCoO2/β-Ga2O3 is strongly influenced by the interfacial effects existing at the abrupt interface with well-defined crystal orientation, as shown in Fig. 1 (E and F).

Fig. 2 High-temperature operation of the PdCoO2/β-Ga2O3 Schottky junctions with a large barrier height.

(A) Current-voltage characteristics of the PdCoO2/β-Ga2O3 Schottky junction with a diameter of 200 μm at 227°C (blue) and 356°C (red). The gray lines are the linear fitting for the forward-bias region. The temperature dependence of the Schottky barrier height is plotted in the inset. (B) Temperature-dependent reverse current density under the bias voltage of −20 V |J−20V| plotted together with the reported values (2530). The ideal Js in Fig. 1C is also shown for ϕb = 1.0 eV (blue), 1.4 eV (green), and 1.8 eV (red). (C) Comparison of the Schottky barrier height with the reported values for elemental metal Schottky junctions (see the Supplementary Materials for the data and references used). Perpendicularly spread line data correspond to the range of the reported Schottky barrier height. The different colors correspond to the different surface orientations of the β-Ga2O3 layers. The linear trend from the reported values is shown as a broken line. The large red square corresponds to the data obtained for PdCoO2/β-Ga2O3.

In addition to the J-V characteristics, we performed capacitance (C) measurements 1/C2V (Fig. 3A) to determine the Schottky barrier height at the interface. The gradients of linear fits to the data in Fig. 3A for two device sizes (diameter D = 100 and 200 μm) indicate that the built-in potential at the Ga2O3 qVbi and the donor density ND are 2.0 eV and 3 × 1017 cm−3, respectively. This ND value is comparable to the nominal donor concentration of a commercial substrate. The junction capacitance measured with V = 0 V is independent of the AC frequency (f) over a broad range from 102 to 106 Hz, with a negligible deep trap-state capacitance Ctrap(f) (inset of Fig. 3B), which suggests the potential application of this junction in high-frequency switching elements.

Fig. 3 Energy band diagram of the PdCoO2/β-Ga2O3 interface.

(A) 1/C2-V plots for the devices with D = 100 and 200 μm measured with an AC frequency of 1 kHz at room temperature. (B) Frequency dependence of the capacitance measured with 0.1-V excitation. (C) Top: Band diagram for the PdCoO2/β-Ga2O3 Schottky junction based on experimentally observed values. The energy difference of the conduction band bottom and the Fermi energy in β-Ga2O3 (ξ) is calculated using ξ = kBTln(NC/ND) and NC = 2(2πm*kBT/h2)3/2, where h is the Planck constant and m* = 0.342m0 is the effective mass of the electron in β-Ga2O3 (24). Bottom: Schematics of the PdCoO2/β-Ga2O3 interface. A conduction electron in the Pd+ layer is shown in red. The bulk-like charged layers of PdCoO2 are schematically depicted, neglecting possible charge reconstructions.

The band diagram for the PdCoO2/β-Ga2O3 interface is depicted in Fig. 3C based on the experimental characteristics discussed above. First, the Schottky-Mott relation, ϕb = ϕm − χs, was adopted to estimate ϕb to be approximately 0.7 eV, based on the work function ϕm for PdCoO2 (4.7 eV; fig. S4) and the reported electron affinity χs of β-Ga2O3 (4.0 eV) (32). Although minor effects, such as energy lowering by an image force at the interface and the Fermi energy in Ga2O3, might make an additional contribution to the estimated value of ϕb (see Materials and Methods), it is difficult to explain the large mismatch between 0.7 eV and the experimentally evaluated result of 1.8 eV. As shown in Fig. 3C, the vacuum level shifted by Δ ≈ 1.1 eV, which contributed to the large ϕbJV. This shift is attributed to the polar nature of PdCoO2, which is composed of Pd+ and [CoO2]. The formation of a polar interface [CoO2]/Ga2O3 (STEM image in Fig. 1F and bottom of Fig. 3C) caused ϕb to increase to 1.8 eV through electric dipole effects. The interface dipole caused by the PdCoO2 polar layered structure agrees well with the calculated surface potential at O- and Pd-terminated PdO (111), which predicts an energy shift of 1.2 eV (33). The contributions of this interfacial dipole model to ϕbJV are analogous to the barrier height control achieved in SrRuO3/Nb:SrTiO3 Schottky junctions by the insertion of [AlO2] or [LaO]+, which increase and decrease, respectively, the Schottky barrier height from its original level at ~1.3 eV to 1.8 and 0.7 eV (34). In the PdCoO2/β-Ga2O3 interfaces, the interface dipole is naturally activated owing to the unique polar layered structure and the [CoO2] initial layer favored by the crystal growth of PdCoO2 electrodes (Fig. 1F).

We examined the uniformity and reproducibility of the junction properties by measuring arrays of PdCoO2 circular devices on β-Ga2O3 with various junction areas (from 100 to 1000 μm), as shown in the sample picture (Fig. 4A). A large ϕbJV of approximately 1.8 eV was obtained, irrespective of the diameter of the devices (Fig. 4B). This result contrasts with the expected inhomogeneous ϕbJV in typical large Schottky junctions owing to the high probability of pinhole-generating regions. Moreover, 27 devices were characterized with D = 100 μm to confirm the uniformity of operation. The J-V data were consistent, as shown in Fig. 4C. A histogram of ϕbJV indicated a reproducible value of ϕbJV = 1.76 eV with a narrow distribution of approximately 0.045 eV. Unlike the broad distribution of ϕbJV values for the polycrystalline metal/β-Ga2O3 junction, as summarized in Fig. 2C, the highly reproducible ϕbJV could result from the layered structural features and the all-oxide high-quality interface with the homogeneous [CoO2]/Ga2O3 polar stacks energetically favored during the thin-film growth (Fig. 1, E and F). Hexagonal interfaces of layered PdCoO2 on other semiconductors, such as SiC and GaN, could also benefit from this interfacial electric dipole effect.

Fig. 4 Uniformity and reproducibility of the large barrier height in the PdCoO2/β-Ga2O3 Schottky junctions.

(A) Optical microscopy image of the PdCoO2/β-Ga2O3 Schottky junction arrays. (B) Schottky barrier height obtained for the devices with different junction sizes. (C) Current-voltage characteristics of the 27 different devices. (D) Histogram of the Schottky barrier height for D = 100-μm devices. The Gaussian fitting (red curve) gives the central value ϕbμ = 1.76 eV and the width of distribution 2σ = 45 meV, where σ is the SD.


Superior Schottky junction properties were demonstrated with large on/off ratios, high-temperature operation at 350°C, no dependence of C-f characteristics, and considerable uniformity and reproducibility. This performance is attributed to the large ϕbJV induced by the naturally formed electric dipoles at the well-regulated polar oxide interface of PdCoO2 and β-Ga2O3. For applications under harsh conditions, PdCoO2 electrodes have considerable advantages owing to their exceptional stability to heat (~800°C), chemicals (acids/bases, pH 0 to 14), and mechanical stress (fig. S5), in addition to high optical transparency (35). The abrupt interface of the layered oxides PdCoO2 and β-Ga2O3 can extend applications of semiconductor devices to hot operating environments, such as those in automobile and aerospace applications.


Substrate preparation

For the devices with acid-cleaned β-Ga2O3, commercially available unintentionally doped β-Ga2O3 (−201) substrates with the nominal ND = 7.8 × 1017 cm−3 (Novel Crystal Technology Inc.) were immersed in an acidic solution (water: 30 to 35.5%; H2O2: 95%; H2SO4 = 1:1:4) for 5 min, followed by rinsing in water for 15 min.

PdCoO2/β-Ga2O3 device fabrication

To pattern the PdCoO2 layer by soft lithography, we used the LaAlO3/BaOx template as a water-soluble sacrificial layer (23). First, an organic photoresist was patterned on the β-Ga2O3 substrates using a standard photolithography process. The LaAlO3 (~40 nm)/BaOx (~100 nm) templates were then deposited by pulsed-laser deposition at room temperature under the base pressure of ~10−7 torr. Removing organic photoresist by hot acetone gave the patterned LaAlO3/BaOx template on the β-Ga2O3 substrates. Just before the deposition of PdCoO2 thin films, the LaAlO3/BaOx/β-Ga2O3 samples were put in O2 plasma for 50 s to remove the residual photoresist. The PdCoO2 thin films were grown by pulsed-laser deposition (35) at a growth temperature of 700°C and an oxygen partial pressure of 150 mtorr. A KrF excimer laser was used to alternately ablate the PdCoO2 stoichiometric target and Pd-PdO mixed phase target. After the thin-film growth, the LaAlO3/BaOx templates were removed by sonication in water together with the unnecessary parts of the PdCoO2 to obtain the circular PdCoO2 electrodes with a diameter of 100 to 1000 μm.

Electrical transport measurement

Current-voltage characteristics of the Schottky junctions were measured via two-wire configuration using a Keithley 2450 source meter. Al wires were bonded to the top surface of the β-Ga2O3 substrates to form ohmic contacts to the β-Ga2O3 substrates. A needle prober was used to contact the PdCoO2 and Pt top electrodes for the room temperature measurement. The capacitance measurements were carried out using an Agilent E4980A precision LCR meter with an AC modulation voltage of 0.1 V. The resistivity of the PdCoO2 thin films was measured using a four-probe configuration.

Effect of image force lowering

For the interface of a metal and an n-type semiconductor with the relative permittivity of εr, the image force lowering Δϕ under zero bias can be formulated asΔφ=q{q/4πεrε0[2qVbiND/εrε0]1/2}1/2

Here, ε0 is the vacuum permittivity. Using the experimentally determined qVbi and ND for the PdCoO2/β-Ga2O3, qVbi = 2.0 eV and ND = 3 × 1017 cm−3, and the reported εr = 10 (36), Δϕ was estimated to be 0.08 eV.

Estimation of the spatial homogeneity of the Schottky barrier height

We analyzed the temperature-dependent Schottky barrier height and the ideality factor using the potential fluctuation model to estimate the homogeneity of the barrier height (37). We considered the spatial distribution of the Schottky barrier height (ϕb) and the built-in potential (Vbi) by introducing the Gaussian distribution P(qVbi) and Pb), with an SD σs around the mean values V¯bi and ϕ¯b.P(ϕb)=1σs2πe(ϕ¯bϕb)2/(2σs2)(2)P(qVbi)=1σs2πe(qV¯biqVbi)2/(2σs2)(3)

As discussed by Werner and Güttler (37), the Schottky barrier height determined by the current-voltage characteristic, ϕbJV, relates to the ϕ¯b and σs asϕbJV=ϕ¯bσs22kBT(4)

Capacitance-voltage (C-V) measurement probes the spatial average of the built-in potential, VbiCV = V¯bi, which relates to the Schottky barrier height ϕbCV to beϕbCV=qV¯bi+kBTln(NC/ND)=ϕ¯b(5)where NC and ND denote the effective density of states in the conduction band and the doping concentration, respectively. Here, we neglected a possible contribution from the image force in the calculation of ϕbCV, which did not change the estimation of σs.

Comparing Eqs. 4 and 5, we foundϕbCVϕbJV=σs22kBT(6)

We fitted the experimental data by Eq. 6, as shown in fig. S3B, to obtain the SD σs = 54 meV, which is less than half of the reported value for Pt/β-Ga2O3s = 130 meV) (38). The ideality factor n(V,T) reflects the voltage-dependent mean barrier ϕ¯b(V) and the SD σs2(V) asn1(V,T)1=ϕ¯b(V)ϕ¯b(0)qV+σs2(V)σs(0)22kBTqVAssuming that ϕ¯b(V) and σs2(V) vary linearly with the bias voltage V, we can parameterize the voltage deformation of the barrier distribution using the coefficients ρ2 and ρ3.ϕ¯b(V)ϕ¯b(0)=ρ2qVσs2(V)σs(0)2=ρ3qVn1(T)1=ρ1(T)=ρ2+ρ32kBT(7)

The experimental data for the PdCoO2/β-Ga2O3 Schottky junction are fitted by Eq. 7, as shown in fig. S3C, to obtain the temperature-independent coefficients ρ2 = −0.073 and ρ3 = −1.93 meV.


Supplementary material for this article is available at

Fig. S1. Basic characterization of PdCoO2 thin films grown on β-Ga2O3 (−201).

Fig. S2. Relationship between work function and lattice constant for typical metal electrodes with a (pseudo-)hexagonal lattice constant close to the representative hexagonal wide-gap semiconductors.

Fig. S3. Temperature dependence of the Schottky barrier height and the ideality factor.

Fig. S4. Determination of the work function for PdCoO2 using the ultraviolet photoelectron spectroscopy.

Fig. S5. Stability of PdCoO2 thin films in a harsh environment.

Table S1. Summary of the metal/β-Ga2O3 junctions reported in literature.

Table S2. Summary of the partially oxidized metal/β-Ga2O3 junctions reported in literature.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.


Acknowledgments: This work is a cooperative program (proposal no. 16G0404) of the CRDAM-IMR, Tohoku University. We thank the NEOARK Corporation for lending a mask-less lithography system PALET. Funding: This work was supported, in part, by a Grant-in-Aid for Specially Promoted Research (no. 25000003), a Grant-in-Aid for Scientific Research (A) (no. 15H02022), and a Grant-in-Aid for Early-Career Scientists (no. 18K14121) from the Japan Society for the Promotion of Science (JSPS), JST CREST (JPMJCR18T2), the Mayekawa Houonkai Foundation, and the Tanaka Foundation. Author contributions: T.H. and A.T. designed the experiments. T.H. prepared the samples, performed transport measurements, and analyzed the data. S.I. captured the HAADF-STEM image. T.H. and A.T. wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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