Metal/BaTiO₃/β-Ga₂O₃ dielectric heterojunction diode with 5.7 MV/cm breakdown field

The potential of different materials for vertical power switching is often assessed by calculating the Baliga Figure of Merit $VBR2RON=μϵEc38.$¹ In the case of wide and ultrawide bandgap materials, the high breakdown fields and the relatively good transport properties make the Baliga Figure of Merit significantly higher than conventional Si electronics. However, the breakdown field predicted for a material is based on a rectifying junction with the barrier height that is the same as the material bandgap energy, such as the PN junction. This is challenging to achieve in several wideband gap materials where bipolar doping is not available or presents technological challenges. Schottky junctions can provide excellent rectification, but the reverse breakdown of Schottky rectifiers is limited by the Schottky barrier height, which is significantly lower than the bandgap in most wideband gap semiconductors.^2–4 In this work, we show, using the case of β-Ga₂O₃, a dielectric heterojunction approach that can enable field management so that high breakdown fields can be achieved even in unipolar junctions.

The large breakdown electric field (6–8 MV/cm)⁵ and electron mobility (250–300 cm²/V s)⁶ provide β-Ga₂O₃ a higher figure of merit than SiC and GaN. The availability of large area, high-quality bulk substrates from melt-growth methods^7–10 also provides a significant advantage for low-cost high-power devices. High voltage β-Ga₂O₃ transistors^11–15 and Schottky barrier diodes^16–19 with various designs have been reported in recent years. However, due to high acceptor activation energy and poor hole transport properties, p-type β-Ga₂O₃ is challenging to use in devices. The maximum effective breakdown field in vertical β-Ga₂O₃ devices is therefore limited by the Schottky barrier height to below 3.5 MV/cm. The breakdown of the β-Ga₂O₃ MOS structure with dielectrics (SiO₂, Al₂O₃, and HfO₂) is also limited by the metal/dielectric barrier height and is seen to occur far below the material breakdown limit of β-Ga₂O₃.

We now discuss the design principle of a dielectric heterojunction diode. The schematics and simulated energy band diagram of the dielectric heterojunction diode are shown in Figs. 1(a)–1(c). It consists of a 20 nm high-k BaTiO₃ layer (ε_r ∼ 260) on a β-Ga₂O₃ lightly doped n-type drift layer. A Schottky metal contact is formed on the BaTiO₃ layer. BaTiO₃ is a perovskite material with a bandgap of 3.4 eV. It has an electron affinity of 3.8 eV,²⁰ which is close to the value of β-Ga₂O₃. Thus, the conduction band offset between BaTiO₃ and β-Ga₂O₃ is expected to be low. The Schottky barrier diode with the same β-Ga₂O₃ drift layer was also simulated as a comparison [Figs. 1(d)–1(f)].

Under reverse bias, the conduction band of the Schottky barrier diode inclines sharply due to the electric field, resulting in a thin triangular electron barrier. As a result, β-Ga₂O₃ Schottky barrier diodes show tunneling breakdown at relatively low peak fields (typically ∼3 MV/cm) due to Fowler-Nordheim tunneling. When the BaTiO₃/β-Ga₂O₃ dielectric heterojunction diode is reverse-biased, the electric field in the β-Ga₂O₃ drift layer is similar to the Schottky diode in the previous case. However, due to the large dielectric constant discontinuity between BaTiO₃ and β-Ga₂O₃, the electric field in BaTiO₃ is lower by a factor $ϵBTOϵGOX(∼26$ in this case) of the value in β-Ga₂O₃. As a result, the conduction band profile in BaTiO₃ remains flat, blocking the electrons tunneling from metal to β-Ga₂O₃ under higher reverse bias. Therefore, the BaTiO₃/β-Ga₂O₃ dielectric heterojunction maintains an effective potential barrier at much higher voltages than the metal/semiconductor junction.

Under forward bias, electrons must flow from the semiconductor, through the high dielectric constant layer, into the metal. For a small value of the conduction band offset between BaTiO₃/β-Ga₂O₃ (as predicted from the electron affinity difference), the dielectric heterojunction will have a small effective barrier to transport. Since BaTiO₃ is an insulator, the injected current is expected to be limited by space-charge limited transport, which has a dependence $J∼μϵV2L3$⁠, where $μ$ is the electron mobility, $ϵ$ is the dielectric constant, and L is the thickness of the dielectric. Therefore, while the mobility of carriers in BaTiO₃ may be low, the high dielectric constant will help to decrease the voltage drop in the dielectric. Therefore, the BaTiO₃/β-Ga₂O₃ dielectric heterojunctions are expected to be turned on under forward bias.

To characterize the breakdown field of the dielectric heterojunction without additional field termination processes, we fabricated Schottky diodes and BaTiO₃/β-Ga₂O₃ diodes on relatively thin drift regions consisting of 150 nm unintentional doped (UID) β-Ga₂O₃ on an n-type substrate. The UID β-Ga₂O₃ drift layer was grown by oxygen plasma-assisted molecular beam epitaxy (MBE), using growth conditions reported earlier.²¹ To prevent further electron depletion into the substrate at high reverse bias, a 10 nm heavily doped n-type (∼5 × 10¹⁹ cm⁻³) β-Ga₂O₃ layer was grown before the 150 nm UID layer. The electron concentration in UID β-Ga₂O₃ was estimated from capacitance-voltage profiling to be lower than 10¹⁶ cm⁻³. A 20 nm BaTiO₃ layer was deposited on β-Ga₂O₃ by physical vapor deposition in Ar/O₂ ambience with a flow rate of 20:2  sccm. A plasma power of 140 W and a chamber pressure of 10 mTorr were maintained during deposition. A deposition rate of 0.5 nm/min was confirmed by ellipsometry. A dielectric constant of 260 ± 20 was measured from C-V measurements (the details are discussed in the supplementary material). A metal stack of Pt/Au (30 nm/100 nm) was deposited by an electron beam evaporator to form square Schottky contact pads (50 μm × 50 μm) on both the β-Ga₂O₃ sample and the BaTiO₃/β-Ga₂O₃ sample. 30 nm Ti followed by 100 nm Au was deposited on the backside of the n-type substrate to form Ohmic contacts.

The β-Ga₂O₃ UID layer thickness of 150 ± 3 nm was confirmed by the C-V measurement on the Schottky junction diodes. Reverse bias measurements of 10 dielectric heterojunctions and 10 Schottky diodes were performed. The breakdown voltage was taken as that required to induce a current density of 1 A/cm². The resulting breakdown voltages for the two types of devices are summarized in Fig. 2(a). The mean breakdown voltage was 83.3 V for the dielectric heterojunctions and 44.5 V for the Schottky junctions. The characteristic I-V curves of devices with near-mean behavior are shown in Fig. 2(b). The Schottky barrier diode had a breakdown voltage of 45 V, which corresponds to a breakdown field of 3 MV/cm. This breakdown field is comparable with previous reports.^14,15 The BaTiO₃/β-Ga₂O₃ heterojunction diode showed a significantly higher breakdown voltage of 85 V, corresponding to a peak electric field of 5.7 MV/cm (calculated assuming background doping = 10¹⁶ cm⁻³ and a 150 nm depletion width). This is the highest breakdown electric field reported for a vertical β-Ga₂O₃ device. The 2D electric field profile of the dielectric heterojunction at the breakdown scenario was simulated using Sivalco ATLAS²² [Figs. 2(b) and 2(c)]. It can be seen from the simulation that when the electric field at the center of the device is 5.7 MV/cm, the edge of the device is expected to have an electric field of 7 MV/cm.

We now discuss the breakdown mechanism of the BaTiO₃/β-Ga₂O₃ dielectric heterojunction. The Poole-Frenkel plot of the dielectric heterojunction [Fig. 3(a)] under reverse bias (40 V–70 V) shows near-linear behavior, suggesting that the breakdown mechanism is governed by trap-assisted tunneling (Poole-Frenkel emission).²³ The corresponding traps could be located in either the BaTiO₃ region or the β-Ga₂O₃ region. The temperature dependent currents under reverse bias were measured, and the Arrhenius plot with respect to the field in BaTiO₃ is plotted in Fig. 3(b). A trap energy level of 0.25 eV was extracted from the slope, assuming that the corresponding traps are located in the BaTiO₃ layer. The same temperature dependent data were fit, assuming an Arrhenius dependence on the electric field in β-Ga₂O₃ [Fig. 3(c)]. This fit suggests a trap energy of 0.6 eV if the traps are in β-Ga₂O₃. The electric field used in this calculation was estimated in the center region of the device. However, the edges of the device have a much higher electric field under reverse bias, and they are likely to be the regions where breakdown occurred. Therefore, the extracted trap energy level may be suggestive but not entirely accurate. Further experiments and studies are needed to confirm the location and energy of the corresponding traps. Our current results show that the breakdown voltage of the dielectric heterojunction is not fundamentally limited by the band structure, suggesting that improvement in the quality of BaTiO₃ and β-Ga₂O₃ may further increase the breakdown field of the dielectric heterojunction.

Under forward bias, the Schottky junction and dielectric heterojunction showed on-resistances of 1.4 mΩ cm² and 1.5 mΩ cm², respectively [Fig. 4(a)]. The 20 nm BaTiO₃ layer added a 0.1 mΩ cm² extra on-resistance once the device is turned on. The turn-on voltage was 1.5 V for the Schottky diode and 3.5 V for the dielectric heterojunction diode. The voltage drop across the BaTiO₃/β-Ga₂O₃ junction could be due to a band offset or due to a resistive drop across the BaTiO₃. To investigate the mechanism, we plotted the IV characteristics on a Fowler-Nordheim²⁴ plot. The linear fit on the Fowler-Nordheim plot [Fig. 4(b)] suggests that the transport is limited by a tunneling mechanism across a triangular barrier. Assuming that the barrier was due to the conduction band offset, the characteristic barrier height was estimated to be 0.08 eV [Fig. 4(c)]. Therefore, it seems likely that the transport is indeed limited by the conduction band barrier between BaTiO₃ and β-Ga₂O₃.

In conclusion, we have proposed and demonstrated the concept of dielectric heterojunctions that use extreme permittivity materials to achieve a high breakdown field in a unipolar device. We showed a BaTiO₃/β-Ga₂O₃ dielectric heterojunction diode with the record-high electric field of 5.7 MV/cm measured in β-Ga₂O₃. The dielectric heterojunction shows a turn-on voltage of 3.5 V and an on-resistance of 1.5 mΩ cm². This structure demonstrated here not only brings up a design for the high performance β-Ga₂O₃ diode but also can be used as a gate dielectric barrier in both lateral and vertical transistors. This dielectric heterojunction concept can also be expanded to other semiconductor materials in which the bipolar device is technically challenging, such as SiC, GaN, ZnO, and diamond. It may also be useful to Si and III-V materials to achieve a faster unipolar device with higher breakdown voltage than typical Schottky barrier diodes.

See the supplementary material for details about the measurement of the BaTiO₃ dielectric constant.

This work was funded by the National Science Foundation ECCS-1809682 and AFOSR GAME MURI (Grant No. FA9550-18-1-0479, Program Manager Dr. Ali Sayir). Aidan J. Lee and Fengyuan Yang acknowledge the support by the Center for Emergent Materials, an NSF MRSEC (Grant No. DMR-1420451).